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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, 4.1.4, 4.1.5 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.
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).