QUIE2T Quantum Information Entanglement-Enabled Technologies

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:

• The generation of entangled states of up to 6 photons [3] and 10 qubits [4] by utilizing more degrees of freedom per qubit;
• Cavity-enhanced source of multi-photon states (see, e.g., [5]);
• The heralded generation of entangled states [6];
• The fast feed-forward technology [7];
• The use of generalized measurements to optimally use finite computational resources [8];
• The demonstration of quantum gates on states that are available “for free” in physical systems via ground-state cooling [9].

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].

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:

• High-efficiency photon detectors based on superconducting materials. In particular, this is a prerequisite for high-fidelity multi-qubit measurements (for the KLM scheme) and the reliable preparation of multi-qubit states (for both the KLM and the cluster state scheme);
• Certifying the fidelity of quantum processes and states. The complexity of tomographically reconstructing a quantum state increases exponentially with the size of the system. Novel methods aim at reducing the number of measurements necessary for the characterization of resource states for quantum information processing;
• Development of single-photon and/or entangled-photon sources is required for OQC. Currently, photon sources combining high-rate and high-quality generation of timed single photons or entanglement are under intense research. In the meantime, bright, albeit non-deterministic sources of correlated photons or entangled-photon pairs are critical to allow for the development and evaluation of circuit technology. Ultra-bright and compact sources have been developed, in particular, using periodically-poled nonlinear waveguides.

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). 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:

• Error models for KLM-style OQC have found that error thresholds for gates in order to achieve fault tolerance are above 1.78%. While this has been achieved for small cluster states [8], it remains a challenge for more complex systems;
• To further reduce the resources required for OQC and to find the limiting bounds on the required resources;
• To achieve massive parallelism of qubit processing by investing in source and detector technologies. Specifically, the development of high-flux sources of single photons and of entangled photons as well as photon-number resolving detectors will be of great benefit to achieve this goal;
• To generate high-fidelity, large multi-photon (or, more generally, many-particle) entangled states. This will be of crucial importance for cluster state quantum computing;
• To find more efficient ways to characterize the quality of states generated for use in various quantum information-processing protocols;
• The integration of the generation, manipulation and detection of photons on integrated circuits is a prerequisite for the implementation of scalable OQC architectures. Recent work has shown tremendous progress towards that goal (see, e.g., [13]).

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).