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Zhongguo kexue. Wulixue Lixue Tianwenxue

Efficient realization of loss-tolerant optical quantum computation

Qing Lin

Published Oct 1, 2011• 1 citation
Publisher

Abstract

Based on two element operations, called controlled-path gate and entangler, the non-destructive multi-photon parity check could be deterministically realized. With these operations, the realization of loss-tolerant optical quantum computation, including the generation of parity states, the realization of single-particle operation and two-particle CNOT operation, could be very simple but deterministic and highly efficient. Moreover, the character of detected free of single photons in the computation, except of the parity-check, will make the requirement of single-photon resources much relax. Compared with the former linear optical schemes, this scheme with cross-phase modulation is simpler but deterministic, and more efficient but with less resource, which will make it more feasible and suitable for large-scale quantum computation.

DOI
10.1360/132011-479

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Based on two element operations, called controlled-path gate and entangler, the non-destructive multi-photon parity check could be deterministically realized. With these operations, the realization of loss-tolerant optical quantum computation, including the generation of parity states, the realization of single-particle operation and two-particle CNOT operation, could be very simple but deterministic and highly efficient. Moreover, the character of detected free of single photons in the computation, except of the parity-check, will make the requirement of single-photon resources much relax. Compared with the former linear optical schemes, this scheme with cross-phase modulation is simpler but deterministic, and more efficient but with less resource, which will make it more feasible and suitable for large-scale quantum computation.
A heavy focus for optical quantum computing is the introduction of error correction, and the minimization of resource requirements. We detail a complete encoding and manipulation scheme designed for circuit-model linear optics quantum computing, incorporating scalable operations and loss-tolerant architecture. We also calculate loss thresholds for the gate systems described, with an efficiency of 8383%83 required for the single-qubit operations, and 9090%90 for the two-qubit controlled-NOT gate.
How to implement multi-qubit gates is an important problem in quantum information processing. Based on cross phase modulation, we present an approach to realizing a family of multi-qubit gates that deterministically operate on single photons as the qubits. A general n-qubit unitary operation is a typical example of these gates. The approach greatly relax the requirement on the resources, such as the ancilla photons and coherent beams, as well as the number of operations on the qubits. The improvement in this framework may facilitate large scale quantum information processing.
Quantum computing is an exciting field that promises great improvements to our ability to solve certain intractable classes of problem. Implementing a quantum computer will require a physical system in which quantum effects are strongly evident. Many different physical systems have been proposed for this task, including ion traps, quantum dots, neutral atoms and photons. This thesis focuses on optical implementations of a quantum computer, and specifically on single-photon designs, as opposed to those utilising coherent states. Photonic systems have shown a great deal of promise for quantum computing tasks since it was shown by Knill, Laflamme and Milburn (KLM) that scalable efficient quantum computing could be performed using only linear optical elements and measurement. This was made viable through the use of error-correcting codes. The work in this thesis covers the use of error-correcting codes in single-photon linear optics quantum computing (LOQC). The central feature of these schemes is the parity code introduced by KLM and used to overcome the gate errors that are inherent in this type of LOQC. First is a discussion of an improved scheme that incorporates the fusion gates used in Browne and Rudolph's cluster state proposal in order to simplify the encoding and gate procedures. This results in high-probability gates with a resource usage comparable to the cluster state schemes. The remainder of the thesis examines the application of further error correcting codes to handle other errors that may arise in any practical implementation of an optical quantum computer. The most significant type of error in any optical system is photon loss, and hence an extension of the parity code is presented that allows loss errors to be detected and corrected. Procedures for performing universal quantum computation whilst employing this encoding are also described. These enable the establishment of loss thresholds for parity-state based LOQC, revealing this code is capable of handling up to 10\% loss in all elements during general computation, or 17\% if it is used solely as an active memory. Although loss is the most common type of optical error, other types of error will also become an issue when attempting to produce large quantum computing systems. An analysis of the error thresholds and resource usage which can be expected when applying a general error correcting code such as the Steane code to this type of LOQC system is also presented. The error thresholds and resource requirements established are greater than those found for cat state optical quantum computing, but fall below those calculated for cluster states. However, the resource requirements of the scheme are significantly smaller than the cluster state requirements for an equivalent circuit. Finally, a new experiment is proposed, achievable with today's technology, for testing the loss-tolerant encoding described earlier. Expansions of the experiment that would demonstrate tolerance of actual experimental error are also discussed.
In 2001, all-optical quantum computing became feasible with the discovery that scalable quantum computing is possible using only single-photon sources, linear optical elements, and single-photon detectors. Although it was in principle scalable, the massive resource overhead made the scheme practically daunting. However, several simplifications were followed by proof-of-principle demonstrations, and recent approaches based on cluster states or error encoding have dramatically reduced this worrying resource overhead, making an all-optical architecture a serious contender for the ultimate goal of a large-scale quantum computer. Key challenges will be the realization of high-efficiency sources of indistinguishable single photons, low-loss, scalable optical circuits, high-efficiency single-photon detectors, and low-loss interfacing of these components.
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By employing displacement operations, single-photon subtractions, and weak cross-Kerr nonlinearity, we propose an alternative way of implementing several universal quantum logical gates for all-optical hybrid qubits encoded in both single-photon polarization state and coherent state. Since these schemes can be straightforwardly implemented only using local operations without teleportation procedure, therefore, less physical resources and simpler operations are required than the existing schemes. With the help of displacement operations, a large phase shift of the coherent state can be obtained via currently available tiny cross-Kerr nonlinearity. Thus, all of these schemes are nearly deterministic and feasible under current technology conditions, which makes them suitable for large-scale quantum computing.