Quantum communication is the art of transferring a quantum state from one location to another, in this way information, or resources such as entanglement, can be distribributed between distant locations [1]. The communication of qubits will be an important ingredient in taking full advantage of what is possible with quantum technologies, from quantum computing and simulation to secure communication based on quantum key distribution (QKD). The first application, quantum cryptography, was discovered independently in the US and Europe. The American approach, pioneered by Steven Wiesner, was based on coding in non-commuting observables, whereas the European approach was based on correlations due to quantum entanglement. From an application point of view, the major interest has focused on QKD, as this offers for the first time a provably secure way to establish a confidential key between distant partners. This key is then first tested and, if the test succeeds, used in standard cryptographic applications -- relying solely on the laws of quantum physics and the ability to implement the protocol as defined by the theory. This has the potential to solve long-standing and central security issues in our information based society.
While the realisation of basic quantum communication schemes is becoming routine work in the laboratory, non-trivial problems emerge in high bit rate systems, long-distance applications and as the network complexity increases. One of the emerging areas of interest for quantum communication schemes is in connecting the nodes within quantum simulators, which can either be all located in the one lab, or more interestingly, in distributed scenarios -- the tools from quantum communication playing the role of wiring circuits for these quantum computers. While there remains many challenges for proof-of-principle laboratory demonstrations, the transition to deployment in real-world environments defines a new set of challenges in the QIPC domain. The issues of scale, range, reliability, and robustness that are critical in this transition cannot be resolved by incremental improvements, but rather need to be addressed by making them the focal point of the research and technology development agenda as we work towards a quantum internet. To succeed this needs to target both the underlying technologies, ranging from fundamental aspects of engineering quantum systems to integrating these quantum systems with fast (classical) opto-electrial systems, as well as the end-user applications themselves. In particular the following need to be addressed:
There are key technological limitations for high-speed quantum communication and fundamental roadblocks for long distances. A significant speed limitation on the distribution of true randomness, a resource for many security protocols, including QKD, is due to relatively slow (~4 Mbps for commercial devices) quantum random number generators (QRNGs)- see Section 4.4. Novel schemes and advanced entanglement enabled technologies, using and possibly combining both discrete and continuous variable encoding aspects, will be required for the next generation devices to surpass current rate limitation. The distances over which quantum information can be communicated face fundamental limitations due to transmission losses in the quantum channels, both free space and fibre. In fibre, this limit is a few hundred kilometres. Recent quantum cryptography experiments already come close to such distances but with impractically low distribution rates. In free space, these distances are even lower. There are two possible solutions to overcome this limitation: use satellite configurations, i.e. free space systems; or, use quantum repeaters, a theoretical concept proposed in 1998 the analogue of fibre optical amplifiers that made global fibre communication feasible. The first clearly requires satellites and systems are currently being developed and tested to meet the associated demands. Several countries already have planned missions to launch quantum systems for further testing. This however only addresses increasing point to point distances. Quantum repeaters require quantum interfaces or memories for the inter-conversion from photonic (distribution) to atomic (storage) systems and while increasing distances, it also opens up the possibility of more complex network structures. This is perhaps one of the most active areas of QIPC research.
One of the great advantages of quantum physics is that it can deliver "correlations with promises". In particular it can deliver strictly correlated strings of bits to two locations with the promise that no copy of these bits exists anywhere in the universe. This promise is guaranteed by the laws of Nature and does not rely on any mathematical assumption. Consequently, these strings of correlated bits provide provably secure keys ready to be used in standard crypto-systems. However, for quantum physics to hold its promise, the quantumness of these distributed systems needs to be ensured. It is of strategic importance to not only develop the technologies to distribute quantum resources, such as entanglement from one location to another one but to be able to ensure that its truly quantum nature is preserved and that these systems are will be described by their abstract security proofs. The gap between theory and experiment has to be reduced. This needs to take several paths: the theory needs to consider the practical implementation and hence the experimental parameters. Experimentalists need to better engineer these systems to avoid potential loopholes. the Another alternative arises from a key test of the quantumness, which consists in measuring correlations and proving that they violate a certain inequality, known as the Bell inequality. This approach has lead to the idea of "Device Independent" security proofs that provides the possibility of characterising the quantum nature of a system. Practical and feasible schemes to test these device independent approaches and ensure the quantum nature of systems will be crucial as communication links and networks become more complex.
From the present situation, where commercial systems already exist, we briefly review the underlying foundational technologies and more generally, quantum communication from the perspective of increasing rates and distances to solutions extending point-to-point QKD towards complex quantum networks for the distribution of quantum resources and for performing new protocols.
Key references
[1] N. Gisin and R. T. Thew, Nature Phot 1, 165 (2007)
Physical approaches and perspectives
All photonic approaches to quantum information technology rely upon an efficient detection technology. Although single photon detectors are commercially available, these are relatively simple digital devices, which detect the presence or absence of one or more photons. Future detector technologies will not only have to have a dramatically higher detection efficiency but also considerable lower dark count rates as well as a timing jitter that does not limit the transmission rates. The commercial detection systems are based on semiconductor avalanche photodiodes (APDs) such as Silicon (400-1000 nm) and InGaAs/InP (1100-1700 nm). These are robust and generally only require electric cooling. Traditionally these detectors have operated at low rates, the InGaAs in particular usually needed to be gated at rates of around 1\,MHz, although recent approaches has seen this significantly increase into the GHz regime. Alternative approaches include superconducting devices, either transition-edge sensors (TES) that have shown near unit efficiencies but remain relatively slow, or superconducting nanowire single photon detectors (SNSPD) based on NbN, that are faster (both low jitter and high count rates) but have only realised moderate efficiencies. Recently, SNSPD using WSi, have been realised that combine high efficiency, low noise and fast operation all in one device. All of these have photon number resolution capability. The need for cryogenic cooling is offset by the potentially high performance. For continuous variable (CV) measurements single photon resolution is not needed. There, apart from the quantum efficiency and bandwidth, the signal to noise ratio of the detector module is important. This is far from an extensive list, but focuses on the most advanced or promising technologies in the context of quantum communication.
European groups working in this field include: S. Cova (Milan, I), A. Fiore (Eindhoven, NL), A. Giudice (Micro Photon devices, I), R. Hadfield (Herriot Watt, UK), R. Leoni (CNR Rome, I), G. Ribordy (IDQ, CH) A. Shields, (TREL, UK), J-C. Villegier (CEA Grenoble, F), H. Zbinden (Geneva, CH), V. Zwiller (Delft, NL).
State of the art
A severe limitation of today’s photon detection technology is the maximum count rate. For example, InGaAs/InP APDs have been traditionally operated in a gated mode with a maximum repetition frequency of 1-10 MHz and a maximum count rate of 100 kcps. However, this field has recently been reinvigorated with novel work on the operating electronics providing advances in rapid gating (GHz) [1,2] and continuous (free-running) [3] operation opening up new regimes of operation and performance. This is also being extended into the Si detection band with high efficiency, >70% and PNR capabilities demonstrated [4]. The superconducting devices have demonstrated photon number resolution capability and high efficiency in TES >90% systems [5]. SNSPDs have lower efficiencies ~24% and higher noise levels, >1 kHz [6], but are capable of a significantly higher count rates (potentially hundreds of MHz) and lower timing jitter (<100 ps). Recently, SNSPD using WSi, have been realised that has high system detection efficiency (>90%), low dark count rate (<1 counts per second, cps), low timing jitter (<100 ps), and short reset time (<100 ns) for telecom wavelengths [7]. Several start-up companies have already begun to commercialise th NbN SNSPD technologies. In the continuous variable regime, several groups report quantum efficiencies approaching 100% using commercially available PIN diodes with increasing bandwidth (>100 MHz) and signal-to-noise ratios. Conceptually, the strict separation between discrete and continuous detection schemes is complemented by hybrid detection approaches [8]. A detailed review of single photon detectors has recently been realised [9].
Challenges
Europe and Japan are currently leading the way for the APD detection schemes, while the US is a clear leader for TES superconducting devices, however, the development of SNSPDs is more widespread with no clear leader at this time. The main challenges for single photon detection for quantum communication are:
Key references
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[9] M. D. Eisaman, J. Fan, A. Migdall and S. V. Polyakov, Rev. Sci. Instrum. 82, 071101 (2011)
Physical approaches and perspectives
Sources of quantum light in the discrete variable regime have traditionally relied on spontaneous parametric down-conversion (SPDC) in bulk crystals. This has been extended to periodically poled materials and waveguided devices, which have significantly higher efficiencies. The development of all-fibre entanglement sources, based on four-wave mixing provide several new approaches ranging from standard fibres to photonic crystal fibres. Deterministic sources that avoid probabilistic multi-pair events, associated with the previous schemes, have advanced to the point where entangled photon pairs can be generated by the optical excitation of the bi-exciton state of a semiconductor quantum dot, although currently the low efficiency of these devices detracts from its potentially deterministic nature. Single photon sources based on NV diamond centres and single molecules in solids have been realised and progress continues on single photon sources in diverse materials for sources ranging from the visible up to 1310 nm. In the continuous variable regime sources of squeezed and entangled light typically rely on either parametric oscillators in bulk crystals or the Kerr effect in optical fibres.
European groups working in this field include: O. Benson (Berlin, D), A. Beveratos (Paris, F), J. Eschner (Saarlandes, D), A. Fiore (Eindhoven, NL), C. Marquardt and G.~Leuchs (Erlangen, D), E. Polzik (Copenhagen, DK), J. Rarity (Bristol, UK), A. Shields (TREL, UK), C. Silberhorn (Paderborn, D), S. Tanzilli (Nice, F), R. T. Thew (Geneva, CH), R. Ursin and A. Zeilinger (Vienna, AT), I. Walmsley and B. Smith (Oxford, UK), G. Weihs (Innsbruck, AT).
State of the art
Challenges
Europe is currently leading in efforts towards coupling narrow-band photonic and atomic systems and plays a leading role for CV sources, competing with Australia and Japan. The USA is ahead in terms of pulsed systems in the telecom regime. There are several regimes of operation under study: atomic systems with narrow bandwidths for quantum repeaters, satellite-based schemes where bandwidth requirements are less critical but the generation rates need to compensate limited transmission time windows due to satellite availability, and in between both of these, pulsed systems for quantum fibre optical networks (teleportation and entanglement swapping) where robustness against fibre length fluctations needs to be balanced with high rates. The increasing complexity and diversity of quantum communication systems has also seen a much more sophisticated approach taken to engineering the sources, and in particular, the nonlinear interactions that are needed. The engineering of factorable, or pure, states of light [10] will be crucial for future quantum communication networks but so far most of this work has taken place in the visible regime- the extension to telecommunication wavelengths will be vital for the next generation of experiments. The main challenges for photon sources are:
Key references
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Physical approaches and perspectives
Challenges
Europe and the US are both well advanced with a range of architectures under study, however, this remains a fledgling domain within the field of QIPC. The field and the range of architectures and materials under investigation is rapidly expanding so we concentrate here on those most closely focused on quantum communication oriented applications. Key challenges for quantum memories and interfaces are:
Key references
Physical approaches and perspectives
Point-to-Point (P2P) QKD systems are the most advanced quantum communication technologies, and as such, much of the progress here will help to reinforce their commercialisation and that of emerging quantum technologies. Nonetheless there are significant and fundamental research efforts ranging from multiplexed fibre optic systems to satellite distribution schemes currently under investigation and taking advantage of both discrete and continous variable encoding schemes.
Fibre Systems
Groups are currently working on fibre QKD systems that encode in polarisation, phase, photon number and time-bins, using both discrete or continuous variables (CV). Weak-pulse (laser pulses attenuated to the single photon level) encoding schemes are by far the most practical and advanced schemes. Commercial systems still have relatively low rates and hence the research pursuit is primairly directed at novel protocols, improved detector performance and greater integration, both on the quantum level as well as the quantum classical interface and information processing. The extension to multiplexed systems has been a recent but necessary step opening up new operating scenarios and facilitating implementation in installed fibre optic networks.
European groups working in this field include: R. Alleaume (SeQureNet, F), J. Capmany (Valencia, E), N. Gisin and H. Zbinden (Geneva, CH), V. Martin (Madrid, E), A. Poppe (AIT, AT), A. Shields (TREL, UK), G. Leuchs (Erlangen, D), P. Grangier (Paris, F), G. Ribordy (IDQ, CH), P. Tombesi (Camerino, I), A. Zeilinger (Vienna, AT).
Free Space Systems
Many current free-space systems focus on polarisation-based encoding. Traditionally dominated by discrete variable systems, work on CV systems has recently been reinvigorated. The CV squeezed states offer potentially higher key rates and longer distances than coherent state CV protocols. The potential for using non-Gaussian states and higher dimensional Hilbert spaces (complex spatial modes/polarisation patterns) may increase the efficiency and capacity of these quantum information protocols. The European Space Agency ESA has supported various studies in the field of quantum physics and quantum information science in space for several years \cite{Ursin:2009a}. The mission proposal Space-QUEST (Quantum Entanglement for Space Experiments) has the objective of performing space-to-ground quantum communication tests from the International Space Station (ISS). The launch plan is compatible with 2014.
State of the art
P2P schemes face fundamental distance limits and recent experiments have approached these for both fibre and free space schemes. In fibre optic systems, >200 km has been achieved in a field trial for weak-pulse schemes [1] as well as >200 km in fibre for entanglement-based schemes [2] in the lab. Demonstrations that QKD and classical communication channels can co-exist have also been made [3] using DWDM channels. CV systems are much more sensitive to distance though 25 km has been realised in the lab [4]. An important milestone, in terms of rates, has also been realised with 1 Mbps secure key rate over 20 km [5]. There are also extensive field trials taking place in the Canary Island involving several leading European groups as part of an European Space Agency feasibility study for quantum communcation via satellite [6]. A weak pulse schemes has demonstrated a >144 km free-space QKD [7]. In a related experiment, the Matera Laser Ranging Observatory (MLRO) in Southern Italy served as transceiver station for faint-pulse exchange with a low-earth orbit retro-reflecting satellite at a perigree of 1485 km [8].
Challenges
Physical approaches and perspectives
Quantum networks extend from trusted node devices built on weak-pulse qkd systems to more advanced entanglement-based scenarios including quantum repeaters. The goal in terms of quantum communication is motivated by increasing both the distance of QKD and the complexity of these quantum networks- architectures are no longer constrained to be P2P. The extension to entangled systems also has the benifit of providing a means of wiring up quantum computing and simulation systems, which can either be compact, small-scale, systems in one lab, or in distributed schemes, and connecting different types of quantum processors. The foundations of these architectures relies on the distribution and control of entanglement across complex quantum networks and central to realising this is the most fascinating quantum phenomenon, teleportation. The development of complex quantum networks provide one of the most significant challenges in experimental quantum physics today. By definition this is highly multi-disciplinary and requires hybrid approaches on both a conceptual and technological level.
State of the art
Challenges
There is no clear leader for quantum networks and long distance quantum communication with dedicated programs in place across Europe and in the USA, Canada, Japan, Australia and China. In the next 5-10 years we should see fibre optic systems that can beat the direct-transmission QKD distance limitation of around 300-400 km. Initially, quantum repeaters that can function over 1-10 km will provide the building blocks for longer transmission systems- it is these building blocks that provide a scalable route towards pan-European and even global scale quantum communication. These distances will obviously need to be extended further, but not necessarily by much, n.b. classical communication links are of the order of 50-100 km between amplification stages. One of the important aspect for quantum repeaters is the scaling of multiple quantum repeater links. Scalable quantum repeater systems will ensure that the concatenation of multiple links will extend quantum communication distances beyond this fundamental (loss-based) limit and away from the P2P network topologies. Effort in the next few years should be focused on engineering the sources, interfaces and detectors specifically adapted to long distance transmission and working in unison- long coherence lengths, and high fidelity Bell-State measurements. Challenges and directions of future work are thus similar to those already mentioned for these different technologies and while many aspects have been realised, all need to be improved and demonstrated in the one systems. Some of the key challenges are:
Key references
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Physical approaches and perspectives
State of the art
Dealing with implementation issues at an applied level requires close collaboration between quantum hackers and those building, and even selling, the QKD systems and technologies. This approach has been well demonstrated for recent detection attacks [2]. DI-QKD, on the other hand, is a relatively new concept and its experimental application requires unprecedented performance of the systems and component technologies. Nonetheless, a couple of recent papers have started to bring this into the realms of experimental feasibility [3, 4]. Central to this was the concept of heralded photon amplifiers [5], which have also been realised experimentally in the visible [6, 7] and more recently, telecom regimes[8]. Self-Testing is another related concept where the effort is to minimise assumptions and to help better characterise quantum systems and technologies. To date this has primarily been a theoretical effort for the moment [9-11]. The adaptation and demonstration of DI-QKD will also be important for future secure networks. In a further extension of this idea, heralded photon amplifiers have been proposed in a recent quantum repeater protocol [12] that is not only one of the most efficient but it also hints at the potential for DI scenarios across quantum networks.
Challenges
Both quantum hacking and device independent security have similar goals, but approach the task from opposite directions: Both have the aim of minimising the assumptions involved in secure quantum communication systems and to bridge the gap between the theoretical proofs and the security of the final implementation. European theory groups have been a driving force in this area, especially for the later, although experimental initiatives have already started in several European groups, as well as in Singapore, Canada and Australia. Some of the key challenges are:
Key references
[1] A. Ekert, Phys. Rev. Lett. 67, 661 (1991)
[2] L. Lydersen et al., Nature Photonics 4, 686 (2010)
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[12] J. Minar, H. de Riedmatten and N. Sangouard, Phys. Rev. A 85, 032313 (2012)
Approach and perspectives
The field of quantum communication is still very young, having been essentially unknown until 20 years ago. As such, one should expect new ideas and leave open space for fundamental research. From the theoretical point of view, there are several problems that have to be considered in the context of quantum communication. First of all, since the field is still very young, one should expect new applications related to both efficiency and secrecy in communication. Examples of the first can be connected to secret voting protocols, digital signatures, or fingerprinting. Examples of the second field could be, for example, connected to dense coding, or agenda protocols. Apart from that, there are still many open theoretical questions of crucial importance for quantum cryptography. These are related to the tolerance to noise of current protocols (both with one and two way communication), the connection between single photon and continuous variable protocols, and the search for more efficient and faster ways of distributing keys and quantifying their security.
State of the art
The main challenges for new applications and protocols are:
Key references
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Information processing nowadays is commonly implemented using quantities such as charges, voltages, or currents in electronic devices which operate on the basis of classical physics. Instead, Quantum Computing (QC) and more generally, quantum information processing (QIP) employ the laws of quantum mechanics for information processing. For such devices, corresponding building blocks are quantum bits (qubits) and quantum registers, and the basic gate operations are given by logical and coherent operations on individual qubits (single qubit operations) and controlled coherent interactions between two qubits (two-qubit operations) such that the state of the target qubit is changed conditional to the state of the controlling qubit. In principle, a large scale quantum computer can be built using these primitives which must be realized by a controllable quantum system, provided the physical system meets the following requirements (DiVincenzo criteria):
At present, there are a number of technologies under investigation for their suitability to implement a quantum computer. No single technology meets currently all of these requirements in a completely satisfactory way. Therefore, the ongoing research on quantum information processing is highly interdisciplinary, diverse and requires a coordinated effort to create synergies while the common goal is the implementation of a working quantum processor. While at present several approaches have demonstrated basic gate operations and are even able to prove that quantum computing has become reality with few qubits, large scale quantum computation is still a vision which requires ongoing research for many years to come.
The long-term goal in quantum computation is, of course, a large-scale quantum computer which will be able to efficiently solve some of the most difficult problems in computational science, such as integer factorization, quantum simulation and modeling, intractable on any present or conceivable future classical computer.
Therefore, the general problems to be solved for QC and QIP are in particular
Quoting a recent article by David DiVicenzo in "Science" (7 october 2011), "during the past decade, a wide array of physical systems - atoms, semiconductors, and superconductors - have been used in experiments to create the basic components of quantum-information processing. Precision control over elementary quantum two-state systems (qubits) is now well advanced, and it is now possible to ask how a complete, functioning quantum computer with many qubits would really work. Although the physical qubits used are still extremely different, it is now time to attack device-independent questions of system functionality."
A. Physical approach and perspective
Ion trap quantum computation is based on schemes devised by Cirac and Zoller [1]. A quantum register is provided by strings of ions, each representing a physical qubit. The system satisfies in principle all DiVincenzo criteria and most of the criteria have been experimentally demonstrated. While the originally proposed system is scalable in principle, practical scalability requires additional techniques such as interconnecting via photons (flying qubits) or moving one or more ions to operate as a messenger for quantum information. A more comprehensive summary of ion trap QIP is contained in the US QIST roadmap [2]. Another related approach is to use electrons confined in a scalable system composed by an array of Penning traps. This scheme was devised by Ciaramicoli et al [3]. Although not yet experimentally implemented, it conceivably satisfies all the DiVincenzo criteria as well.
Currently, experimental ion trap QIP is pursued by about 20 groups worldwide, 12 of which are located in Europe [R. Blatt (Innsbruck, AT), T. Coudreau (Paris,F), M. Drewsen (Aarhus, DK), J. Eschner (Saarbrücken, DE), P. Gill (Teddington, UK), W. Hensinger (Sussex), W. Lange (Sussex, UK), T. Schätz (MPQ, DE), F. Schmidt-Kaler (Mainz, DE), D. Segal (London, UK), A. Steane (Oxford, UK), Ch. Wunderlich (Siegen, DE). Experiments with trapped electrons are currently being set up only in Europe by the groups of G. Werth (Mainz, DE) and F. Schmidt-Kaler (Mainz, DE).
On the theory side there is J.I. Cirac (MPQ Garching, DE), K. Molmer (Aarhus, DK), M. Plenio (Ulm, DE), E. Solano (Bilbao,ES) and P. Zoller (Innsbruck, AT); for trapped electrons P. Tombesi (Camerino, IT).
B. State of the art
With trapped ions, qubits are implemented using either two levels out of the Zeeman- or hyperfine manifold or employing a forbidden optical transition of alkaline earth, or alkaline earth-like ions. The DiVincenzo criteria are currently met as follows:
C. Strengths and weaknesses
At present, ion trap QIP provides most of the requirements for first-generation quantum computation experiments. In particular, the long coherence times of the ionic two-level systems provide a robust quantum memory. Moreover, the near-unity state detection and the availability and operability of a universal set of gate operations make it already a test-bed for small-scale quantum computation. Furthermore, techniques to build large-scale ion trap quantum computers were outlined and their function was shown in first steps.
On the downside, motional decoherence by stochastically fluctuating fields (originating from trap electrodes) is not completely understood and must be reduced. Spontaneous emission must be avoided by all means; therefore decoherence-free subspaces need to be explored. Current technical constraints, such as the availability of laser sources, their respective stability and purity as well as fast optical detection and switching, need to be improved.
However, aside from the technical difficulties of scaling ion trap QIP up to larger devices, there is no fundamental problem in sight.
D. Short-term goals (3-5 years)
E. Long-term goals (10 years and beyond)
E. Key references
[1] J.I. Cirac and P. Zoller, “Quantum computation with cold trapped ions”, Phys. Rev. Lett. 74, 4091 (1995)
[2] D. Wineland, “Ion trap approaches to quantum information processing and quantum computing”, in ‘A Quantum Information Science and Technology Roadmap, Part 1: Quantum Computation’, Version 2.0, section 6.2 and references therein; available from http://qist.lanl.gov [2]
[3] G. Ciaramicoli, I. Marzoli and P. Tombesi “Scalable Quantum Processor with Trapped Electrons”, Phys. Rev. Lett. 91, 017901(2003).
A. Physical approach and perspective
Neutral atoms and molecules provide a promising test bed for the development of scalable general purpose quantum processors, and for quantum simulators as special purpose quantum computers involving a very large number of qubits. As in the case of ions, qubits can be represented by long-lived internal atomic and molecular states in electronic ground states (hyperfine levels, rotational states), or in metastable excited electronic states, which can be manipulated by optical and microwave fields. The unique promises of neutral atom quantum computing rest in particular on the well developed cooling and trapping techniques, as exemplified by laser cooling, realization of Bose Einstein condensates and quantum degenerate Fermi gases, in combination with optical, magnetic and electric traps, realized in free space or in cavities or on atom chips. Such techniques provide an ideal starting point to build and prepare large scale quantum registers with high fidelity. At present these trapping and cooling techniques are being extended to molecules, including, for example, electric on-chip traps for polar molecules. The scenarios of quantum computing with neutral atoms are directly linked to the development of specific trapping techniques. First, traps can be developed allowing the independent manipulation of the centre-of-mass degrees of freedom of individual atoms and molecules, including the addressing of single qubits, which is a necessary requirement for general purpose quantum computing; and massively parallel, identical manipulations of large number of qubits, as realized for example in optical lattices, are relevant in the context of quantum simulators of translation invariant condensed matter systems.
Entanglement of neutral atom or molecule qubits is based on the following physical mechanisms
Both scenarios can be played either in free space, or by using cavity QED techniques, where the atomic or molecular qubit is strongly coupled to a high-Q cavity. This can be done in the optical domain by coupling to an electronic excitation, or in the microwave regime for a transition between Rydberg states or rotational states of a polar molecule. Two-qubit gates between distant qubits can be achieved via photon exchange as quantum data bus, in close formal analogy to the phonon data bus of collective oscillation modes in trapped ions. These cavity QED setups also provide a natural interface to quantum communication with photons.
Atoms and molecules can be stored in optical lattices, corresponding to an array of microtraps generated by counterpropagating laser fields. The dynamics of cold atoms loaded into optical lattices can be described by a Hubbard model, with atoms hopping between lattice sites, and interacting via collisions. Thus cold atoms in optical lattices provide a direct way to simulating condensed matter systems with a large number of bosons or fermions. In addition, loading an optical lattice from an atomic Bose Einstein condensate provides via the superfluid-Mott insulator transition the preparation of a Mott phase with exactly one atom per lattice site, and thus the preparation of a very large number of atomic qubits. These atoms can be entangled in parallel operations with qubit-dependent controllable 2-particle interactions, provided, for example, by coherent collisional interactions in combination with movable qubit (spin) dependent optical lattices. This provides the basis for a digital quantum simulator, for example of a spin lattice system, where the time evolution generated by the Hamiltonian is decomposed into a series of single and two-qubit gates performed in parallel on all qubits (spins).
A major recent development is the possibility to image and (at least partially) address individual atoms in optical lattices. When coupled to atom-atom interactions using either cold collisions or Rydberg dipole-dipole interactions, this opens the way to performing nearly individual measurements on large arrays of entangled atoms, which would be a crucial steps towards quantum simulators and even quantum computers.
For single atoms strongly coupled to an optical cavity, single photons for the purpose of exchanging quantum information between remote locations can be generated on demand and with high quantum efficiency. Protocols for generating a stream of photons with entanglement mediated and controlled by a single intracavity atom have been proposed. In addition to these deterministic mechanisms for entanglement, probabilistic protocols can be developed which are based on free space atoms emitting photons where entanglement is achieved by appropriate photon detection.
Currently, quantum computing with neutral atoms is investigated experimentally in several dozen laboratories worldwide, with half of them located in Europe. The European groups working with a controllable number of atoms include I. Bloch (Munich, DE), T. Esslinger (Zurich, CH), P. Grangier (Palaiseau, FR), S. Haroche (Paris, FR), D. Meschede (Bonn, DE), G. Rempe (Garching, DE), and H. Weinfurter (Munich, DE). Related experiments, sometimes done in an AMO context broader than QIP only, are also performed by W. Ertmer (Hannover, DE), E. Hinds (London, UK), J. Reichel (Paris, FR), and J. Schmiedmayer (Vienna, AT). The experimental program is strongly supported by implementation-oriented theory groups like H. Briegel (Innsbruck, AT), K. Burnett (Oxford, UK), J. I. Cirac (Garching, DE), A. Ekert (Cambridge, UK), P. L. Knight (London, UK), M. Lewenstein (Barcelona, ES), K. Mølmer (Aarhus, DK), M. B. Plenio (London, UK), W. Schleich (Ulm, DE), P. Tombesi (Camerino, IT), R. Werner (Braunschweig, DE), M. Wilkens (Potsdam, DE), & P. Zoller (Innsbruck, AT). In fact, European theory groups have played a crucial role in the development of QIPC science from the very beginning. The close collaboration between experiment and theory in Europe is unique, largely thanks to the support provided by the European Union.
B. State of the art
I. Quantum memories: The strength of using neutral atoms for QIPC is their relative insensitivity against environmental perturbations. Their weakness comes from the fact that only shallow trapping potentials are available. This disadvantage is compensated by cooling the atoms to very low temperatures. So far, several different experimental techniques for trapping and manipulating neutral atoms have been developed:
Optical tweezers and arrays of optical traps allow for the preparation of a well-defined quantum state of atomic motion, as can be achieved by either cooling single atoms into the ground state of the trapping potential, or by loading a Bose-Einstein condensate into an optical lattice. Given recent developments, both approaches have the potential for individual atom manipulations, and for massive parallelism, with many pairs of atoms colliding at once. The landmark results attained are:
Atom chips: The ability to magnetically trap and cool atoms close to a surface of a micro-fabricated substrate (for example using micro-magnetic potential wells produced by micron-sized current carrying wires or microscopic permanent magnets) has led to an explosive development of atom chips in the past few years. Such devices are very promising building blocks for quantum logic gates due to their small size, intrinsic robustness, strong confinement, and potential scalability. The main accomplishments they have attained include:
Traps for polar molecules at the individual level have recently been proposed, based on microwave or electric fields, and are the subject of growing experimental investigation. On the experimental side,
Techniques using atomic ensembles either in vapour cells, optical traps, or cryo-cooled rare-earth doped crystals. These methods are extensively discussed under the "Quantum communications" heading, and we refer the reader to sections 4.1.3 [3], 4.1.4 [4], 4.1.5 [5] for details. We note that studies related to quantum repeaters, involving both quantum memories and some data processing, are currently establishing a strong bridge between quantum communications and quantum computing, under the general goal of achieving efficient quantum information processing.
II. Entangling gates: a variety of schemes have been proposed theoretically, based on interatomic interactions which may be either direct (for instance collisional, possibly enhanced by Feshbach resonances, or between dipoles of Rydberg excited atoms) or mediated by a quantum data bus, i.e. a different degree of freedom (for instance photons, freely propagating or within a high-finesse cavity mode).
Optical tweezers and arrays of optical traps are ideal to perform collisional gates, which require the preparation of a well-defined quantum state of atomic motion. With optical lattices, highly parallelized quantum gates were implemented by state-selectively moving the atoms, and making them interact using cold collisions. This landmark experiment has pioneered a new route towards large-scale massive entanglement and quantum simulators with neutral atoms. With single atoms in optical tweezers, a series of experiments in 2009-2010 were able to obtain fast atom-atom entanglement and quantum gates using the Rydberg blockade mechanism, as initially proposed in 2000. This scheme is very promising for neutral atoms, because it is very fast (sub-microsecond), does not require to move the atoms, and is relatively insensitive to the thermal motion of the trapped atoms.
Cavity QED, possibly in combination with optical dipole traps, is a very promising technique for realizing an interface between different carriers of quantum information, implemented either with free-space atoms emitting photons in a random direction (probabilistic approach), or with atoms in high-finesse cavities where the strong atom-photon coupling guarantees full control over photon emission and absorption (deterministic approach). The latter approach can be realized both with Rydberg atoms in microwave cavities as well as with ground-state atoms in optical cavities. If each atom resides in its own cavity, the scheme guarantees addressability and scalability in a unique way. As quantum information is exchanged via flying photons, the individual qubits of the quantum register can easily be separated by a large distance. The photon-based scheme is therefore ideal to build a distributed quantum network. The main achievements in this sector include:
C. Present challenges
The technology needed to perform single-atom experiments is relatively new (less than 10 years), but it has done very significant progress recently. In particular, neutral-atom systems have now demonstrated two-qubit operations using Rydberg blockade.
Optical tweezers and arrays of optical traps are most advanced in manipulating individual neutral-atom qubits.
Atom chips: experiments with atom chips are still facing a large number of challenges for implementing QIPC, but a lot of progress has been made.
Polar molecules: Research with polar molecules has just started and, hence, is still facing a large number of experimental challenges. Some of these are:
Cavity QED: The main difficulty in implementing QIPC protocols in present demonstration experiments is the enormous technological complexity required to obtain full control over both atoms and photons at the single-particle level.
In the microwave domain, a method of deterministically transporting single atoms in and out of a cavity, for example by means of an optical conveyor belt, is needed to address the individual atoms of a stationary quantum register.
A major challenge for theory is to characterize and optimize the suitability of each of the available and proposed experimental systems as platforms for general-purpose quantum computing or rather for quantum simulation.
In this direction, quantum simulations are making steady progress, especially in relation with the paradigmatic problems of strongly interacting bosons or fermions. For instance, it has been possible to cross-validate a new theoretical approach by using precision experiments on ultracold atoms, or to propose methods to synthesize gauge fields with cold-atom systems. Various types of interaction blockades (i.e. when strong interactions in a confined, few-body system prevent a particle from occupying an otherwise accessible quantum state) are also actively explored, both theoretically and experimentally.
D. Key references
A tutorial review on QIPC with atoms, ions and photons can be found in, e.g.:
[1] C. Monroe, ‘‘Quantum Information Processing with Atoms and Photons’’, Nature 416, 238-246 (2002)
[2] J.I. Cirac and P. Zoller, ‘‘New Frontiers in Quantum Information with Atoms and Ions’’, Physics Today 38-44 (March 2004)
Useful reviews on the physics in either many-body systems and Rydberg atoms, and their applications to QIP, can be found in, e.g.:
[3] Immanuel Bloch, Jean Dalibard, Wilhelm Zwerger, “Many-Body Physics with Ultracold Gases”, Rev. Mod. Phys. 80, 885 (2008)
[4] M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms”, Rev. Mod. Phys. 82, 2313 (2010).
A. Physical approach and perspective
Quantum computation with superconducting Josephson junction (JJ) based circuits exploits the intrinsic coherence of the superconducting state, into which all electrons are condensed. The systems form effective two(multi)-level artifical atoms where quantum information is stored in different degrees of freedom: charge, flux or phase. The "old" distinction in terms of charge, flux, and phase qubits is however a bit outdated: all JJ-qubits are now closer to the phase regime than to the charge regime in order to defeat charge noise and achieve long coherence times. Systems are fabricated with thin film technology and operated at temperatures below 100 mK. Measurements are performed with integrated on-chip detectors. Coupling between qubits can be made strong, especially using microwave resonators and cavities - circuit/cavity quantum electrodynamics (cQED). This also provides opportunities for coupling widely different types of qubits in hybrid devices, inluding atoms, ions and impurity spins in quantum dots, crystals, and microtraps. The state of the art is described in [1-5], including comprehensive technical accounts in [4,5].
About 30 groups work on superconducting quantum bits in Europe, Japan, China and the USA. European experimental groups: Saclay, France (D. Esteve, D. Vion, P. Bertet); Delft, The Netherlands (J. Mooij, C.P.J.M. Harmans); Chalmers, Sweden (P. Delsing, C. Wilson); ETH Zürich, Switzerland (A. Wallraff); PTB, Germany (A. Zorin); Jena, Germany (E. Ilichev); KIT Karlsruhe, Germany (A. Ustinov); Grenoble, France (O. Buisson); HUT, Helsinki, Finland (S. Paraoanu); TUM Munich (R. Gross); and others. European theory groups: KIT Karlsruhe , Germany (G. Schön, A. Shnirman); SNS Pisa, Italy (R. Fazio); LMU Munich (F. Marquardt); Chalmers, Sweden (V. Shumeiko, G. Johansson, G. Wendin); Catania, Italy (G. Falci, E. Paladino); Basel, Switzerland (C. Bruder); Grenoble, France (F. Hekking); Toulouse, France (D. Shepelyansky); Bilbao, Spain (E. Solano, J. Siewert); and others.
B. State of the art
Referring to the seven DiVincenzo criteria [6], the state of the art for QIP with JJ-qubits can be described as follows:
It should be emphasized that spectacular progress has been accomplished during the last few years (2010-2012) by Josephson qubit quantum processors. Without quoting all articles, a nine-quantum-element solid-state quantum processor has been implemented, and used to run a three-qubit compiled version of Shor's algorithm to factor the number 15, and successfully find the prime factors 48% of the time. A Toffoli gate has been implemented with three superconducting transmon qubits coupled to a microwave resonator, with a fidelity of 68.5%. A "quantum machine" has been demonstrated, with seven quantum elements: two superconducting qubits coupled through a quantum bus, two quantum memories, and two zeroing registers. This machine has been used to implement quantum Fourier transform, with 66% process fidelity, and the 3-qubit Toffoli-class OR phase gate, with 98\% phase fidelity. Other experiments involve the deterministic production of 3-qubit GHZ states with fidelity 88%, and a QND detection scheme that measures the number of photons inside a high-quality-factor microwave cavity on a chip.
Though this topic remains controversial, it may be time to quote also the Canadian company D-Wave, which has built devices of increasing scale based on inductively coupled superconducting flux qubits. Several recent experiments report interesting physics in this device, providing evidence of macroscopic tunneling [17] and quantum annealing [18] in cells of 8 qubits and over timescales that far exceed the individual qubit coherence time. More studies are needed to understand the capabilities of these devices as optimization processors.
C. Strengths and weaknesses
Strengths:
Weaknesses:
D. Short-term goals (3-5 years)
E. Long-term goals (10 years and beyond)
F. Key references
[1] Proceedings of Nobel Symposium 141: Qubits for Future Quantum Computers (ed. G. Johansson), Phys. Scr. T137 (2010).
[2] J. Clarke and F.K. Wilhelm: “Superconducting Qubits”, Nature Insight 453, 1031 (2008).
[3] R. J. Schoelkopf and S. M. Girvin, "Wiring up quantum systems", Nature 451, 664 (2008).
[4] G. Wendin and V.S. Shumeiko, "Quantum bits with Josephson junctions", Low Temp. Phys. 33, 724 (2007).
[5] J.M. Martinis, "Superconducting Phase Qubits", Quantum Information Processing 8, 81 (2009).
[6] http://qt.tn.tudelft.nl/~lieven/qip2007/QIP3_divincenzo_criteria.pdf [6] [7] J.M. Fink, R. Bianchetti, M. Baur, M. Goeppl, L. Steffen, S. Filipp, P.J. Leek, A. Blais, and A. Wallraff: “Collective Qubit States and the Tavis-Cummings Model in Circuit QED”, Phys. Rev. Lett. 103, 083601 (2009).
[8] L. DiCarlo, J. M. Chow, J. M. Gambetta, L.S. Bishop, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf: “Demonstration of Two-Qubit Algorithms with a Superconducting Quantum Processor”, Nature 460, 240 (2009).
[9] V.E. Manucharyan et al., "Fluxonium: single Cooper pair circuit free of charge offsets", Science 326, 113-116 (2009).
[10] J.H. Plantenberg, P.C. de Groot, C.J.P.M. Harmans and J. E. Mooij, "Demonstration of controlled-NOT quantum gates on a pair of superconducting quantum bits", Nature 447, 14 (2007).
[11] R.C. Bialczak, M. Ansmann, M. Hofheinz, E. Lucero, M. Neeley, A. O'Connell, D. Sank, H. Wang, J. Wenner, M. Steffen, A. Cleland, J. Martinis, "Quantum Process Tomography of a Universal Entangling Gate Implemented with Josephson Phase Qubits", Nature Physics 6, 409–413 (2010).
[12] M. Ansmann, H. Wang, R.C. Bialczak, M.. Hofheinz, E. Lucero, M. Neeley, A. D. O'Connell, D. Sank, M. Weides, J. Wenner, A. N. Cleland and J..M. Martinis, "Violation of Bell's inequality in Josephson phase qubits", Nature 461, 504-506 (2009).
[13] P.C. de Groot, A.F. van Loo, J. Lisenfeld,2, R.N. Schouten, A. Lupascu, C.J.P.M Harmans, and J.E. Mooij, "Low-crosstalk bifurcation detectors for coupled flux qubits", submitted to Applied Physics Letters (2009).
[14] F. Mallet, F.R. Ong, A. Palacios-Laloy, F. Nguyen, P. Bertet, D. Viuon, and D. Esteve, "Single-shot qubit readout in circuit quantum electrodynamics" Nature Physics 5, 791 (2009).
[15] M. Hofheinz, H. Wang, M. Ansmann, R.C. Bialczak, E. Lucero, M. Neeley, A. D. O'Connell, D. Sank, J. Wenner, J.M. Martinis and A.N. Cleland, "Synthesizing arbitrary quantum states in a superconducting resonator", Nature 459, 546-549 (2009).
[16] M. Sandberg, C.M. Wilson, F. Persson, T. Bauch, G. Johansson, V. Shumeiko, T. Duty, and P. Delsing, "Tuning the field in a microwave resonator faster than the photon lifetime", Appl. Phys. Lett. 92, 203501 (2008).
[17]M. W. Johnson et al. , Nature 473, 194–198 (2011).
[18] S. Boixo, T. Albash, F. M. Spedalieri, N. Chancellor, and Daniel A. Lidar, arXiv:1212.1739.
A. Physical approach and perspective
III-V Semiconductor heterostructures (e.g. GaAs, InP, InAs, etc) form the backbone of today’s opto-electronics combining ultrafast electronics (e.g. HEMT), low-power optics together with the conversion between electronics and optics. The industrial development of this material class has also been fruitfully utilized in the field of QIPC. Employing nanofabrication and/or self-assembling techniques, quantum dots have been defined that can be addressed electrically and/or optically. Each quantum dot contains one electron, the spin of which serves as the qubit (earlier quantum dot work on electron charge qubits and on excitonic qubits has been phased out, because of the short coherence times). The emerging field of quantum opto-electronics can provide an interface between solid state qubits and single-photon quantum optics.
Currently, quantum dot (QD) spin based quantum information processing (QIP) is pursued by ~20 groups worldwide, 11 of which are located in Europe [L. Kouwenhoven (Delft, NL), L. Vandersypen (Delft, NL), K. Ensslin (ETH-Zurich, CH), J. Finley (TU-Munich, DE), M. Bayer (Dortmund, DE), M. Atature (Cambridge, UK), D. Zumbuhl (Basel, CH) R. Warburton (Basel, CH) and A. Imamoglu (ETH-Zurich, CH)], as well as G. Burkard (Konstanz, DE), D. Loss (Basel, CH) and Y. Nazarov (Delft, NL) on the theory side.
B. State of the art
Two main technologies are used to form quantum dots, self-assembly and nanofabrication. Self-assembled quantum dots are controlled and detected mostly by optical means; lithographically defined quantum dots are controlled and detected electrically. Despite these differences, much of the underlying physics is the same in these two systems. The state-of-the art is as follows:
Lithographically defined quantum dots
Self-assembled quantum dots
C. Short-term goals (3-5 years)
D. Long-term goals (10 years and beyond)
E. Key references
[1] D. Loss and D. DiVincenzo, ‘‘Quantum computation with quantum dots’’, Phys. Rev. A 57, 120–126 (1998)
[2] R. Hanson, L.P Kouwenhoven, J.R. Petta, S. Tarucha, and L.M.K. Vandersypen, "Spins in few-electron quantum dots", Reviews of Modern Physics 79, 1217 (2007)
[3] R. Hanson and D.D. Awschalom, "Coherent manipulation of single spins in semiconductors ", Nature 453, 1043 (2008)
A. Physical approach and perspective
Optical quantum computing (OQC) exploits measurement-based quantum computing schemes with photons as physical qubits. The interaction between separate photonic qubits is induced by measurement, as opposed to a direct interaction via nonlinear media. The two main physical architectures for OQC are based on proposals by Knill, Laflamme and Milburn [1], the KLM architecture, and by Raussendorf and Briegel [2], the one-way quantum computer with cluster states.
KLM allows universal and scalable OQC using only single photons, linear optics and measurement. KLM's seminal work is based on the important findings of Gottesman, Chuang and Nielsen concerning the role of teleportation for universal quantum computing. The physical resources for universal (optical) quantum computation in the KLM scheme are multi-particle entangled states and (entangling) multi-particle projective measurements.
Cluster-state quantum computing has become an exciting alternative to existing proposals for quantum computing, and a linear-optics approach is one possible implementation. It consists of a highly entangled multi-particle state called a cluster state, combined with single-qubit measurements and feedforward. These constituents are sufficient to implement scalable, universal quantum computation. Different algorithms only require different “patterns” of single-qubit operations on a sufficiently large cluster state. Since only single-particle projections, together with the ability to construct the initial highly entangled cluster state, are needed to operate such a one-way quantum computer, the cluster-state approach might offer significant technological advantages over existing schemes for quantum computing: this includes reduced overall complexity and relaxed physical demands on the measurement process (as compared to sensitive multi-particle projections) as well as a more efficient use of physical resources.
Currently, the linear optics approach to quantum computation is pursued by the following European groups: K. Banaszek (Torun, PL) , M. Bourennane (Stockholm, SE), F. DeMartini (Rome, IT), N. Gisin (Geneva, CH), P. Grangier (Orsay, FR), A. Karlsson (Stockholm, SE), P. Mataloni (Rome, IT), J. OBrien(Bristol,UK), J. Pan (Heidelberg,DE), J. Rarity (Bristol, UK), A. Shields (Cambridge, UK), I. Walmsley (Oxford, UK), H. Weinfurter (Munich, DE), and A. Zeilinger (Vienna, AT).
B. State of the art
Important key elements for linear-optics quantum computation, namely the generation of entangled states, quantum state teleportation and entanglement swapping have already been realized early in the field (e.g. teleportation in 1997 and entanglement swapping in 1998). The latest developments include:
Several practical designs implementing the KLM scheme have been developed. Experimental methods for the preparation of photonic quantum states that serve as ancillas in the measurement-based schemes now achieve typical fidelities above 99%. Using post-selected events based on coincidence detection has allowed for a range of demonstrations of non-deterministic two-qubit gates: a fully characterized two-photon gate operating with >90% fidelity, four-photon CNOT gates both with entangled ancilla and with teleportation, a KLM non-linear sign-shift gate and a three-photon simulation of the entangled-ancilla gate. These gates can be made scalable with additional resources. Several of these gates have been used in simple applications such as demonstrations of quantum error correction and Bell measurement for teleportation.
Proposals for the optical implementation of cluster-state quantum computing have been put forward and are promising significant reductions in physical resources by two orders of magnitude as compared to the original KLM scheme. Moreover, a variety of modifications have been suggested to reduce the resource requirements in KLM architectures. The realization of photonic four-qubit cluster states allowed to demonstrate the feasibility of one-way quantum computing through a universal set of one- and two-qubit operations, as well as the implementation of Grover’s search algorithm [10]. An essential element of one-way quantum computing is to feed-forward the results of measurements to sequentially occurring measurements in order to correct naturally occurring errors during the computation. This has been achieved in a recent experiment using linear optics [7]. Nevertheless, linear optics, as well as other state-of-the-art techniques of implementing one-way quantum computing algorithms, are still limited to a finite amount of resources available for computational algorithms. As long as this limitation exists, it is paramount to optimize the use of existing resources. For example, it has been shown that the use of generalized measurements can reduce the necessary resources for a given algorithm significantly [8].
Experimental demonstrations have been carried out for topological error correction with an eight-photon cluster state, or of "blind" quantum computing in which the input, computation, and output all remain unknown to the computer. Several experiments has also been done to explore the feasibility of optical continuous-variable qubits, based on superposition of coherent states (often called Schroedinger's cat states"), which have been successfully teleported.
Integration of linear optics technology is an important step towards the practical implementation of large-scale computational networks. Recent achievements in this direction were to manipulate single-photon states and multi-photon entanglement directly on-chip [11]. A compiled version of Shor’s algorithm has been implemented on an integrated wave-guide chip[12], and quantum walks of correlated particles offer the possibility of studying large-scale quantum interference and quantum simulation [13].
Enabling technologies for OQC are:
C. Strengths and weaknesses
One of the main advantages of photonic implementations of quantum computing are low decoherence (due to the photon’s weak coupling to the environment), fast processing, compatibility to fiber optics and integrated optics technologies. Another advantage of OQC is that the active feed forward necessary in the one-way model can be implemented via fast optical switches. With present technologies this can be done in less than 100 nanoseconds (in the future probably down to 10 nanoseconds) [7]. Optical quantum systems are also very promising for realizing either digital quantum simulators [10], which are based on discrete gate operations, or analog quantum simulators, where an initial quantum state is prepared and then continuously evolved to the quantum state of interest. It is the particular advantage of photons that single-qubit operations can be achieved with almost unity fidelity and that tuneable inter-qubit interactions can be achieved among arbitrary qubits. Current drawbacks of the OQC approach are low photon-creation rates, low photon-detection efficiencies, and the difficulties with the intermediate storage of photons in a quantum memory (see also Section 4.1.3 [3]). The low efficiencies quoted above are presently an important practical limitation to the scalability of optical circuits, in the sense that they exponentially damp the success probability of most quantum operations.
D. Challenges
The main challenges for fault-tolerant OQC can be summarized as follows:
E. Key references
[1] E. Knill, R. Laflamme, G. J. Milburn, “A scheme for efficient quantum computation with linear optics’’, Nature 409, 46 (2001).
[2] R. Raussendorf ,H. J. Briegel, “A one-way quantum computer’’, Phys. Rev. Lett. 86, 5188 (2001).
[3] C. Lu et al., “Experimental entanglement of six photons in graph states”, Nature Physics 3, 91 (2007).
[4] Gao et al. , “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state”, Nature Phys. 6, 331 (2010).
[5] R. Krischek et al.,"Ultraviolet enhancement cavity for ultrafast nonlinear optics and high-rate multiphoton entanglement experiments", Nature Photonics 4, 170 (2010)
[6] C. Wagenknecht et al., “Experimental demonstration of a heralded entanglement source”, Nature Photonics 4, 549 (2010); Barz et al., “Heralded generation of entangled photon pairs”, Nature Photonics 4, 553 (2010).
[7] R. Prevedel et al., "High speed linear optics quantum computing using active feed-forward", Nature 445, 65 (2007).
[8] D. N. Biggerstaff et al., "Cluster-State Quantum Computing Enhanced by High-Fidelity Generalized Measurements.", Phys. Rev. Lett. 103, 240504 (2009) .
[9] R. Kaltenbaek, J. Lavoie, B. Zeng, S. D. Bartlett, K. J. Resch, “Optical one-way quantum computing with a simulated valence-bond solid”, Nature Physics 2010 (in Press).
[10] P. Walther et al., “Experimental one-way quantum computing”, Nature 434, 169 (2005).
[11] J. C. F. Matthews, A. Politi, A. Stefanov, J. L. O'Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits”, Nature Photon 3, 346 (2009).
[12] A. Politi et al., Shor’s Quantum Factoring Algorithm on a Photonic Chip, Science 325, 1221 (2009). [13] A. Peruzzo et. al. “Quantum Walks of Correlated Photons”, Science 329, 1500 (2010).
A. Physical approach and perspective
Storage and processing of information can be carried out using individual atomic and molecular spins in condensed matter. Systems falling into this category include dopant atoms in semiconductors like phosphorous or deep donors in silicon or color centers in diamond, nitrogen or phosphorus atoms in molecules like C60, rare earth ions in dielectric crystals and unpaired electrons at radiation induced defects or free radicals in molecular crystals. The main attraction of spins in low-temperature solids is that they can store quantum information for up to several thousand seconds [1] on the other hand certain spin systems are shielded well enough from their environments such that room temperature operation seem feasible. Specific systems have been selected based on criteria like: dephasing time, optical access, single quantum state readout, and nanostructuring capabilities. While most of these systems are scalable in principle, technical progress in single quantum state readout, addressability and nanoengineering is necessary.
Another solid basis for quantum information processing, which relies on new molecules engineered with features suitable for qubit encoding and entanglement, is provided by Single Molecular Magnets (SMMs). Current research activity focuses on the control of the coherent spin dynamics in molecular spin clusters, which implies the control of decoherence mechanisms both at synthetic level and in terms of modelling. While most of the experiments are currently performed on bulk crystals, the final goal of manipulating single molecular spins is drawing increasing attention towards the grafting of molecules at surfaces and the development of techniques for readout.
Research groups engaged in QIP research regarding impurity spins in solids in Europe include A. Briggs (Oxford, UK), P. Grangier (Orsay, FR), O. Guillot-Noël and P. Goldner (Paris, FR), W. Harneit (Berlin, DE), S. Kröll (Lund, SE), J.L. LeGouët (Orsay, FR), M. Mehring (Stuttgart, DE), K. Mølmer (Aarhus, DK), J.F. Roch (Cachan, FR), M. Stoneham (London, UK), D. Suter (Dortmund, DE), J. R. Hanson (Delft, NL), J. Wrachtrup (Stuttgart, DE). Research groups working on QIP with molecular spin clusters in Europe include D. Loss (Basel, CH), B. Barbara and W. Wernsdorfer (Grenoble, FR), M. Affronte and F. Troiani (Modena, IT), D. Gatteschi (Florence , IT), R. E. P. Winpenny and G. Timco (Manchester, UK).
B. State of the art
Impurity spins: Atomic and molecular spins in solids have received considerable attention as qubits. Already Kane’s [1] proposal has underlined the basic challenges and opportunities of such systems in quantum computing. In the meantime a number of related systems like dilute rare earth ions, color centers, random deep donors in silicon with optically controlled spin and defects in wide and narrow band gap semiconductors have underlined their potential usefulness in QIP [2]. Most approaches use electron or nuclear spin degrees of freedom as quantum bits. The specific advantages of spin systems includes long decoherence times [3] and access to highly advanced methods for precise manipulation of quantum states. The experimental techniques that have made liquid state NMR the most successful QIP technique in terms of precise manipulation of quantum states so far are currently being transferred to solid-state systems. These systems may be able to overcome the scalability problems that plague liquid state NMR while preserving many of the advantages of today’s liquid state work.
In detail the following landmark results have been achieved:
Single molecular magnets: Quantum dynamics of spins in molecular clusters has been deeply studied by a number of fundamental works in the last decade. Decoherence and dephasing mechanisms have been investigated in assemblies: the intrinsic coherence times are expected to be longer than microseconds (preliminary experiments provide a lower bound of few tens of ns); similarly, the switching rates for one-qubit and two-qubit gates are estimated to be on the order of hundreds of picoseconds.
Recent important achievements are:
C. Strengths and weaknesses
Impurity spins: The strength of defect center QIP in solids are the long decoherence times of spins even under ambient conditions and the precise state control. Depending on the system, electrical as well as optical single spin readout has been shown (fidelity of 80%). Substantial progress in the nanopositioning of single dopants with respect to control electrodes has been achieved. Weaknesses are: Electrical and optical readout of spin states has been shown up to now for only a single type of defect. Nanopositioning of defects is still a major challenge (which has seen dramatic progress for phosphorus in silicon). However there are schemes, based on deep donors in Si, where nanopositioning is not needed. Instead the randomness is exploited so as to make maximum use of spatial and spectral selection to isolate qubits and their interactions. Manipulation and readout is optical. The situation is similar for rare earth crystals, but in this case a fully scalable scheme still needs to be developed.
Single molecular magnets: The bottom-up approach used by supra-molecular chemistry offers simple and relatively cheap processes for the fabrication of quantum nanosized molecules exhibiting multi-functionality like the switchability of magnetic states with light, resonance at RF-MW radiation, etc. Moreover, the control on and the sharp definition of eigenstates and eigenvalues in magnetic molecules provides an extraordinary stimulus for the development of new quantum algorithms and schemes. In the latter case, the main issue would be to prove that single, isolated molecules behave not much differently from what is observed in experiments performed on assemblies of molecules.
D. Short-term goals (3-5 years)
Impurity spins: Impurity systems form a bridge for transferring quantum control techniques between atomic and solid state systems. Close interaction between the atomic physics and solid state communities is a key ingredient for achieving this.
Single molecular magnets: The main goals can be summarized as follows:
E. Long-term goals (10 years and beyond)
For impurity spins the main long-term challenges are
For single molecular magnets, the long-term challenges can be summarized as follows:
F. Key references
[1] B. Kane, “A silicon-based nuclear spin quantum computer”, Nature 393, 133 (1998)
[2] R. Hanson, D. Awschalom. "Coherent manipulation of single spins in semiconductors" Nature 453, 1043 (2008), P. Neumann et al. "Multipartite entanglement of single spins in diamond", Science 320, 1326 (2008)
[3] E. Yablonowitch, H.W. Jiang, H. Kosaka, H.D. Robinson, D.S. Rao, T. Szkopek “Optoelectronic quantum telecommunications based on spins in semiconductors” , Proc. IEEE 91, 761 (2003)
[4] M.N. Leuenberger, D. Loss, “Quantum Computing in Molecular Magnets’’, Nature 410, 789 (2001)
[5] F. Troiani A. Ghirri, M. Affronte, P. Santini, S. Carretta, G. Amoretti, S. Piligkos, G. A. Timco, R. E. P. Winpenny, “Molecular engineering of antiferromagnetic rings for quantum Computation”, Phys. Rev. Lett. 94, 207208 (2005)
The development of quantum information science (QIS) was initially driven by theoretical work of scientists working on the boundary between Physics, Computer Science, Mathematics, and Information Theory. In the early stages of the development of QIS, theoretical work has often been far ahead of experimental realization of these ideas. At the same time, theory has provided a number of proposals of how to implement basic ideas and concepts from quantum information in specific physical systems. These ideas are now forming the basis for successful experimental work in the laboratory, driving forward the development of tools that will form the basis for all future technologies which employ, control and manipulate matter and radiation at the quantum level.
Today one can observe a broad and growing spectrum of theoretical activities. Investigations include, to name just a few examples,
An important class of theoretical work is concerned with implementations of these abstract concepts in real physical systems, such as trapped ions, ultra-cold ions in optical lattices, or systems from cavity-QED.
In fact, many of these theoretical proposals have formed the starting point as well as the guide for experimental work in the laboratories, as is described in the other sections of this document. What is more, the transfer of concepts from quantum information theory to other fields of physics such as condensed matter physics or quantum field theory has proved very fruitful and has attracted considerable interest recently.
It is important to realize that these activities are often interdisciplinary in nature and span a broad spectrum of research in which the different activities are benefiting from each other to a large degree. Thus it does not seem to be advisable to concentrate research on too narrowly defined topics only. Theory groups in Europe have been consistently attained international leadership in the entire spectrum of research (see more below). This has been facilitated by a flexible and topically broad financing on European and national levels in the past.
In the following we give a brief outline of the current status and the perspectives of the main areas of quantum information theory.
Quantum algorithms and complexity
Following Deutsch's fundamental work in 1985 that demonstrated the potential power of quantum algorithms and quantum computers, Shor demonstrated in 1994 that integers can be efficiently factorized on a quantum computer. Factoring is the task of decomposing an integer, say 15, into a product of prime numbers: 15=3*5. Its importance is immense because many modern cryptographic protocols (for instance the famous RSA cryptosystem) are based on the fact that factoring large integers, as well as computing discrete logarithms, is a hard problem on a classical computer. Shor's result means that quantum computers could crack most classical public-key cryptosystems used at present. It has lead to extensive work on developing new quantum algorithms. Progress has been made on the Hidden Subgroup problem (which generalizes Shor's algorithm) in the case of non-Abelian groups, like affine groups, the dihedral group, or solvable groups with small exponent. A quantum algorithm was discovered for finding solutions to Pell's equation, which is an important problem in algebraic number theory. Strong links have been established between known quantum algorithms and lattice problems. Finally Grover's quantum "data base'' search algorithm allows a quantum computer to perform an unstructured search quadratically faster than any classical algorithm. Although Grover's only yields a quadratic speed-up over classical algorithms it can be widely used in computer science tasks, like sorting, matrix multiplication bipartite matching to name a few. For all these problems quantum computers give an important advantage over classical computers. Grover's algorithms can be cast in terms of quantum random walks which has lead recently to new quantum algorithms for searching game trees. These algorithms will be widely applicable in the area of algorithmic game theory, scientific computing etc.
Very recently a new quantum algorithm has been developed for approximating solutions to linear equations. This algorithm demonstrates an exponential advantage over any classical algorithm. In order to understand to what extent quantum computers outperform classical computers we need to determine where efficient quantum computation, BQP, fits within the classification of complexity classes, like P, NP, and PSPACE. General methods for proving impossibility results, that is limitations of quantum computers, have been developed and applied with great success. Notable are the polynomial method and the quantum adversary method.
Finally, another important line of research is to understand when quantum systems can be efficiently simulated on a classical computer. This allows identifying quantum situations and resources that do not lead to any improvement over classical computation.
Key references
[1] D. Deutsch, "Quantum theory, the Church-Turing principle and the universal quantum computer", Proc. R. Soc. Lond. A 400, 97 (1985)
[2] P. W. Shor, "Algorithms for quantum computation, discrete log and factoring", FOCS’35, 124 (1994)
[3] L. Grover, "A fast quantum mechanical algorithm for database search", STOC’28, 212 (1996)
[4] A. Ambainis, D. Aharonov, J. Kempe and U. Vazirani, "Quantum walks on graphs", 33rd ACM Symp. on Theory of Computing (2001)
[5] R. Beals, H. Buhrman, R. Cleve, M. Mosca, and R. de Wolf, "Quantum lower bounds by polynomials",Journal of the ACM 48(4) (2001)
[6] A. Ambainis, "Quantum lower bounds by quantum arguments", Journal of Computer and System Sciences 64, 750 (2002)
[7] E. Farhi, J. Goldstone and S. Gutmann. "A Quantum Algorithm for the Hamiltonian NAND Tree" [ quant-ph/0702144]
[8] A. W. Harrow, A. Hassidim, and S. Lloyd, "Quantum algorithm for solving linear systems of equations", Phys. Rev. Lett. 15, 150502 (2009)
[9] R. Jozsa, A. Miyake, "Matchgates and classical simulation of quantum circuits", Proc. R. Soc. A 464, 3089 (2008)
Quantum communication protocols
Following the success of quantum algorithms quantum communication complexity was developed by initial work of Yao (qubit model) and Cleve and Buhrman (entanglement assisted model). The setting is that of multiple quantum computers trying to solve computational tasks, minimizing the amount of communication. There has also been considerable development of new protocols for quantum communication over the last decade. Useful protocols that found applications outside that of communication complexity are Quantum Fingerprinting and the Hidden Matching problem. These protocols demonstrate an exponential improvement in the communication over classical protocols. Applications are in many areas, like interactive games and approximation algorithms, lower bound for classical and quantum computers, as well as the development of new non-locality tests. Main open questions in this area are to understand the power that entanglement assisted model offers. This is poorly understood, but recently some progress has been made by connecting this question for restricted games, called XOR games, to functional analysis. An intriguing interplay between quantum communications complexity, non-locality, approximation algorithms, and functional analysis is becoming available.
Key references
[1] A. Yao, "Quantum circuit complexity", Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science, 352 (1993)
[2] H. Buhrman, R. Cleve, and A. Wigderson, "Quantum vs. classical communication and computation", Proceedings of the 30th Annual ACM Symposium on Theory of Computing (STOC 1998)
[3] R. Cleve, P. Høyer, B. Toner, and J. Watrous, "Consequences and limits of nonlocal strategies", Proc. of 19th IEEE Conference on Computational Complexity (2004)
[4] D. Gavinsky, J. Kempe, I. Kerenidis, R. Raz, and R. de Wolf, "Exponential separations for one-way quantum communication complexity, with applications to cryptography", SIAM Journal on Computing, 38, 1695 (2008)
[5] Z. Bar-Yossef, T. S. Jayram, I. Kerenidis, "Exponential separation of quantum and classical one-way communication complexity", SIAM J. Comput. 38 (2008)
[6] J. Briët, H. Buhrman, T. Lee, and T. Vidick, "Multiplayer XOR games and quantum communication complexity with clique-wise entanglement", [quant-ph/0911.4007]
[7] H. Buhrman, R. Cleve, S. Massar, and R. de Wolf, "Nonlocality and communication complexity", Rev. Mod. Phys. 81 (2010)
[8] M. Junge, C. Palazuelos, D. Perez-Garcia, I. Villanueva, and M. M. Wolf, "Operator Space theory: a natural framework for Bell inequalities", Phys. Rev. Lett. 104, 170405 (2010)
Quantum cryptographic protocols
The most import feat of quantum computers is that they can efficiently factor integers into their prime factors. This in turns means that most of the cryptographic protocols that are used today, whose security is based on the assumption that factoring is hard, will be rendered obsolete once a quantum computer is built. But all is not lost, quantum information processing opens up possibilities that are classically impossible. The well known key distribution protocol, due to Bennett and Brassard, establishes that two parties, who trust each other, can generate a secret shared key in such a way that if there is an eavesdropper trying to obtain the key or part thereof, will be detected with high probability. Once a secure key is established classical protocols, like the one-time pad, allow for secure message transmission. Such secure key distribution schemes are classically impossible! Moreover quantum key distribution schemes (QKD) are already commercially available.
It is natural and important to figure out what other protocols are possible using quantum technology. Unfortunately it was realized by Mayers, Lo and Chau that the schemes that are rendered insecure by Shor's factoring algorithm, asymmetric or public key cryptography, can not be unconditionally secure in the quantum world, something that QKD is. This again does not mean all is lost. Quantum information processing is able to realize tasks that are impossible classically such as biased Coin Tossing and Quantum Bit String Generation, Quantum String Commitment, resilient and unconditionally secure Digital Signatures, or Private Information Retrieval. We expect that the existing protocols will be improved and will gradually be implemented in the laboratory (as was recently the case for quantum bit string generation). We also expect the development of new protocols for quantum communication. For instance, recently improved protocols for quantum money with classical verification have been proposed. Also, position-based cryptographic was also analyzed in the quantum regime. While this form of cryptography is impossible against unbounded quantum adversaries, it might be possible against adversaries with bounded entanglement.
Another strand has initiated secure protocols under mild assumptions. A very promising one is the bounded storage model. The assumption is that it is impossible to build quantum memories that store reliably huge amounts of qubits for a few seconds. Currently storing reliably a single qubit for a millisecond is already very challenging. It turns out that schemes, similar in flavor to QKD, allow for secure, under the bounded storage assumption, quantum implementations of a primitive called oblivious transfer (OT). Having this primitive as a building block allows one to build all cryptographic schemes that are used in practice today. More important these implementations appear technically not much more demanding than those of QKD.
However when we have built a quantum computer that is able to efficiently and reliably factor integers, we need to find cryptographic protocols that are secure under computational assumptions, like current cryptographic protocols are secure under the assumption that factoring is hard. This line of research is part of post quantum cryptography. Progress has been made by Regev who developed a protocol based on the hardness of certain lattice problems.
Key references
[1] C. H. Bennett and G. Brassard, ``Quantum cryptography: Public key distribution and coin tossing'', in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, p. 175 (1984)
[2] A. Ambainis, "A new protocol and lower bounds for quantum coin flipping'', Journal of Computer and System Sciences, 134 (2004)
[3] A. Chailloux and I. Kerenidis, ``Optimal quantum strong coin flipping'', 50th Annual Symposium on Foundations of Computer Science (FOCS) (2009)
[4] L-P. Lamoureux, E. Brainis, D. Amans, J. Barrett, and S. Massar ``Provably secure experimental quantum bit-string generation'', Phys. Rev. Lett. 94, 050503(4) (2005)
[5] D. Gavinsky, "Quantum Money with Classical Verification", arXiv:1109.0372
[6] F. Pastawski, N. Y. Yao, L. Jiang, M. D. Lukin, and J. I. Cirac, "Unforgeable Noise-Tolerant Quantum Tokens", arXiv:1112.5456
[7] H. Buhrman et al., "Position-Based Quantum Cryptography: Impossibility and Constructions", arXiv:1009.2490
[8] S. Wehner, C. Schaffner, and B. Terhal, "Cryptography from Noisy Storage", Phys. Rev. Lett. 100, 220502 (2008)
[9] O. Regev, "On lattices, learning with errors, random linear codes, and cryptography'', In Proc. 37th ACM Symp. on Theory of Computing (STOC), 84 (2005).
Computational models and architectures
There are many different ideas of how to make quantum systems compute. While these different computational models are typically equivalent in the sense that one can simulate the other with only polynomial overheads in resources, they may be quite different in practice, when it comes to a particular class of problems. They also have to satisfy very different needs from the perspective of the requirements on the hardware. What is more, they suggest different procedures to achieve fault tolerant computation, many of them yet to be explored in detail. At the moment the main contenders of fundamental architectures are:
Most recently, we have seen a series of theoretical work analyzing the connection between the different computational models. The benefit of these works lies in a better understanding of the capabilities and advantages of the individual models, and of the essential features of a quantum computer. It will also turn out what model will eventually give rise to the most feasible architecture. In the future we expect that optimized models (i.e. taking the best out of the different approaches) will be developed. We also expect that these models will have an increasing impact on (i) the formulation of new quantum algorithms and (ii) the evaluation of physical systems regarding their suitability for fault-tolerant quantum computation. Both of these points are of great importance for the field: While new algorithms will further enlarge the range of applications for quantum computers, new methods for fault-tolerant computation will hopefully make it technologically less challenging to realize scalable quantum computers in the laboratory.
Key references
[1] D. Deutsch, "Quantum computational networks", Proc. R. Soc. Lond. A 425, 73 (1989)
[2] A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, "Elementary gates for quantum computation", Phys. Rev. A 52, 3457 (1995)
[3] E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda, "A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem", Science 292, 472 (2001)
[4] B. Schumacher and R. Werner, "Reversible cellular automata", [quant-ph/0405174]
[5] R. Raussendorf and H.-J. Briegel, "A one-way quantum computer", Phys. Rev. Lett. 86, 5188 (2001)
[6] D. Gross and J. Eisert, "Novel schemes for measurement-based quantum computation", Phys. Rev. Lett. 98, 220503 (2007)
[7] S. Diehl, A. Micheli, A. Kantian, B. Kraus, H. P. Büchler, and P. Zoller, "Quantum states and phases in driven open quantum systems with cold atoms", Nature Physics 4, 878 (2008)
[8] F. Verstraete, M. M. Wolf, and J. I. Cirac, "Quantum computation, quantum state engineering, and quantum phase transitions driven by dissipation", Nature Physics 5, 633 (2009)
Quantum simulation
Quantum simulators may become the first application of quantum computers, since with modest requirements one may be able to perform simulations which are impossible with classical computers. At the beginning of the 80's it was realized that it will be impossible to predict and describe the properties of certain quantum systems using classical computers, since the number of variables that must be stored grows exponentially with the number of particles. A quantum system in which the interactions between the particles could be engineered would be able to simulate that system in a very efficient way. This would then allow, for example, studying the microscopic properties of interesting materials permitting free variation of system parameters. Potential outcomes would be to obtain an accurate description of chemical compounds and reactions, to gain deeper understanding of high temperature superconductivity, or to find out the reason why quarks are always confined.
A quantum simulator is a quantum system whose dynamics or static properties can be engineered such that it reproduces the behaviour of another physical system which one is interested to describe. The former can be conceived in a "digital" fashion, where continuous dynamics is approximated by gates using a Trotter formula, or in an analogue way. In principle, a universal quantum computer would be an almost perfect quantum simulator since one can program it to undergo any desired quantum dynamics. However, a quantum computer is very difficult to build in practice and has very demanding requirements. Fortunately, there are physical systems in which one can engineer certain kind of interactions and thus simulate other systems which so far are not well understood.
Key experimental platforms are ultra-cold atoms in optical lattices or trapped ions, both architectures having seen remarkable progress in recent years. In those systems, one does not necessarily require to individually address the qubits, or to perform quantum gates on arbitrary pairs of qubits, but rather on all of them at the same time. Ideas like optical superlattices or the suitable exploitation of Feshbach resonances in the former class of physical systems add further flexibility. Besides, one is interested in measuring physical properties (like magnetization, conductivity, etc.) which are robust with respect to the appearance of several errors (in a quantum computer without error correction, even a single error will destroy the computation). For example, to see whether a material is conducting or not one does not need to know with a high precision the corresponding conductivity. Molecular energies within chemical precision can also be computed by quantum simulations. The use of 30 to 100 qubits for those algorithms exceeds the limitations of classical computing of molecular energies. Important theoretical open questions are related to certifying success of a quantum simulation or to show hardness of the equivalent classical problem.
Key references
[1] S. Lloyd, "Universal quantum simulators", Science 273, 1073 (1996)
[2] J. I. Cirac and P. Zoller, "Goals and opportunities in quantum simulation", Nature Physics 8, 264 (2012)
[3] E. Jane, G. Vidal, W. Duer, P. Zoller, and J. I. Cirac, "Simulation of quantum dynamics with quantum optical systems", Quant. Inf. Comp. 3, 15 (2003)
[4] C. H. Bennett, J. I. Cirac, M. S. Leifer, D. W. Leung, N. Linden, S. Popescu, and G. Vidal, "Optimal simulation of two-qubit Hamiltonians using general local operations", Phys. Rev. A 66, 012305 (2002)
[5] M. A. Nielsen, M. J. Bremner, J. L. Dodd, A. M. Childs, and C. M. Dawson, "Universal simulation of Hamiltonian dynamics for qudits", Phys. Rev. A 66, 022317 (2002)
[6] A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, and M. Head-Gordon, "Simulated quantum computation of molecular energies'', Science 309, 1704 (2005)
[7] D. Jaksch and P. Zoller, "The cold atom Hubbard toolbox", Ann. Phys. 315, 52 (2005)
[8] M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, "Complex dynamics in coupled arrays of micro-cavities", Laser and Photonics Reviews 6, 527 (2008)
[9] S. Trotzky, Y.-A. Chen, A. Flesch, I. P. McCulloch, U. Schollw{\"o}ck, J. Eisert, and I. Bloch,, "Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas", Nature Physics 8, 325 (2012)
[10] I. Bloch, J. Dalibard, and S. Nascimbene, "Quantum simulations with ultracold quantum gases", Nature Physics 8, 267 (2012)
[11] P. Hauke, F. M. Cucchietti, L. Tagliacozzo, I. Deutsch, and M. Lewenstein, "Can one trust quantum simulators?", Rep. Prog. Phys. 75, 082401 (2012)
Topological quantum information processing and computation
Topological quantum computation (TQC) is an approach to quantum information processing that eliminates decoherence at the hardware level by encoding quantum states and gates in global, delocalized properties of the hardware medium.
Most of the current quantum computing schemes assume nearly perfect shielding from the environment. Decoherence makes quantum computing prone to error and nonscalable, allowing only for very small "proof of principle" devices. Error correction software can in principle solve this problem, but progress along this path will take a long time. While much of the current research on other approaches to quantum computation is focused on improving control over well-understood physical systems, TQC research promises fundamental breakthroughs.
Delocalized, or topological degrees of freedom are intrinsically immune to all forms of noise which do not impact the entire medium at once and coherently. For media which exhibit an energy gap, kept at low enough temperatures, this is in fact all conceivable noise. If such materials can be constructed or found in nature, they will allow a much cleaner and faster realization of scalable quantum computation than other schemes.
TQC can be realized in effectively planar (2D) systems whose quasiparticles are anyons, that is they have nontrivial exchange behavior, different from that of bosons or fermions. If, in a system of three or more anyons, the result of sequential exchanges depends on the order in which they are performed, they are called non-Abelian anyons. Systems with non-abelian anyons allow for scalable quantum computation: many-anyon systems have an exponentially large set of topologically protected low-energy states which can be manipulated and distinguished from one another by experimental techniques, such as anyon interferometry recently realized in fractional quantum Hall systems.
A physical system which harbours anyons is said to be topologically ordered, or in a topological phase. One of the most important goals is to study such phases and their non-Abelian anyonic quasiparticles. The most advanced experiments in this direction are done in the context of the fractional quantum Hall effect (FQHE), where phases with fractionally charged Abelian anyons have already been seen and strong experimental evidence for the existence of non-Abelian anyons is emerging. In addition, very promising results have recently been obtained on engineered topologically ordered phases in Josephson junction arrays.
In addition to its natural fault-tolerance, topological quantum computation - though computationally equivalent to the conventional quantum circuit model - is a unique operational model of computation, which represents an original path to new quantum algorithms. New algorithms for approximation of certain hard \#P hard computational problems have already been developed and this is opening up new areas of quantum algorithmic research.
The research objectives cover all aspects of topological quantum computation and include:
Key references
[1] C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, "Non-Abelian anyons and topological quantum computation", Rev. Mod. Phys. 80, 1083 (2008)
[2] G. P. Collins, "Computing with quantum knots", Scientific American 294, 56 (2006)
[3] M. H. Freedman, M. J. Larsen, and Z. Wag, "A modular functor which is universal for quantum computation", Commun. Math. Phys. 227, 605 (2002)
[4] A. Yu. Kitaev, "Fault-tolerant quantum computation by anyons", Ann. Phys. 303, 1 (2003)
[5] G. Kells, J. K. Slingerland, and J. Vala, "Description of Kitaev's honeycomb model with toric-code stabilizers", Phys. Rev. B 80, 125415 (2009)
[6] W. Bishara, P. Bonderson, C. Nayak, K. Shtengel, and J. K. Slingerland, "Interferometric signature of non-Abelian anyons", Phys. Rev. B 80, 155303 (2009)
[7] M. Dolev, M. Heiblum, V. Umansky, A. Stern, and D. Mahalu, "Observation of a quarter of an electron charge at the : nu = 5/2 quantum Hall state", Nature 452, 829 (2008)
[8] I. P. Radu, J. B. Miller, C. M. Marcus, M. A. Kastner, L. N. Pfeiffer, and K. W. West, "Quasiparticle properties from tunneling in the nu = 5/2 fractional quantum hall state", Science 320, 899 (2008)
[9] S. Gladchenko, D. Olaya, E. Dupont-Ferrier, B. Doucot, L. B. Ioffe, and M. E. Gershenson, "Superconducting nanocircuits for topologically protected qubits", Nature Physics 5, 48 (2008)
[10] R. L. Willett, L. N. Pfeiffer, and K. W. West, "Measurement of filling factor 5/2 quasiparticle interference with observation of charge e/4 and e/2 period oscillations", Proc. Natl. Acad. Sci. 106, 8853 (2009)
[11] M. B. Hastings, "Topological order at non-zero temperature", Phys. Rev. Lett. 107, 210501 (2011)
Quantum error correction and purification
The ability to carry out coherent quantum operation even in the presence of inevitable noise is a key requirement for quantum information processing. To cope with this decoherence problem, active strategies (quantum error correcting codes) as well as passive ones (error avoiding codes) have been developed.
Error correcting codes allow one to reduce errors by suitable encoding of logical qubits into larger systems. It has been shown that, with operations of accuracy above some threshold, the ideal quantum algorithms can be implemented. Recent ideas involving error correcting teleportation have made the threshold estimate more favorable by several orders of magnitude. This path has to be continued and adapted to realistic error models and to alternative models of quantum computation like the adiabatic model or the cluster model (see section 4.3.3).
In error avoiding codes, no active monitoring/intervention on the system is in principle necessary, since errors are simply circumvented. Error avoiding is based on the symmetry structure of the system-environment interaction that in some circumstances allows for the existence of decoherence-free subspaces (DFS), i.e. subspaces of the system Hilbert state-space over which the dynamics is still unitary. The prototype noise model for which this situation occurs is provided by the so-called collective decoherence, where all the qubits are affected by the environment in the same way. For encoding a single logical noiseless qubit for general collective decoherence (dephasing), four (two) physical qubits are needed. DFSs have been experimentally demonstrated in a host of physical systems, and their scope extended by generalizing the idea of symmetry-aided protection to noiseless subsystems.
A fruitful connection with the theory of entanglement purification, which has been developed primarily in the context of quantum communication, and has been used in protocols such as the quantum repeater, is also emerging. Entanglement purification or distillation is a method to "distill'' from a large ensemble of impure and noisy (low-fidelity) entangled states a smaller ensemble of pure (high-fidelity) entangled states. Remarkably, not all entangled states can be distilled, which implies the existence of an irreversible form of entanglement known as bound entanglement. It seems that appropriately generalized procedures can be employed also in general quantum computation (e.g. for quantum gate purification, or for the generation of high fidelity resource states) while benefiting from the relaxed thresholds that exist for entanglement purification.
Key references
[1] A. M. Steane, "General theory of quantum error correction and fault tolerance", in ‘The physics of quantum information’, (D. Bouwmeester, A. Ekert, A. Zeilinger, eds.), pp. 242-252, Springer, Berlin (2000)
[2] J. Preskill, "Fault-tolerant quantum computation", in "Introduction to quantum computation and information", (H. K. Lo, S. Popescu, T. Spiller, eds.) pp. 213-269, World Scientific, Singapore (1998)
[3] C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, "Mixed-state entanglement and quantum error correction", Phys. Rev. A 54, 3824 (1996)
[4] P. Zanardi and M. Rasetti, “Noiseless Quantum Codes”, Phys. Rev. Lett. 79, 3306 (1997)
[5] D. Deutsch, A. Ekert, R. Josza, C. Macchiavello, S. Popescu, and A. Sanpera, "Quantum privacy amplification and the security of quantum cryptography over noisy channels", Phys. Rev. Lett. 77, 2818 (1996)
[6] M. Horodecki, P. Horodecki, R. Horodecki, "Mixed-state entanglement and distillation: Is there a 'bound' entanglement in nature?", Phys. Rev. Lett. 80, 5239 (1998)
[7] H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, "Quantum repeaters: The role of imperfect local operations in quantum communication", Phys. Rev. Lett. 81, 5932 (1998)
[8] A. M. Steane, "Overhead and noise threshold of fault-tolerant quantum error correction", Phys. Rev. A 68, 042322 (2003)
[9] E. Knill, "Quantum computing with very noisy devices", Nature 434, 39 (2005)
Geometric methods for fault-tolerant quantum computing
An alternative approach to achieve fault-tolerant quantum computation is by geometric means. In this approach, quantum information is encoded in a set of energy degenerate states, depending on dynamically controllable parameters. Quantum gates are then enacted by driving the control parameters along suitable loops. These transformations, termed holonomies, are suitable to realize a set of universal quantum gates. Implementation schemes of geometrical computation have been proposed for several different physical systems, most notably for trapped ions. The existing protocols for fault tolerant quantum computation have been specifically designed for phenomenological uncorrelated noise, while few results are known for a scenario with memory effects, i.e. non-Markovian noise, arising from the Hamiltonian interaction with the environment. In particular this raises the question of fault tolerant schemes for phenomenological noise with memory.
Key references
[1] J. A. Jones, V. Vedral, A. Ekert, and G. Castagnoli, “Geometric quantum computation using nuclear magnetic resonance”, Nature 403, 869 (2000)
[2] P. Zanardi and M. Rasetti, “Holonomic quantum computation”, Phys. Lett. A 264, 94 (1999)
[3] L.-M. Duan, J. I. Cirac, and P. Zoller, “Geometric manipulation of trapped ions for quantum computation”, Science 292, 1695 (2001)
[4] R. Alicki, M. Horodecki, P. Horodecki, and R. Horodecki, “Dynamical description of quantum computing: Generic non-locality of quantum noise”, Phys. Rev. A 65, 062101 (2002)
[5] M. Terhal and G. Burkard, “Fault-tolerant quantum computation for local non-Markovian noise”, Phys. Rev. A 71, 012336 (2005)
Quantum control theory for quantum information devices
Quantum error correction enables fault-tolerant quantum computation to be performed, provided that each elementary operation meets a certain fidelity threshold, but unfortunately, this puts extremely demanding constraints on the allowable errors. Threshold estimates vary between 0.01\% to fractions of a percent, but none of the candidate physical implementations available to date has met such requirements yet. Therefore the main open challenge is a practical one: Will the necessary fidelity ever be reached in practice for elementary operations, and maintained while scaling up qubit number and system complexity? This will ultimately determine the winning hardware platform for future quantum information devices, analog to what has happened with silicon for conventional computing.
One feature is common to all candidate QIP implementations: the need for an extremely accurate control of the quantum dynamics at the individual level, with much better precision than has been achieved before. Optimal control theory is a very powerful set of methods developed over the last decades to optimize the time evolution of a broad variety of complex systems, from aeronautics to economics. The basic underlying idea is to pick a specific path in parameter space to perform a specific task. This is expressed mathematically by a cost functional that depends on the state of the system and is minimized with respect to some control parameters. More recently, this approach is being successfully applied to quantum systems, e.g., in the context of ultra-fast laser pulses and light-assisted molecular reactions. A big advantage is that, in a quantum-mechanical situation, the goal can be reached via interference of many different paths in parameter space, rather than just one. This allows, for instance, to exploit faster non-adiabatic processes, allowing to perform more gate operations within the decoherence time, which is crucial to apply fault-tolerant error correction. In future work, these ideas will also be more closely tied to methods of quantum systems identification.
Over the last few years, quantum optimal control theory (QOCT) has been applied to different aspects of quantum information processing, in particular to the implementation of scalable quantum gates with real physical systems, and it has become a powerful standard tool. The figure of merit to be optimized in this case is the fidelity, defined as the projection of the physical state obtained by actually manipulating the chosen system onto the logical state that the gate aims at obtaining. Several examples, from atoms in optical lattices and atom chips to trapped ions and superconducting charge qubits, have indicated systematic improvements in fidelity beyond the fault-tolerance threshold, taking into account experimentally available configurations and known sources of imperfection.
Key references
[1] N. Khaneja, R. Brockett, and S. J. Glaser, “Time optimal control in spin systems”, Phys. Rev. A 63, 032308 (2001)
[2] T. Schulte-Herbrueggen, A. K. Spoerl, N. Khaneja, S. J. Glaser, "Optimal control-based efficient synthesis of building blocks of quantum algorithms seen in perspective from network complexity towards time complexity", Phys. Rev. A 72, 042331 (2005)
[3] C. Brif, R. Chakrabarti, and H. Rabitz, "Control of quantum phenomena: Past, present, and future", arXiv:0912.5121 [quant-ph]
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[5] R. Hildner, D. Brinks, N. F. van Hulst, "Femtosecond coherence and quantum control of single molecules at room temperature", Nature Physics 7, 172 (2011)
Theory of entanglement
Secret correlations are an important resource already in classical cryptography where, for perfect secrecy, sender and receiver hold two identical and therefore perfectly correlated code-books whose contents are only known to them. Such secret correlations can neither be created nor enhanced by public discussion. Entanglement represents a novel and particularly strong form of such secret correlations. Therefore, entanglement is a key resource in quantum information science. Its role as a resource becomes even clearer when one is considering a communication scenario between distant laboratories. Then, experimental capabilities are constrained to local operations and classical communication (LOCC) as opposed to general non-local quantum operations affecting both laboratories. This is an important setting in quantum communication but also distributed quantum computation and general quantum manipulations. The resulting theory of entanglement aims to answer three basic questions.
Firstly, we wish to characterize and verify entangled resources to be able to decide, ideally in an efficient way, when a particular state that has been created in an experimental set-up or a theoretical consideration contains the precious entanglement resource. While the problem of entanglement detection has been shown to be hard, there exist numerical techniques that work well in many situations. For the experimental verification of this resource, the tool of entanglement witnesses allows to detect entanglement with local measurements only, and thus is easily implementable with present technology. Secondly, we wish to determine how entangled state may be manipulated under LOCC. In many situations an experimental setting will yield a certain type of entangled state that may suffer certain deficiencies. It may not be the correct type of state or it may have suffered errors due to experimental imperfections and be entangled. Once characterization methods have determined that the resulting state contains entanglement one can then aim to transform the initial state into the desired final state. Thirdly, it will be important to quantify the efficiency of all the processes and procedures as well as the entanglement resources that have been identified in the above two areas of research. If we have found entanglement in a state, then one will need to know how much of it there is.
Considerable progress in this area has been made in recent years, in particular in the case of bi-partite entanglement, but we are still far away from a comprehensive understanding of this key resource for quantum information processing. Research in this area will continue to play a central role in the field, and we expect that an increasing effort will be undertaken towards the classification and quantification of entanglement in multi-party entangled states. It is worth pointing out that insights in the theory of entanglement are not only important the field of QIS itself, but they have now reached the stage where they are being applied to other areas of physics (see Subsection 4.3.10).
Key references
[1] R. F. Werner, "Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model", Phys. Rev. A 40, 4277 (1989)
[2] M. Horodecki, P. Horodecki and R. Horodecki, "Separability of mixed states: necessary and sufficient conditions", Phys. Lett. A 1, 223 (1996)
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[10] Recent tutorial reviews include M. B. Plenio and S. Virmani, “An introduction to entanglement measures”, Quant. Inf. Comp. 7, 1 (2007); R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement”, Rev. Mod. Phys. 81, 865 (2009)
Multi-party entanglement and applications
Research on multi-particle entanglement is on the one hand expected to be focused on novel protocols for quantum information processing in the multi-partite setting. Entanglement in quantum systems embodying more than two constituents is fundamentally different from two-party entanglement, allowing for novel applications. This work on novel protocols includes work on instances of secret sharing or multi-partite fingerprinting. Notably, such multi-partite fingerprinting schemes would allow for the determination whether a number of databases are identical with little resources.
For quantum computation purposes it seems a major milestone to develop computation schemes that require minimal local control over interactions, such as in novel measurement-based computation schemes using multi-particle entangled resources as in cluster-state based approaches or in linear optics quantum computation. Alternatively, quantum cellular-automata based approaches may offer the potential of implementing quantum computation with little requirements of local control. Research work towards a complete understanding of the classification and quantification of multi-particle entanglement is expected to support such work, notably using methods from convex and global optimization, which give rise to novel methods for classification and quantification of entanglement. Laboratory quantum states such as random states or graph states as generalizations of cluster states may facilitate such studies.
On the other hand, there are good reasons to believe that a refined picture of criticality and phase transitions can be reached with the help of tools coming from the theory of entanglement. These ideas help in devising new simulation methods of ground states of many-body Hamiltonians in solid state physics (and many-body quantum systems in general). Finally, studies seem to indicate that questions in quantum field theory may become significantly more accessible using methods from entanglement theory (see also section 4.3.10)
Key references
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Device independent certification of security in quantum information
Device independent quantum information processing represents a novel approach in which the goal is to design information protocols whose performance is independent of the internal working of the devices used in the implementation. The new framework exploits the non-local correlations exhibited by local measurements on entangled quantum particles, which certify the quantumness of the underlying state and measurements. That is the quantumness is certified by the violation of a Bell inequality.
This approach allows a qualitative increase of the security of quantum cryptography: QKD becomes secure even if the source of entangled states is not controlled and/or the measurement devices unknown. It also allows the generation and quantification of certified quantum randomness. The same basic philosophy can be applied to "self testing of quantum computers": by using quantum non locality one can test (in polynomial time) that a quantum computer indeed operates as it should, without the need to model how individual gates act, or the need to carry out the full tomography of the whole computer. Finally, these techniques may also find an application in estimation problems, as they allow estimating interesting quantum properties of an unknown system only from the observed measurement statistics.
From a theoretical point of view, the main goal is to understand the possibilities and limitations of this new approach. From a more practical point of view, a major theoretical and experimental challenge is to make these proposals practical. On the experimental side by realising long distance Bell inequality violation with the detection loophole closed. On the theoretical side by improving the existing protocols, or by relaxing some of the assumptions.
Key references
[1] D. Mayers and A. Yao, "Self testing quantum apparatus", Quantum Inform. Comput. 4, 273 (2004)
[2] J. Barrett, L. Hardy, and A. Kent, "No Signalling and Quantum Key Distribution", Phys. Rev. Lett. 95, 010503 (2005)
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Noisy communication channels
The proper understanding of the capacities of quantum communication channels is at the heart of the study of quantum communication tasks. Of particular importance are the transmission of classical or quantum information, or establishing secret keys. The general framework for distilling classical keys from quantum states have been also established, opening the possibility of secure communication on extremely noisy channels. But it is also known that one can use noise and perfect side communication to implement other cryptographic primitives like bit commitment and oblivious transfer. Channel capacities are of central interest in several different settings, being reflected notably by the classical capacity of quantum channels, quantum capacities, and entanglement-assisted capacities.
The central question is essentially what resources are required for transmitting classical or quantum information using quantum channels, such as optical fibers in a practical realization. A problem that was left open until recently was whether an increased capacity can be obtained by employing entangled signal states (multiple uses) as opposed to single uses of the channel. This problem is widely known as the additivity problem for the Holevo capacity or - as it turned out, equivalently, the additivity problem for the minimum output entropy. This problem could recently be solved in seminal work, in that it turned out that entangled inputs indeed do help. Similarly, it has been shown theoretically that two quantum channels, each with a quantum capacity of zero, can have a non-zero capacity when used together. The key problem of identifying the classical information capacity for Gaussian channels - in the context of the promising field of continuous-variable quantum information, with practical importance in quantum communication with fibers - is still open, despite recent progress. These findings open up new exciting questions about the role of entanglement in quantum communication. Also, the exact relationship between entanglement and the correlations useful for establishing secret keys is not yet entirely understood.
Finally, it is to be expected that more problems, as well as new perspectives, will arise when one considers multi-user channels, i.e. with more than one sender/receiver. While single-sender-receiver settings serve well to study bipartite correlations, such problems have an immediate impact on understanding multi-partite correlations and their role in quantum communication via noisy channels. Also, quantum analogues of certain basic classical network theory primitives have been identified, and the evidence for new non-classical features, such as negative partial information established. Further investigations will be needed to identify differences and similarities in the classical and quantum network theories.
Key references
[1] C. H. Bennett, G. Brassard, C. Crépeau, and M.-H. Skubiszewska, "Practical quantum oblivious transfer", Lecture Notes in Computer Science 576, 351 (1991)
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"Quantum proofs" for classical problems
A very exciting aspect of theoretical work in QIS is the impact that it is beginning to make on other fields of science. In the case of classical computing such insights include the first exponential bounds on certain locally decodable codes, classical proof systems for lattice problems, bounds on the query complexity of local search problems, an efficient classical cryptographic scheme whose security is based on quantum considerations, and a quantum method to compute how many Toffoli gates are required to realize a reversible classical computation. The potential that QIS is offering for classical computing and mathematics may be understood by the following analogy. Real analysis is a very successful discipline but it contained a number of unsolved problems that were only solved by considering complex numbers, i.e. going to a larger space in which to describe the problem. By analogy we expect that moving from classical state space into the much larger quantum mechanical state space we will find novel approaches towards the solution of problems that ostensibly lie entirely within the classical realm.
For instance, a 20-year old problem on the existence of no polynomial-size linear program whose associated polytope projects to the traveling salesman polytope was recently solved using techniques from one-way quantum communication protocols. In this sense, quantum information theory offers novel proof tools for "quantum proofs" for classical problems, hence quantum information theory having a significant impact outside quantum theory. Similarly, recent ideas from quantum state tomography developing a notion of quantum compressed sensing are now routinely used in classical compressed sensing and the theory of image processing.
The entanglement between two systems cannot be shared with many others, a principle called monogamy: this leads to a fruitful relationship between entanglement theory and classical cryptography, and in particular between entanglement distillation and the classical key agreement scenario. Since the two schemes shares similar objects, quantities and relations, it is expected that the parallel growth of these domains will lead to a deeper understanding of both of them. For instance, it has been conjectured the existence of a classical cryptographic analog of bound entanglement, named bound information. While its existence remains unproven for two parties, a proof has been obtained in a multipartite scenario.
Key references
[1] I. Kerenidis and R. de Wolf, "Exponential lower bound for 2-query locally decodable codes via a quantum argument", quant-ph/0208062
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[5] D. Gross, Y.-K. Liu, S. T. Flammia, S. Becker, and J. Eisert, "Quantum state tomography via compressed sensing", arXiv:0909.3304 [quant-ph]; D. Gross, "Recovering low-rank matrices from few coefficients in any basis", arXiv:0910.1879 [quant-ph]
[6] A. Drucker and R. de Wolf, "Quantum proofs for classical problems", arXiv:0910.3376 [quant-ph]
[7] S. Fiorini, S. Massar, S. Pokutta, H. R. Tiwary, and R. de Wolf, "Linear vs. semidefinite extended formulations: Exponential separation and strong lower bounds", Proc. 43rd ACM Symposium on Theory of Computing (STOC), 95 (2012)
Fundamental quantum mechanics and decoherence
Quantum information was born, in part, via research on the famous Einstein-Podolski-Rosen paradox and the issue of quantum non-locality. In turn, quantum information led the discussion to move beyond purely qualitative aspects of non-locality to defining and investigating quantitative aspects. In particular, it is now understood that non-locality is one of the central aspects of quantum mechanics. More generally, quantum information profits substantially from studying the fundamental aspects of quantum mechanics and, at the same time, yields new points of view, raising hopes of gaining a deeper understanding of the very basis of quantum mechanics.
The study of decoherence is intertwined with the field of quantum information science in at least three ways. Key challenges of the next years in the study of decoherence with methods, tools and intuition from quantum information science will include the following:
Apart from contributing to a better understanding of the classical-to-quantum transition, quantum information theory also provides new insights into the foundations of quantum physics. In fact, information concepts have been successfully applied to get a better understanding of which correlations are possible within our current description of nature, based on quantum physics and why quantum physics is not maximally non-local.
Key references
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[2] L. Viola, "On quantum control via encoded dynamical decoupling", quant-ph/0111167
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Quantum effects in opto-mechanical and nano-mechanical systems
Recently, partly driven by experimental progress, theoretical ideas have been proposed to cool mechanical physical systems such as massive micro-mirrors to close to their quantum ground state, giving rise to observable quantum effects. In particular, opto-mechanical systems, where mechanical degrees of freedom are coupled to coherent optical systems, allow for such a cooling by suitably exploiting radiation pressure effects. Such systems may give rise to ultra-sensitive force sensors as well as to primitives for quantum information devices. They can also be combined with other physical architectures to give rise to promising hybrid architectures and interfaces. Indeed, following a remarkably fast-paced development in cooling techniques using radiation pressure, largely driven by a European research effort, the laser cooling of a nano-mechanical oscillator into its quantum ground state has been achieved recently, opening up new perspectives for using such devices in QIPC applications.
Key references
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Quantum coherence in biological systems
The experimental observation of quantum coherence during excitation energy transfer and the subsequent elucidation of the role that noise and coherent dynamics plays in such systems represent a very intriguing recent development at the boundary of quantum physics and biology. An increasing number of biological systems are now being investigated for the possible functional role of quantum dynamics including for example magneto-reception in birds and olfaction. The question to what extent quantum dynamics plays a role in biological systems is now receiving increasing attention from the perspective of quantum information theory. Indeed, principles and techniques, numerical, analytical and conceptual, that have been developed over the last two decades in quantum information science may find a new area of application here and contribute to an understanding of the role of noise, coherent dynamics and their interplay in such systems. This potentially fruitful new arena is now beginning to be explored bringing together quantum information scientists with bio-physicists from theory and experiment thus opening up a new arena of interdisciplinary research.
Key references
[1] G. S. Engel, T. R. Calhoun, E. L. Read, T.-K. Ahn, T. Mancal, Y-C. Cheng, R. E. Blankenship, and G. R. Fleming, "Evidence for wavelike energy transfer through quantum coherence in photosynthetic complexes", Nature 446, 782 (2007)
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[9] “Quantum effects in biological systems”, Edited by M. Mohseni, Y. Omar, G. Engel, and M. B. Plenio, Cambridge University Press 2012
Complexity of simulating many-body systems
In recent years, a strong link between quantum information science and the study of condensed matter systems has been established, in particular to research on strongly correlated quantum systems, so systems that play a key role in the understanding of phenomena such as high-temperature superconductivity. This link is less surprising as it may at first seem: After all, quantum correlations are distributed and shared in an intricate manner in ground states of local quantum many-body systems. The quantitative theory of entanglement can provide new insights into the exact structure of such quantum correlations, in turn opening up new perspectives for the development of new algorithms for the simulation of such quantum many-body problems. Indeed, the significant findings in this field may be seen as a further justification for the importance of the study of entanglement.
Notably, ground states of local systems typically satisfy what is called an "area law", in that the entanglement of a subregion scales only with the surface area of that region. That is to say, they have very little entanglement, an assertion that can be made quantitative. Exploiting this observation, one arrives at the insight that only few effective degrees of freedom are being exploited by natural systems, compared to the exponentially larger Hilbert space. Suitably parameterizing this set by means of what is called tensor networks hence gives rise to new efficient simulation algorithms for the study of strongly correlated systems. Matrix-product states, projected entangled pair states, tree tensor networks or states from entanglement renormalization from a real-space renormalization ansatz are examples of such an approach. These are sets of states, described by polynomially many real parameters, for which one can still efficiently compute local expectation values by means of suitable tensor contractions, and which still grasp the essential physics of the problem.
In such a language, certain elementary obstacles of classical simulations of quantum systems such as in time evolution also become clear, and quantitative links to the theory of criticality and quantum phase transitions can be established. Ideas like Lieb-Robinson bounds, relating to the speed of information propagation in quantum lattice systems, provide key insights into the distribution of correlations in local quantum many body problems with respect to static of dynamical properties. Ideas of quantum information science can hence relate to
This demonstrates that the research into entanglement, its characterization, manipulation and quantification will not only continue to have impact within quantum information but is now reaching the stage where its insights are being applied to other areas of physics, with potentially enormous benefits, both intellectually but perhaps also commercially.
Key references
[1] K. Audenaert, J. Eisert, M. B. Plenio, and R. F. Werner, “Entanglement properties of the harmonic chain”, Phys. Rev. A 66, 042327 (2002)
[2] J. I. Latorre, E. Rico, and G. Vidal, "Ground state entanglement in quantum spin chains", Quant. Inf. Comp. 4, 048 (2004)
[3] M. B. Plenio, J. Eisert, J. Dreissig, and M. Cramer, "Entropy, entanglement, and area: Analytical results for harmonic lattice systems", Phys. Rev. Lett. 94, 060503 (2005)
[4] F. Verstraete and J. I. Cirac, "Renormalization algorithms for quantum many-body systems in two and higher dimensions", cond-mat/0407066
[5] J. Kempe, A. Kitaev, and O. Regev, "The complexity of the local Hamiltonian problem", SIAM Journal of Computing, Vol. 35, 1070 (2006)
[6] G. Vidal, "Entanglement renormalization", Phys. Rev. Lett. 99, 220405 (2007)
[7] L. Amico, R. Fazio, A. Osterloh, and V. Vedral, "Entanglement in many-body systems", Rev. Mod. Phys. 80, 517 (2008)
[8] F. Verstraete, J. I. Cirac, V. Murg, "Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems", Adv. Phys. 57, 143 (2008)
[9] J. Eisert, M. Cramer, M. B. Plenio, "Area laws for the entanglement entropy", Rev. Mod. Phys. 81 (2010)
Connection between QIP and quantum chemistry
Related to the previous field, quantum information theory can help in gaining an understanding the quantum correlations that are present in physical problems from quantum chemistry. Ideas of monogamy and entanglement distribution are related to the quantum representability problem, being of key importance in theoretical quantum chemistry. New ideas inspired by quantum information theory relate to proofs of hardness of certain questions in quantum chemistry, as well as to new simulation methods of such physical systems, contributing to the wider context of gaining a deeper understanding of complex quantum systems.
Key references
[1] A. Klyachko, "Quantum marginal problem and N-representability", J. Phys. A Conf. Ser. 36, 72 (2006)
[2] Y.-K. Liu, M. Christandl, and F. Verstraete, "N-representability is QMA-complete", Phys. Rev. Lett. 98, 110503 (2007)
As shown in the examples above, quantum information science is a broad interdisciplinary effort whose key aim is to provide a theoretical basis for the control and exploitation of nature at the level of individual quanta. European research has played a leading role in its development and has established a strong set of world leading centers. The field is thriving and strongly expanding both by continuing enhancement of efforts in existing sub-areas but also through the innovation of new research directions.
A key area is the development of new approaches towards the realization of quantum information processing, both at the device dependent and independent level, as well as the concrete exploration of existing experiments that aim towards the practical implementation of quantum information processing. European researchers have made pioneering contributions to this area both on the theoretical level and, often in close collaboration, also experimentally. Major centers exist in various European countries (see below). These centers form the cores of a number of EU networks providing a level of interconnection on the European level.
Quantum information science has emerged from groundbreaking purely theoretical work and its major breakthroughs so far have generally been theory driven. This abstract work addresses entanglement theory, quantum algorithms, quantum communication and the applications of QIS to other fields such as condensed matter physics, field theory and the solution of problems in classical information theory by quantum methods. Researchers involve physicists, mathematicians, computer scientists and engineers demonstrating its strongly interdisciplinary character. Europe has made groundbreaking contributions to this area that has led the development of the field as a whole. It should be noted that the research landscape in these theoretical areas is still fluid and novel directions continue to emerge. A particular growth area is the application of the ideas emerging in QIS to other areas of physics, mathematics and computer science, often providing entirely new problem solving techniques to existing areas. Intuitively this is due to the ability to access the full quantum mechanical state space rather than the much smaller classical state space which permits novel techniques to attack previously unsolved problems. Many new insights can be expected from this approach that will drive science forward in many areas.
Major centers exist in Austria, Belgium, Denmark, France, Germany, Netherlands, Poland, Spain, UK, and Switzerland. They have been linked through various EU project as well as through a European Science Foundation program on QIS addressing the need for this type of research for strong interconnections, the ability for informal collaborative visits to facilitate exchange of ideas. This is of particular importance in those aspects of theoretical research that are strongly interdisciplinary and where no single country possesses a critical mass of research.
Theoretical research in QIS in Europe has prospered through the efficient support for collaboration by the European Union, the European Science Foundation and the national funding bodies. In the face of growing international competition from North America, Japan and Australia it will be essential that flexible support compatible with innovative work will continue to be provided.
Even if the main thrust of the ongoing investigations in QIPC still belongs to basic research, one can already identify some of its areas that are closer to potential applications and even ready for commercial exploitation (a (in)complete list of industries that are interested in QIPC can be browsed at the QUROPE industry database [7]).
In particular:
A fresh look at QIPC from the broadest possible perspective also allows the identification of technologies that have gone past the proof-of-principle phase and are approaching the real world deployment stage. These Quantum Information Technologies (QITs) which are designed to control and manipulate single or entangled quantum systems for (quantum) information processing and communication, can be split into two main categories, being
In what follows we detail the most promising technologies belonging to the first category, and the most needed ones as far as the second category is concerned.
Quantum Random Number Generators (QRNG)
Our information based society consumes lots of random numbers for a wide range of applications like, e.g., cryptography, PIN numbers, lotteries, numerical simulations, etc. The production of random numbers at high rates is technically challenging; at the same time, given the pervasiveness of the deployment of random numbers, poor random number generators can be economically very damaging. Today, there are three kinds of random number generators on the market: computer-based pseudo-random number generators, discretised thermal noise and quantum based. The first kind produces sequences of numbers that look random, but are in fact the result of a deterministic process. The second kind is based on the complexity of thermal noise; however thermal relaxation times make these random number generators relatively slow, in the range of tens of Kbit/second. On the other hand, quantum physics provides the only truly source of randomness in Nature. Moreover, in the basic configuration (a photon impinging on a beam splitter followed by two detectors associated to the bit values 0 and 1) the origin of the randomness is clearly identified. Today's commercial quantum random number generators produce about 4 Mbit/second. Their drawback is a significant cost compared to thermal noise based devices, but one expects that (near) future QRNG will provide higher rates at lower costs.
Quantum Metrology
Quantum entanglement provides instances of quantum states of objects that can be designed to be very robust to unwanted noise, while at the same time being extremely sensitive to a quantity we need to measure. This sensitivity can be exploited to overcome the classical limits of accuracy in various kinds of measurements, for example in ultra-high-precision spectroscopy, or in procedures such as positioning systems, ranging and clock synchronisation via the use of frequency-entangled pulses. For instance, in the latter case, picosecond resolution at 3 km distance has been attained. Large scale laser interferometers with kilometre arm lengths are currently being built or started operating in Europe, the USA and Japan with the hope to achieve the first direct detection ever of gravitational waves and thus to open a new field of astronomy. For these detectors the classical sensitivity limit is a serious restriction. It is likely that for the first detection one will have to implement continuous variable entangled light beams in the two interferometer arms to overcome the classical limits. A collaboration of scientists from Europe, USA and Australia (LIGO Scientific Cluster) has recently reported 3dB quantum noise reduction in the sensitivity of the German GEO 600 gravitational wave detector through injection of squeezed laser light at kilohertz frequencies.
State-of-the-art atom clocks have reached the level of accuracy limited by quantum noise of atoms. Entanglement of atoms in clocks may allow surpassing this limit by generation of spin squeezed states of atoms. Work towards this goal is going on in Europe and in the US.
Single quantum particles can be used as nanoscopic probes of external fields. Along these lines, atomic-scale (up to few nanometers) resolution in the measurement of the spatial structure of an optical field via a single ion, as well as sub-shot-noise atomic magnetometry via spin squeezing and real-time feedback have been already experimentally demonstrated. Solid state implementations of quantum sensors exploit the quantum features of artificial atoms such as defect color centers, most prominently nitrogen vacancies in diamond. They are now being used as ultrasensitive probes for magnetic and electric fields, with enhanced resolution through quantum control techniques. While electron spin resonance in diamond NV centers was known for a long time, it took the understanding of interaction between a spin with a many-body spin bath, i.e. quantum many body physics, to develop such exquisite magnetic field sensors that surpass existing sensing capabilities by many orders of magnitude. It allows performing NMR on a single nuclear spin, and it is expected to yield to single molecule NMR at ambient condition. The quantum properties of these single spins within fluorescent particles are now also being used to study in-situ dynamical probes of biological environments, for example by optically detecting magnetic resonance of individual fluorescent nanodiamonds that are distinguished through their individual Rabi frequency inside living cells. Such single-spin probes in biological systems may open up a host of new possibilities for quantum-based imaging in the life sciences.
The quantum regime is being explored and applied also in the manipulation of nanomechanical devices like rods and cantilevers of nanometer size, currently under investigation as sensors for the detection of extremely small forces and displacements. Several groups in both Europe and the US have now achieved the preparation of nano- and micromechanical systems in their motional quantum ground states and measurement sensitivities beyond the standard quantum limit through squeezed motional states are within reach.
One of the main steps in the development of quantum correlation and quantum entanglement tools was a practical design of ultra-bright sources of correlated photons and development of novel principles of entangled states engineering. This also includes entangled states of higher dimensionality and entangled quantum states demonstrating simultaneous entanglement in several pairs of quantum variables (hyper-entanglement), and calibration of single-photon detectors without any need for using traditional blackbody radiation sources. This unique possibility of self-referencing present in the optical system that is distributed in space-time is the main advantage of quantum correlation and entanglement. The fact that spontaneous parametric down-conversion (SPDC) is initiated by vacuum fluctuations serves as a universal and independent reference for measuring the optical radiation brightness (radiance). It gives the possibility of accurately measuring the infrared radiation brightness without the need of using very noisy and low sensitivity infrared detectors. Development of periodically poled nonlinear structures has opened the road for practical implementation of sources with high intensity of entangled-photon flux and with ultra-high spectral bandwidth for biomedical coherence imaging. Recent demonstrations have shown the possibilities for multi-photon interferometry beyond the classical limit. It has been shown that weak field homodyning could yield enhanced resolution in phase detection. First experimental implementations of quantum ellipsometry indicated the high potential of quantum polarisation measurement. The basic physical principles of optical coherence tomography with dispersion cancellation using frequency entangled photon pairs for sub-micron biomedical imaging have been demonstrated in model environments. The use of quantum correlations led to the design of a new technique for characterizing chromatic dispersion in fibers. The intrinsically quantum interplay between the polarisation and frequency entanglement in CSPDC gave rise to a polarisation mode dispersion measurement technique that provides an order of magnitude enhancement in the resolution.
Quantum Imaging
It is possible to generate quantum entanglement between the spatial degrees of freedom of light, an aspect which enables one to use quantum effects to record, process and store information in the different points of an optical image, and not only on the total intensity of light. One can then take advantage of a characteristic feature of optical imaging, which is its intrinsic parallelism. This opens the way to an ambitious goal, with a probable significant impact in a mid-term and far future: that of massively parallel quantum computing. In a shorter perspective, quantum techniques can be used to improve the sensitivity of measurements performed in images and to increase the optical resolution beyond the wavelength limit, not only at the single photon counting level, but also with macroscopic beams of light. This can be used in many applications where light is used as a tool to convey information in very delicate physical measurements, such as ultra-weak absorption spectroscopy, Atomic Force Microscopy etc. Detecting details in images smaller than the wavelength has obvious applications in the fields of microscopy, pattern recognition and segmentation in images, and optical data storage, where it is now envisioned to store bits on areas much smaller than the square of the wavelength. Furthermore, spatial entanglement leads to completely novel and fascinating effects, such as "ghost imaging", in which the camera is illuminated by light which did not interact with the object to image, or "quantum microlithography", where the quantum entanglement is able to affect matter at a scale smaller than the wavelength.
Key references
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Quantum Interfaces
Quantum interfaces between quantum information carriers (quantum states of light) and quantum information storage and processors (atoms, ions, solid state) are required as essential parts of a full-scale quantum information system. Such interfaces should thus be developed for connecting quantum computers in small networks, or more generally for quantum communication purposes. Let us first contrast the quantum technology required here to its classical counterpart. In classical optical communication, information is transferred encoded in pulses of light, which are possibly amplified, and then detected by photo detectors, transformed into electrical current pulses, amplified by electronics, and sent to computers, phones, etc. This transformation of light into electrical signals forms a classical light-matter interface. But in quantum information processing, classical amplification or detection of light is inadequate, because it destroys the quantum state by adding extra noise to it. Hence a quantum interface has to be developed, in order to transfer the quantum state of propagating qubits (or propagating continuous variables), e.g. photons, to or from stationary qubits (or stationary continuous variables), e.g. atoms. Quantum interfaces usually involve storage elements (quantum memories), and processing elements (deterministic or conditional quantum gates). They often involve also long-distance quantum teleportation of long lived states of stationary systems, which allow for communication and quantum secret sharing tasks. Such long lived entanglement shared over a long distance requires transfer of entanglement from a long distance carrier, e.g. light, to long lived objects, e.g. atoms, realized by the quantum interface. Many different quantum technologies can be used to implement the interfaces, e.g. atomic ensembles, cavity QED, solid state devices, etc.
Researchers from Europe have recently implemented an elementary quantum network consisting of two atom-cavity systems connected through a 60 m optical fibre link, and demonstrating both faithful quantum state transfer and entanglement generation between the stationary atoms of the two nodes. Entangling stationary qubits over large distances through optical links has by now also been realized in several other physical systems. These realizations include the entanglement of ions in spatially separated ion traps over 1 m, the entanglement of neutral atoms over separations up to 20 m, and the entanglement of electronic spins, nuclear spins and optical phonons, respectively, each located in distant solid state samples.
Heralded single-photon and entangled photon-pair sources
Point to point earth based quantum communication is limited in distance by the losses of optical fibers. For long distance quantum communication ($>$500km) protocols with quantum repeaters are needed. Such schemes require, among other things, high quality sources of pairs of entangled photon, either on demand or heralded. Today's sources are probabilistic, based on spontaneous parametric down conversion. Future sources should keep or improve on the optical quality of the existing ones (compatible with single-mode optical fibers, Fourier-transform limited, and coherence length of several centimetres), provide larger rates and yields (probability of a photon pair) while reducing the probability of multi-pairs. The exact type of entanglement is not essential, but should involve two photons, one in each of two quantum channels (i.e. the entanglement obtained by bunching two single photons on a beam splitter is not appropriate). At least one of the photons should be at the telecom wavelength around 1.55 microns. Depending on the protocol, the second photon can be around the same wavelength or at a shorter one, below one micron (but one should bear in mind that future progress in quantum communication protocols may affect the required specifications). Efficient coherent upconversion of single photons has recently been demonstrated, which may relax the requirement for source specifications, as photons can be converted to the wanted wavelength.
Another promising outlook for long-distance quantum communication is to use satellite based platforms, which would allow the distribution of either single-photon qubits or of entanglement through space-born photon sources, hence allowing quantum communication on a global scale. Space-qualified sources for single photons and for entangled photons are now becoming available and first proof-of-concept tests are being prepared all over the world, including in Europe, Canada, Japan, Singapore and China. Heralded single-photon sources are also of relevance for ground based quantum communication, as the absence of multi-photon events allows for genuine security of quantum information through the no-cloning theorem, and for photonic quantum information processing, where they allow for the implementation of generalized (POVM) measurements.
Significant progress has been also made in solid-state based single-photon and entangled photon sources, including emission from semiconductor quantum dots and nitrogen vacancies in spin.
On-chip architectures for quantum computing and quantum simulation
The DiVincenzo criteria for quantum computing are currently approached from different directions. Also, in the current efforts to establish few-qubit quantum simulators, a set of less stringent requirements for quantum simulations has been suggested (by Cirac and Zoller).
To date, ion traps offer the possibility to precisely manipulate and read out single qubits and to perform entangling gate operations, while the size of the system is currently limited to a few qubits. In contrast, with neutral atoms large ensembles of entangled qubits have been created while the manipulation of single atoms and their detection present a major challenge. Both these approaches - bottom up for ions and top down for atoms - need to be further developed to take quantum computation the next scale. Chip technology for trapping ions or neutral atoms will play a major role in this development. For neutral atoms, chip traps offer precise positioning that enables controlled interactions and detection of single atom states. The first on-chip implementation of a high-finesse fibre resonator has very recently been demonstrated, offering at the same time a tool for manipulation, entanglement and detection of ions. Also, single-site addressing of atoms inside an optical lattice has now been realized. These technologies may be used in the future to establish an interface between stationary (atoms) and flying qubits (photons). For ions, the chip traps serve to increase the number of qubits that can be handled. The segmentation of trap electrodes in microscopic traps allows for a multitude of miniature ion traps on one chip. Future developments have to meet two major challenges: finding a trap technology that features small heating rates and long coherence times, and a trap design that allows for transport of the ions (along with their contained quantum information) between all miniature traps on the chip. An integration of optical cavities as demonstrated for neutral atoms would be desirable, too.
Other on-chip implementations are also being pursued: in the context of photonic quantum simulations, integrated wave guides have recently enabled the first realization of efficient boson sampling, a task that can in principle not be efficiently computed on a classical computer. In the long run, the embedding of integrated waveguides in fiber networks may allow for securely delegated quantum computations. The main limitation for photonic waveguide technology to date is the overall optical loss that is acquired from photon generation, from optical coupling into and out of the wave guide and from (inefficient) photon detection. However, the latest advances in source- and detector technology in principle allow designing all relevant components (source, quantum gates, detectors) on one chip, thereby minimizing these losses. Optical microcavities and nano- and micro-optomechanical devices provide additional flexibility for photonic on-chip architectures in form of narrow linewidths, delay lines, optical nonlinearities or phononic quantum transducers.
Quantum processor architectures based on superconducting quantum circuits have recently been developed by researchers both in Europe and in the US. Today, these devices have already been used successfully to demonstrate, for example, logic gates like the three-qubit Toffoli-class OR phase gate, a combination of a quantum central processing unit (quCPU) and a quantum random-access memory (quRAM) which comprise two key elements of the quantum version of a classical von Neumann architecture. Also a three-qubit compiled version of Shor's algorithm to factor the number 15 and three-qubit quantum error correction has been implemented. Increasingly long coherence times (approaching the second regime) are now being reached through novel architectures. The next major challenge in the field is to improve the fidelity of the quantum logic operations and to interface the microwave domain to the optical domain, possibly through hybrid opto-electro-mechanical architectures.
Solid state quantum registers are now being implemented through nitrogen vacancy centers in diamond, as they allow for a simple optical interface and long-lived electronic spin qubit storage, whose lifetimes could even be improved additionally by dynamic decoupling techniques. Entanglement between pairs of NV centers have been created, both probabilistically over 3 meters distance using photons as a quantum channel and deterministically between neighboring centers via microwave fields acting on both NV centers operating even in a room temperature environment. With respect to quantum information processing a Grover algorithm between two spins has successfully been implemented. In order to bring these promising developments to the stage of real life technologies, further improvements are required with respect to fabrication techniques to place NV centers with high spatial control, to improvements on the collection efficiencies for light and to quantum gate operations and qubit storage for quantum registers.
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QIPC relies on the manipulation and control of ensembles of qubits behaving according to the laws of quantum physics. From the perspective of classical macroscopic physics, and indeed for the normal world-view not trained on quantum phenomena, these laws are counter-intuitive. In this sense QIPC aims to turn paradoxes into products. On the other hand, macroscopic physics is itself ultimately based on the quantum laws. This raises the question why the paradoxical traits of quantum mechanics do not manifest themselves in everyday experience, i.e., how the classicality of the world emerges from quantum mechanics. Roughly, the answer is that the quantum paradoxes all require the superposition principle, i.e., coherence, and that in complex systems coherence is shifted to less and less accessible degrees of freedom and thus effectively lost. This process, known as "decoherence" is thus a crucial element for the formation of the world as we know it. Seen form the other side, i.e., a QIPC application, decoherence is the universal enemy, ever trying to wash out the hard won coherence. In either case decoherence marks the boundary between quantum and classical phenomena.
The quantum-classical boundary which is set by decoherence has a very rich structure. It is certainly not merely a question of system size, since suitable collective degrees of freedom of some large systems can exhibit remarkable coherence in some collective degrees of freedom. Many clever ways of extending the quantum side for QIPC have been designed. Clearly, a sufficient isolation from the environment at large is required. Some methods rely on the observation and manipulation of the environment itself, combined with feedback procedures counteracting the effects of decoherence on the system under study. Other methods, borrowing from the error correction schemes of classical computers, are at least in principle even more powerful. They are based on the redundant coding of the information in an ensemble of entangled qubits, monitoring the effects of decoherence on a subset of these qubits and applying correction procedures on others to restore the initial quantum state affected by decoherence. The progress towards the implementation of these methods, a prerequisite for large scale quantum computing to ever become feasible, is discussed in other parts of this report.
Here, we focus on other aspects of this field of research. The first concerns a change in physical world-view, which is stimulated by QIPC research, and is spreading to the physics community and, possibly, to the society as a whole. In the discussions of the founding fathers of quantum theory, the quantum-classical boundary was explored in thought experiments, often with paradoxical conclusions. Many QIPC experiments with atoms and photons can be viewed as modern realizations of these thought experiments. This stimulates a much more concrete view of the old paradoxes, both theoretically, through establishing new ways to model quantum phenomena and the discovery of new principles, and experimentally through a fantastically increased control of fully coherent processes. This body of knowledge is now making its way into the teaching of quantum physics at universities. The formation of an reliable intuition for the quantum world is certainly an important ingredient in the education of students in physics and the study of QIPC is an excellent way to acquire this intuition. The students attracted by the aesthetical qualities of this physics will be the researchers of tomorrow, who will apply their skills to QIPC or to other fields.
Secondly, and perhaps more fundamentally, these experiments also raise some issues at the forefront of physics. In QIPC, physicists learn to build systems of increasing size in quantum superposition, the Schrödinger cat states. This research is still in its infancy and many important issues remain to be explored, some of which are listed here:
Links:
[1] tel:10 033038
[2] http://qist.lanl.gov
[3] http://qurope.eu/content/413-quantum-memories-and-interfaces
[4] http://qurope.eu/content/414-towards-high-rates
[5] http://qurope.eu/content/415-towards-long-distances-quantum-repeaters
[6] http://qt.tn.tudelft.nl/~lieven/qip2007/QIP3_divincenzo_criteria.pdf
[7] http://qurope.eu/db/industries
[8] http://qurope.eu/content/id-quantique-sa
[9] http://qurope.eu/content/magiq-technologies-inc
[10] http://qurope.eu/content/smart-quantum