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arXiv:quant-ph/0308071 · Physical Review A

Comparison of linear optics quantum-computation control-sign gates with ancilla inefficiency and an improvement to functionality under these conditions

Austin P. Lund, T. B. Bell, Timothy C. Ralph

Published Aug 25, 2003• 17 citations
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Abstract

We compare three proposals for nondeterministic control-sign gates implemented using linear optics and conditional measurements with nonideal ancilla mode production and detection. The simplified Knill-Laflamme-Milburn gate [Ralph et al., Phys. Rev. A 65, 012314 (2001)] appears to be the most resilient under these conditions. We also find that the operation of this gate can be improved by adjusting the beam splitter ratios to compensate to some extent for the effects of the imperfect ancilla.

DOI
10.1103/physreva.68.022313

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We compare three proposals for nondeterministic control-sign gates implemented using linear optics and conditional measurements with nonideal ancilla mode production and detection. The simplified Knill-Laflamme-Milburn gate [Ralph et al., Phys. Rev. A 65, 012314 (2001)] appears to be the most resilient under these conditions. We also find that the operation of this gate can be improved by adjusting the beam splitter ratios to compensate to some extent for the effects of the imperfect ancilla.
Knill, Laflamme, and Milburn showed that linear optics techniques could be used to implement a nonlinear sign gate. They also showed that two of their nonlinear sign gates could be combined to implement a controlled-phase gate, which has a number of practical applications. Here we describe an alternative implementation of a controlled-phase gate for a single-rail target qubit that only requires the use of a single nonlinear sign gate. This gives a much higher average probability of success when the required ancilla photons are generated using heralding techniques. This implementation of a controlled-phase gate destroys the control qubit, which is acceptable in a number of applications where the control qubit would have been destroyed in any event, such as in a postselection process.
Ever since Knill, Laflamme and Milburn [Nature (London) 409, 46 (2001)] showed that nondeterministic quantum logic operations could be performed with linear optical elements, additional photons (ancilla) and projective measurements, the idea of linear-optics quantum computation has attracted considerable interest. Our group has recently demonstrated several devices of this kind. We give an overview of recent experimental results, including the quantum parity check, the destructive controlled-NOT, and a cyclical quantum memory. The need for high-efficiency detection of single photons, and for detectors capable of distinguishing photon number will be discussed. Some experimental improvements towards meeting that need will be presented.
Knill, Laflamme, and Milburn [Nature 409, 46 (2001)] showed that linear optics techniques could be used to implement a nonlinear sign gate. They also showed that two of their nonlinear sign gates could be combined to implement a controlled-phase gate, which has a number of practical applications. Here we describe an alternative implementation of a controlled-phase gate that only requires the use of a single nonlinear sign gate. This gives a much higher average probability of success when the required ancilla photons are generated using heralding techniques. This implementation of a controlled-phase gate destroys the control qubit, which is acceptable in a number of applications where the control qubit would have been destroyed in any event, such as in a postselection process.
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.
Abstract Knill, Laflamme, and Milburn showed that linear optics techniques could be used to implement a nonlinear sign gate. They also showed that two of their nonlinear sign gates could be combined to implement a controlled-phase gate, which has a number of practical applications. Here we describe an alternative implementation of a controlled-phase gate that only requires the use of a single nonlinear sign gate. This gives a much higher average probability of success when the required ancilla photons are generated using heralding techniques. This implementation of a controlled-phase gate destroys the control qubit, which is acceptable in a number of applications where the control qubit would have been destroyed in any event, such as in a postselection process.
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.