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New Journal of Physics

Analysis of experimental error sources in a linear-optics quantum gate

T Nagata, Ryo Okamoto, Holger Friedrich Hofmann, Shigeki Takeuchi

Published Apr 30, 2010• 9 citations
Publisher

Abstract

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.

DOI
10.1088/1367-2630/12/4/043053

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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.
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.
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.
The origin of errors in quantum computation implemented by linear optics is studied. The systematic errors of quantum gates, phase relaxation, amplitude dumping, and misreadout are considered as error sources, and the errors which occurred in a four-bit Deutsch-Jozsa algorithm experiment are categorized according to the sources. The increase in the error rate with the expansion of the input size in the Deutsch-Jozsa algorithm is also studied and it was found that the demonstration of 11 qubits using linear optics and a single photon with less than a 20% error rate is achievable by the technique used in the experiment.
One of the main problems that optical quantum computing has to overcome is the efficient construction of two-photon gates. Theoretically these gates can be realized using Kerr-nonlinearities, but the techniques involved are experimentally very difficult. We therefore employ linear optics with projective measurements to generate these non-linearities. The downside is that the measurement-induced nonlinearities achieved with linear optics are less versatile and the success rate can be quite low. This project is mainly the result of a literature study but also a theoretical work on the physics behind quantum optical multiports which is essential for realizing two-photon gates. By applying different postcorrection techniques we increase the probability of success in a modifed non-linear sign shift gate which is foundational for the two photon controlled-NOT gate. We prove that it's not possible to correct the states by only using a single beam splitter. We show that it might be possible to increase the probability of success using a more complex setup with at least two error-correcting beam splitters.
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.