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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Theory and experimental requirements of imperfect two-qubit linear optical photonic gates

A. Matthew Smith, Dmitry B. Uskov, Michael L. Fanto, L. Ying, Lev Kaplan

Published May 1, 2012• 0 citations
Publisher

Abstract

We propose an experiment in Linear Optical Quantum Computing (LOQC) in the style rst suggested by Knill, La amme, and Milburn. This experiment is intended to test the theories proposed in the authors' previous work on imperfect LOQC gates using number-resolving photon-detectors. We develop a simple physical apparatus capable of producing controllable delity less than 1 and success rates higher than the current theoretical maximum (S=2/27) for perfect delity. This experimental setup is within the reach of many experimental groups and would provide an interesting experiment in photon-based quantum computing.

DOI
10.1117/12.920477

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We propose an experiment in Linear Optical Quantum Computing (LOQC) in the style rst suggested by Knill, La amme, and Milburn. This experiment is intended to test the theories proposed in the authors' previous work on imperfect LOQC gates using number-resolving photon-detectors. We develop a simple physical apparatus capable of producing controllable delity less than 1 and success rates higher than the current theoretical maximum (S=2/27) for perfect delity. This experimental setup is within the reach of many experimental groups and would provide an interesting experiment in photon-based quantum computing.
Here we propose an experiment in Linear Optical Quantum Computing (LOQC) using the framework first developed by Knill, Laflamme, and Milburn. This experiment will test the ideas of the authors' previous work on imperfect LOQC gates using number-resolving photon detectors. We suggest a relatively simple physical apparatus capable of producing CZ gates with controllable fidelity less than 1 and success rates higher than the current theoretical maximum (S=2/27) for perfect fidelity. These experimental setups are within the reach of many experimental groups and would provide an interesting experiment in photonic quantum computing.
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.
The field of linear optical quantum computation (LOQC) will soon need a repertoire of experimental milestones. We make progress in this direction by describing several experiments based on Grover's algorithm. These experiments range from a relatively simple implementation using only a single nonscalable controlled-NOT (CNOT) gate to the most complex, requiring two concatenated scalable CNOT gates, and thus form a useful set of early milestones for LOQC. We also give a complete description of basic LOQC using polarization-encoded qubits, making use of many simplifications to the original scheme of Knill, Laflamme, and Milburn [E. Knill, R. Laflamme, and G. J. Milburn, Nature (London) 409, 46 (2001)].
We discuss the effects of imperfect photon detectors suffering from loss and noise on the reliability of linear optical quantum computers. We show that for a given detector efficiency there is a maximum achievable success probability, and that increasing the number of ancillary photons and detectors used for one controlled sign flip gate beyond a critical point will decrease the probability that the computer will function correctly. We have also performed simulations of some small logic gates and estimate the efficiency and noise levels required for the linear optical quantum computer to function properly. We find that the construction of a 9999%99 reliable controlled sign flip gate would require photon detectors with an efficiency greater than 0.999987.
We propose a linear optical scheme to implement the nondeterministic two-qubit controlled phase gate with the certain success probability. The proposed setup involves simple linear optical elements, a pair of the two-photon polarization entangled states, and the conventional photon detectors that only distinguish the vacuum and nonvacuum Fock number states. A sophisticated single-photon detector distinguishing one or two photon states is unnecessary. This can greatly simplify the experimental realization of a linear optical quantum computer.
The use of photons as qubits is a promising implementation for quantum computation. The inability of photons to interact, especially with the environment, makes them an ideal physical candidate. However, this also makes them a difficult system to perform two qubit gates on. Recent breakthroughs in photonic quantum computing have shown methods around the requirement of direct photon-photon interaction. In this thesis we study three recently discovered schemes for optical quantum computation. \n \n We first investigate the so called linear optical quantum computing (LOQC) scheme, exploring a method to improve the original proposal by constructing a photon-number QND detector that succeeds with a high probability. In doing this we present a new type of LOQC teleporter, one that can detect the presence of a single photon in an arbitrary polarisation state when the input state is a sum of vacuum and multi-photon terms. This new type of teleporter is an improvement on the original scheme in that the entangled states required can be made offline with fewer entangling operations. \n \n We next investigate the so called quantum bus (qubus) scheme for photonic quantum computing. We show a scheme to measure the party of n qubit states by using a single qubus mode, controlled rotations and displacements. This allows for the syndrome measurements of any stabilizer quantum error correcting code. We extend these results to a fault tolerant scheme to measure an arbitrary Pauli operator of weight n, incorporating so called single bit teleportations. We investigate the construction of a Toffoli gate by using a single qubus mode, controlled rotations and displacements that works with a success probability of at least 25%. We also investigate the use of single bit teleportations to construct a universal set of gates on coherent state type logic and in the construction of cluster states. \n \nWe finally investigate the optical Zeno gate, a gate that uses the Zeno effect in the form of two photon absorbers to induce a CSIGN. We model realistic two photon absorption and include realistic single photon loss for this gate, examining the use of encoding to overcome the single photon loss, showing that our results are competitive with the leading equivalent LOQC scheme.