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Nanosystems Physics Chemistry Mathematics

Modeling of linear optical controlled-z quantum gate with dimensional errors of passive components

Fedor Dmitrievich Kiselev, E.Y. Samsonov, Artur V. Gleim

Published Dec 28, 2019• 2 citations
Publisher

Abstract

Linear optical quantum computing can be realized using photonic integrate circuits (PICs).It is advantageous in comparison to other physical implementations of quantum computing due to simplicity of qubit encoding using photons and low decoherence times.Passive components like beamsplitters and phaseshifters are key elements for such PICs.In this article, we present modeling of linear optical controlled-Z gate with imperfections of beamsplitters and phaseshifters taken into account.Results showed that errors occur which cannot be detected by projection measurements and post-selection proposed by Knill, Laflamme and Milburn.We studied how these errors and success probability changes with the increase of dimensional errors using Monte-Carlo simulation.The obtained results can be used for design and calibration stages of chip manufacturing.

DOI
10.17586/2220-8054-2019-10-6-627-631

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Linear optical quantum computing can be realized using photonic integrate circuits (PICs).It is advantageous in comparison to other physical implementations of quantum computing due to simplicity of qubit encoding using photons and low decoherence times.Passive components like beamsplitters and phaseshifters are key elements for such PICs.In this article, we present modeling of linear optical controlled-Z gate with imperfections of beamsplitters and phaseshifters taken into account.Results showed that errors occur which cannot be detected by projection measurements and post-selection proposed by Knill, Laflamme and Milburn.We studied how these errors and success probability changes with the increase of dimensional errors using Monte-Carlo simulation.The obtained results can be used for design and calibration stages of chip manufacturing.
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 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.
As primitives for entanglement generation, controlled phase gates have a central role in quantum computing. Especially in ideas realizing instances of quantum computation in linear optical gate arrays, a closer look can be rewarding. In such architectures, all effective nonlinearities are induced by measurements. Hence the probability of success is a crucial parameter of such quantum gates. In this paper, we discuss this question for controlled phase gates that implement an arbitrary phase with one and two control qubits. Within the class of post-selected gates in dual-rail encoding with vacuum ancillas, we identify the optimal success probabilities. We construct networks that allow for implementation using current experimental capabilities in detail. The methods employed here appear specifically useful with the advent of integrated linear optical circuits, providing stable interferometers on monolithic structures.
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.
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Here we propose an experiment in Linear Optical Quantum Computing (LOQC) using the framework first developed by Knill, Laflamme, and Milburn. This experiment will test the ideas of the authors' previous work on imperfect LOQC gates using number-resolving photon detectors. We suggest a relatively simple physical apparatus capable of producing CZ gates with controllable fidelity less than 1 and success rates higher than the current theoretical maximum (S=2/27) for perfect fidelity. These experimental setups are within the reach of many experimental groups and would provide an interesting experiment in photonic quantum computing.