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

How can we minimize errors in a linear-optics quantum gate?

Tomohisa Nagata, Ryo Okamoto, 真人 谷田, Holger Friedrich Hofmann, Shigeki Takeuchi

Published Jul 29, 2010• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.868214

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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.
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.
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.
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.
A quantum computation algorithm is demonstrated using single photons and linear optics. Quantum registers are realized by modes and polarization of photons, and the unitary transformations for them are implemented with linear optics. For each quantum computation, the answer to the Deutsch Jozsa problem for any 4 bit digit is given by a single-photon detection signal with a small error rate. The origin of the error is also studied and categorized according to the sources: systematic errors of quantum gates, phase relaxation, amplitude dumping, and misreadout. It is suspected that a demonstration of 11 qubits using linear optics anda single photon with less than a 20 % error rate is achievable by the technique used in the experiment. As a further objective, an idea to construct controlled-NOT gate using quantum phase gate (QPG) given by Chuang et. al., is introduced and experiments on the QPGs are also reviewed.
Scaling up linear-optics quantum computing will require multi-photon gates which are compact, phase-stable, exhibit excellent quantum interference, and have success heralded by the detection of ancillary photons. We investigate the design, fabrication and characterisation of the optimal known gate scheme which meets these requirements: the Knill controlled-Z gate, implemented in integrated laser-written waveguide arrays. We show device performance to be less sensitive to phase variations in the circuit than to small deviations in the coupler reflectivity, which are expected given the tolerance values of the fabrication method. The mode fidelity is also shown to be less sensitive to reflectivity and phase errors than the process fidelity. Our best device achieves a fidelity of 0.931 ± 0.001 with the ideal 4 × 4 unitary circuit and a process fidelity of 0.680 ± 0.005 with the ideal computational-basis process.
A constructive method for simulating small-scale quantum circuits by use of linear optical devices is presented. It relies on the representation of several quantum bits by a single photon, and on the implementation of universal quantum gates using simple optical components (beam splitters, phase shifters, etc.). This suggests that the optical realization of small quantum networks with present-day quantum optics technology is a reasonable goal. This technique could be useful for demonstrating basic concepts of simple quantum algorithms or error-correction schemes. The optical analog of a nontrivial three-bit quantum circuit is presented as an illustration.