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Frontiers in Optics

Scalable Generation of Graph-State Entanglement through Realistic Linear Optics

Timothy P. Bodiya, Luming Duan

Published Jan 1, 2006• 3 citations
Publisher

Abstract

Linear optics, combined with practical photon source and single-photon detectors, has provided a powerful tool to test a number of quantum information protocols. In the linear optics implementations, the post-selection technique based on photon detections typically plays a critical role. As one scales up the system, the post-selection technique generally leads to very inefficient (exponential) scaling of the overall efficiency, which limits the implementation to small systems. In the past few years, two approaches have been proposed to circumvent this obstacle for different kinds of quantum information processing. In the first approach, a remarkable proposal, generally referred to as linear optics quantum computation, was first put forward by Knill, Laflamme, and Mil-burn (KLM) [1] and then improved by a number of others. In this approach, one overcomes the scaling problem for linear optics computation through quantum error correction by requiring the efficiencies for the photon source and the detectors to attain a high threshold value [1]. The threshold efficiency has been improved considerably in the past few years, with the most recent estimate about Linear optics, combined with practical photon source and single-photon detectors, has provided a powerful tool to test a number of quantum information protocols. In the linear optics implementations, the post-selection technique based on photon detections typically plays a critical role. As one scales up the system, the post-selection technique generally leads to very inefficient (exponential) scaling of the overall efficiency, which limits the implementation to small systems. In the past few years, two approaches have been proposed to circumvent this obstacle for different kinds of quantum information processing. In the first approach, a remarkable proposal, generally referred to as linear optics quantum computation, was first put forward by Knill, Laflamme, and Mil-burn (KLM) [1] and then improved by a number of others. In this approach, one overcomes the scaling problem for linear optics computation through quantum error correction by requiring the efficiencies for the photon source and the detectors to attain a high threshold value [1]. The threshold efficiency has been improved considerably in the past few years, with the most recent estimate about 99.4%− 99.7% [2]. In the second approach proposed in Ref. [3], one uses linear optics for implementation of scalable quantum communication through the quantum repeater protocol. This approach overcomes the inefficient scaling through the divide-and-conquer method. In this protocol, one does not have a threshold requirement on the source and the detector efficiencies, which allows its implementation with the state-of-the-art photon detectors.

DOI
10.1364/ls.2006.lwa1

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Linear optics, combined with practical photon source and single-photon detectors, has provided a powerful tool to test a number of quantum information protocols. In the linear optics implementations, the post-selection technique based on photon detections typically plays a critical role. As one scales up the system, the post-selection technique generally leads to very inefficient (exponential) scaling of the overall efficiency, which limits the implementation to small systems. In the past few years, two approaches have been proposed to circumvent this obstacle for different kinds of quantum information processing. In the first approach, a remarkable proposal, generally referred to as linear optics quantum computation, was first put forward by Knill, Laflamme, and Mil-burn (KLM) [1] and then improved by a number of others. In this approach, one overcomes the scaling problem for linear optics computation through quantum error correction by requiring the efficiencies for the photon source and the detectors to attain a high threshold value [1]. The threshold efficiency has been improved considerably in the past few years, with the most recent estimate about Linear optics, combined with practical photon source and single-photon detectors, has provided a powerful tool to test a number of quantum information protocols. In the linear optics implementations, the post-selection technique based on photon detections typically plays a critical role. As one scales up the system, the post-selection technique generally leads to very inefficient (exponential) scaling of the overall efficiency, which limits the implementation to small systems. In the past few years, two approaches have been proposed to circumvent this obstacle for different kinds of quantum information processing. In the first approach, a remarkable proposal, generally referred to as linear optics quantum computation, was first put forward by Knill, Laflamme, and Mil-burn (KLM) [1] and then improved by a number of others. In this approach, one overcomes the scaling problem for linear optics computation through quantum error correction by requiring the efficiencies for the photon source and the detectors to attain a high threshold value [1]. The threshold efficiency has been improved considerably in the past few years, with the most recent estimate about 99.4%− 99.7% [2]. In the second approach proposed in Ref. [3], one uses linear optics for implementation of scalable quantum communication through the quantum repeater protocol. This approach overcomes the inefficient scaling through the divide-and-conquer method. In this protocol, one does not have a threshold requirement on the source and the detector efficiencies, which allows its implementation with the state-of-the-art photon detectors.
Quantum technology is a fundamentally new way of harnessing Nature and it has potential for a truly revolutionary innovation and promise the next generation of products with exciting and astounding properties that will affect our lives profoundly. They will have a great influence in defence, aerospace, energy and telecommunications sectors. If this process is to continue in the future, new, quantum technology must replace or supplement what we have now. In particular, Quantum Information Technology can support entirely new modes of information processing based on so called quantum bits or qubits. Its eventual impact may be as great as or greater than that of its classical predecessor. There is almost daily progress in developing promising technologies for realizing quantum information processing with various advantages over its classical counterpart. Logic gates and wires are becoming smaller, and soon they will be made out of only a handful of atoms. Photons are unsurpassed as qubits in terms of decoherence times, mobility, and achievability of high-fidelity single-qubit operations. Thus far, entanglement experiments in optics have been very clean, and an optical quantum processor would obviously have an advantage in connecting to a quantum “network” (no need to convert between stationary and flying qubits). All-optical quantum computing became feasible when, in 2001, a breakthrough known as the KLM (Knill-Laflamme-Milburn) scheme showed that scalable quantum computing is possible using only single-photon sources, detectors, and linear optical circuits. This scheme relies on quantum interference with auxiliary photons at a beam splitter and single-photon detection to induce not-deterministic interactions. Nowadays, the limits of the original KLM linear optics quantum computing proposal, as well as the more recent cluster and graph-state approaches, in addition to various nonlinear optical approaches are explored, but several challenges must be overcome. The most important issues are the practical scalability of quantum circuits, the ability to perform quantum logic gates with error rates below the fault-tolerant threshold and their incorporation into large-scale quantum circuits with realistic physical resources and single-photon detectors packed on an optical chip. Optical integrated circuits offer great potential for realizing previously unfeasible large-scale quantum circuits. However, this architecture suffers not only of the overhead of multiple sources, detectors and ancillary qubits, but it needs to maintain the complete coherence between single photons in which qubits are encoded. The idea to reduce the overhead due to multiple single photon sources with very high degree of reciprocal coherence exploits the possibility to encode the whole state space in a complex optical circuit based on Multiple Rail (MR) Architecture: a particular state in input is encoded in the quantum superposition of a coherent light beam trough the different waveguides, so that it is possible to reproduce the mathematical and physical aspects of quantum entanglement in classical beams of light. Multiple Rail Architecture provides the realization of so called Classical or, better, Intra-System Entanglement. In practics a reconfigurable optical matrix of interconnected MachZehnder provides the representation of the complex Hilbert-Schmidt space where the quantum operation lives. This integrated system on chip can be both Photonics and/or Plasmonics. By exploiting this idea we are able to obtain all the universal quantum gates as SWAP, CNOT, CPHASE, TOFFOLI for two qubits and for multiqubits cases. The most important goal is the possibility to perform deterministic Bell measurements: in usual optical schemes the probability of success of Bell measurements is ½, while the novel architecture provides the possibility to discriminate all Bell states, so that the teleportation can become completely deterministic.
One of the earliest proposals for implementing quantum computation was based on encoding each qubit in two optical modes, each containing exactly one photon. However, it is extremely difficult to unitarily couple two optical modes containing few photons. In 2001, Knill, Laflamme, and Milburn (KLM) found a way to circumvent this restriction and implement efficient quantum computation using only passive linear optics, photodetectors, and single photon sources. This efficient linear optical quantum computing (LOQC) is distinct from other linear optical schemes that are not efficiently scalable. The technological requirements for even the simplest gates in the KLM proposal initially seemed out of reach. However, Ralph, White, Munro and Milburn soon showed that, in principle, demonstrations of key gates and techniques could be achieved with current technology. The objective of the research undertaken in this project was to produce, in three years, a prototype two-qubit gate for photons using the KLM linear optics quantum computation approach, and to develop a blue-print for a multiple qubit device that might be implemented over a longer time scale. A non-deterministic two-qubit gate was demonstrated that operates with high fidelity. A number of key tasks were demonstrated using this gate, and several theoretical investigations of short, medium, and longer term issues for the LOQC approach were successfully completed.
Photonic qubits play an important role in quantum information processing. However, to date, efficient high-speed single photon sources and photon number resolving (PNR) detectors are still difficult to make. Here, we use phase-randomized coherent states and threshold detectors, combined with decoy-state post-processing, to simulate single photon sources and PNR detectors and perform various quantum information processing tasks. We propose a simple linear regression method to predict Fock state statistics based on observable statistics from coherent-state probes, combined with random/structured sampling of probe settings. Compared with traditional decoy-state post-processing based on linear programming and Cartesian product grid sampling, our method enables drastically improved accuracy and much reduced probe resources. It works particularly well for unknown unitary circuits of interest with fixed-size Hilbert space dimensions. For instance, it can accurately simulate 4-photon interference in linear optics with just 32 input/output probe settings and 6-photon interference with 256 probe settings. Moreover, it also works for non-unitary (such as lossy, nonlinear, or arbitrary) quantum channels. This enables a wide variety of applications that can be implemented with easily attainable coherent light sources and threshold detectors, such as characterization of small-scale linear optical quantum computing circuits or quantum sensing/metrology devices.
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.