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arXiv:quant-ph/0312226

A feasible gate for scalable linear optics quantum computation using polarization optics

Kaoru Sanaka, Kevin J. Resch

Published Dec 31, 2003• 1 citation
arXivHTMLPDF

Abstract

Knill, Laflamme, and Milburn (KLM) proved that it is possible to build a scalable universal quantum computer using only linear-optics elements and conditional dynamics [Nature (London) {\bf 409}, 46 (2001)\cite{Knill}]. However, the practical realization of the quantum logic gate for the scheme is still technically difficult. A major difficulty is the requirement for sub-wavelength level stabilization of the interlocking interferometers. Following our recent experimental work[Phys. Rev. Lett.{\bf 92}, 017902 (2004)\cite{Sanaka2}], we describe a more feasible scheme to implement the gate that greatly reduces the experimental stability requirements. The scheme uses only polarizing beam splitters and half-wave plates.

DOI
10.48550/arxiv.quant-ph/0312226

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Knill, Laflamme, and Milburn (KLM) proved that it is possible to build a scalable universal quantum computer using only linear-optics elements and conditional dynamics [Nature (London) {\bf 409}, 46 (2001)\cite{Knill}]. However, the practical realization of the quantum logic gate for the scheme is still technically difficult. A major difficulty is the requirement for sub-wavelength level stabilization of the interlocking interferometers. Following our recent experimental work[Phys. Rev. Lett.{\bf 92}, 017902 (2004)\cite{Sanaka2}], we describe a more feasible scheme to implement the gate that greatly reduces the experimental stability requirements. The scheme uses only polarizing beam splitters and half-wave plates.
The first section of the work investigates light modes as a means of implementing optical qubits and qudits. The modes considered are polarization mode, path mode, transverse spatial mode, frequency mode, temporal bin-mode and temporal mode. Subsequently, mathematical model of linear optical elements like beam splitters (BS) and phase shifters are deduced and their capability of representing any single qubit optical gate is exposed. Finally Knill, Laflamme and Milburn (KLM) method of using linear optical elements to promote nonlinear operations based on nonlinear (nondeterministic) sign-flip gate (NS) is explained, and designs of two qubits conditional sign flip gate (c-z1/16) and CNOT gate, both based on KLM method, are demonstrated. So, universal set of quantum gates based on linear optics is possible.
Linear optics quantum logic gates are the best tool to generate multiphoton entanglement. Simplifying a recent approach [Phys. Rev. A 65, 062324 (2002); 66, 024308 (2002); Nature (London) 426, 264 (2003); Phys. Rev. Lett. 93, 080502 (2004)], we were able to implement the conditional phase gate with only one second-order interference at a polarization dependent beam splitter, thereby significantly increasing its stability. The improved quality of the gate is evaluated by analyzing its entangling capability and by performing full process tomography. The achieved results ensure that this device is well suited for implementation in various multiphoton quantum information protocols.
Linear optics with photon counting is a prominent candidate for practical quantum computing. The protocol by Knill, Laflamme, and Milburn [2001, Nature (London) 409, 46] explicitly demonstrates that efficient scalable quantum computing with single photons, linear optical elements, and projective measurements is possible. Subsequently, several improvements on this protocol have started to bridge the gap between theoretical scalability and practical implementation. The original theory and its improvements are reviewed, and a few examples of experimental two-qubit gates are given. The use of realistic components, the errors they induce in the computation, and how these errors can be corrected is discussed.
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)].