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

Analysis of errors in an optical controlled-NOT gate

Tomohisa Nagata, Ryo Okamoto, Keiji Sasaki, Shigeki Takeuchi

Published Aug 11, 2009• 0 citations
Publisher

Abstract

The errors in linear optics controlled not (C-NOT) gates are analyzed considering the polarization-dependent phase sifts, in addition to the incorrectness of the beam splitting ratios. It is shown that the phase sifts at the optical components is as crucial as other error sources discussed in the previous studies. Such a phase shift unintentionally changes the linearly-polarized photons into a elliptically polarized ones. The operators for a beam splitting device and the process matrix of the C-NOT operation including such errors are also given.

DOI
10.1117/12.829607

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The errors in linear optics controlled not (C-NOT) gates are analyzed considering the polarization-dependent phase sifts, in addition to the incorrectness of the beam splitting ratios. It is shown that the phase sifts at the optical components is as crucial as other error sources discussed in the previous studies. Such a phase shift unintentionally changes the linearly-polarized photons into a elliptically polarized ones. The operators for a beam splitting device and the process matrix of the C-NOT operation including such errors are also given.
Possible error sources in an experimentally realized linear-optics controlled-Z gate (Okamoto et al 2005 Phys. Rev. Lett. 95 210506) are analyzed by considering the deviations of the beam splitting ratios from the ideal values (δ R H , δ R V ), the polarization-dependent phase shift (birefringence) of the optical components (δϕ) and the mode mismatch of input photons (δξ). It is found that the error rate is linearly dependent on δ R V and δξ, while the dependence on δ R H and δϕ is approximately quadratic. As a practical result, the gate is much more sensitive to small errors in R V than in R H . Specifically, the reflectivity error for vertical polarization must be less than 0.1% to realize a gate with an error of less than 0.1%, whereas the reflectivity error for horizontal polarization can be up to 1%. It is also shown that the effects of different error sources are not independent of each other (linear error model). Under certain conditions, the deviation from the linear error model exceeds 10% of the total error. The method of analysis used illustrates the basic features of errors in general linear optics quantum gates and circuits, and can easily be adapted to any other device of this type.
Possible error sources in an experimentally realized linear-optics controlled-Z gate[1] are analyzed by considering the deviations of the beam splitting ratios from the ideal values (δRH,δRV), the polarization-dependent phase shift (birefringence) of the optical components (δφ) and the mode mismatch of input photons (δξ). It is found that the error rate is linearly dependent on δRV and δξ , while the dependence on δRH and δφ is approximately quadratic. As a practical result, the gate is much more sensitive to small errors in RV than in RH. Specifically, the reflectivity error for vertical polarization must be less than 0.1% to realize a gate with an error of less than 0.1%, whereas the reflectivity error for horizontal polarization can be up to 1%. It is also shown that the effects of different error sources are not independent of each other (linear error model). Under certain conditions, the deviation from the linear error model exceeds 10% of the total error. The method of analysis used illustrates the basic features of errors in general linear optics quantum gates and circuits, and can easily be adapted to any other device of this type.
In our paper, we report the analysis of errors in the C-NOT gate using a high-precision test-bed. From the result of previous experiment, we have identified two main causes of errors: one is the mismatch between optical modes, and the other is the un-intentional phase shift between two polarization, horizontal polarizations and vertical polarization. To evaluate these factors more precisely, we construct a test-bed setup in which piezo-electric stages are used to avoid mode mismatch, and the extinction ratio of polarization is kept below 10-3. In the poster, we will report the experimental results with the test-bed and the analysis of errors in detail.
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.
It has previously been shown that probabilistic quantum logic operations may be performed using linear optical elements, additional photons (ancilla), and post-selection based on the output of single-photon detectors. Here we describe the operation of several quantum logic operations of an elementary nature, including a quantum parity check and a quantum encoder, and we show how they may be combined to implement a controlled-NOT (CNOT) gate. All of these gates may be constructed using polarizing beam splitters that completely transmit one state of polarization and totally reflect the orthogonal state of polarization, which allows a simple explanation of each operation. We also describe a polarizing beam splitter implementation of a CNOT gate that is closely analogous to the quantum teleportation technique previously suggested by Gottesman and Chuang [Nature 402, 390 (1999)]. Finally, our approach has the interesting feature that it makes practical use of a quantum-eraser technique.
We present a linear-optical scheme for a controlled-phase gate with tunable phase shift programmed by a qubit state. In contrast to all previous tunable controlled-phase gates, the phase shift is not hard-coded into the optical setup, but can be tuned to any value from 0 to π by the state of a so-called program qubit . Our setup is feasible with current level of technology using only linear-optical components. We provide an experimental feasibility study to assess the gate’s implementability. We also discuss options for increasing the success probability up to 1/12; this approaches the success probability of an optimal non-programmable tunable controlled-phase gate.