From Three-Photon Greenberger-Horne-Zeilinger States to Ballistic Universal Quantum Computation

Abstract

Single photons, manipulated using integrated linear optics, constitute a promising platform for universal quantum computation. A series of increasingly efficient proposals have shown linear-optical quantum computing to be formally scalable. However, existing schemes typically require extensive adaptive switching, which is experimentally challenging and noisy, thousands of photon sources per renormalized qubit, and/or large quantum memories for repeat-until-success strategies. Our work overcomes all these problems. We present a scheme to construct a cluster state universal for quantum computation, which uses no adaptive switching, no large memories, and which is at least an order of magnitude more resource-efficient than previous passive schemes. Unlike previous proposals, it is constructed entirely from loss-detecting gates and offers a robustness to photon loss. Even without the use of an active loss-tolerant encoding, our scheme naturally tolerates a total loss rate ∼ 1.6% in the photons detected in the gates. This scheme uses only 3-GHZ states as a resource, together with a passive linear-optical network. We fully describe and model the iterative process of cluster generation, including photon loss and gate failure. This demonstrates that building a linear optical quantum computer need be less challenging than previously thought.In 2001, Knill, Laflamme and Milburn [1] showed that scalable quantum computation was possible using only linear optical elements -without the need for deterministic two-photon interactions. However, their proposal was more a proof of principle than a feasible construction as the scheme required tens of thousands of optical elements to acquire gates with a high probability of success. Since then, several proposals have developed the idea of a linear optical quantum computer (LOQC), including Nielsen's proposal [2] of combining linear optics with cluster states, Browne and Rudolph's fusion mechanisms [5] to efficiently create optical cluster states and Kieling's et al proposal [4] of building an imperfect cluster that can be renormalized using ideas of percolation theory. While alternative schemes for LOQC [5] using parity state encoding [6] or small amplitude coherent states [7] have been proposed, we do not address these approaches in this manuscript.Recent demonstrations [8][9][10][11][12] have made significant progress towards experimental linear-optical quantum computing. In particular, the use of integrated photonics to implement large-scale, complex interferometers on a chip shows great promise. However, active feed-forward remains challenging, it requires fast switching which is a dominant source of photon loss and has not yet been experimentally demonstrated in an integrated device.Of previous approaches to linear optical quantum computing, only Kieling et al's proposal [4] is ballistic -meaning that active switching is not required for the process of cluster state generation. It is thus the most suitable previous approach to LOQC in an integrated setting. It has a number o...

Resource Costs for Fault-Tolerant Linear Optical Quantum Computing

“…Without qubit loss, 3D cluster states tolerate phase errors with a rate up to 3% on each qubit; conversely, without computational errors, they tolerate up to 24.9% qubit losses [25]; and with both computational errors and qubit loss, the threshold of errors decreases approximately linearly with the loss rate. Thus, cluster states are particularly well suited to LOQC, as they can be efficiently prepared with linear optics: There is no fundamental difficultly caused by a high rate of entanglement failure during the creation of the cluster state, provided that once it is created it surpasses these thresholds [6,7,26,27].…”

Large-scale quantum photonic circuits in silicon

“…Recent studies on resource requirements of scalable linear optics quantum computing [27] and all-optical quantum repeaters [108] suggest that these systems will require a large number of photonic elements. While new protocols for the efficient generation of cluster states based on percolation theory [18,109,110] may reduce these resource requirements and the number of feed-forward elements, large unitary transformations on many optical modes will still be necessary. Even in boson sampling, recent predictions indicate a crossover to the postclassical computing regime for between n = 20 and 30 photons populating m n modes [24][25][26].…”

“…Additional scaling of these systems may require low-loss coupling to large numbers of waveguides and the integration of many high-efficiency single photon detectors. Experimental demonstrations of large unitary evolution circuits [33,48], chip-to-chip quantum state transfer [38,49], fast all-optical switching [111], and the integration of many SNSPDs on a single silicon chip [44], along with recent theoretical proposals for more resource-efficient linear optical quantum computing [18,110], may soon enable the demonstration of large-scale linear quantum optics circuits that are hard to simulate on classical computers.…”

“…This result motivated more efficient theoretical proposals [12][13][14][15] for linear optical quantum computing and related linear optics experiments [16,17]. Large entangled states may be produced without the demanding feed-forward operations using the percolation approach [18], though feed-forward is still necessary in the subsequent cluster state quantum computation [19]. As Boson Sampling [20,21] does not feed-forward or error correction, it promises a near-term win of a quantum system over classical machines [22], but still requires hundreds of spatial modes [23][24][25][26].…”

Limitations of two-level emitters as nonlinearities in two-photon controlled-phase gates

“…Key requirements for the successful implementation of photonic quantum computing architectures are (i) efficient sources of single indistinguishable photons, and (ii) a method to coherently interact two such photons [1][2][3][4][5][6][7]. Since these requirements were first stated, single-photon sources have steadily improved [7][8][9][10], with the most promising platforms based on few-level emitters, most notably semiconductor quantum dots [11][12][13] which now boast near-unity indistinguishability with (source to first objective) efficiencies above 70%.…”