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Physica Scripta

Modeling two-qubit Grover’s algorithm implementation in a linear optical chip

E.O. Samsonov, Fedor Dmitrievich Kiselev, Y Shmelev, V. I. Egorov, R. Goncharov, A. A. Santev, B. E. Pervushin, Artur V. Gleim

Published Dec 23, 2019• 7 citations
Publisher

Abstract

Abstract This paper introduces a model of Grover’s algorithm suitable for implementation in a linear photonic chip. We compare two known realizations of its main components, two-qubit CZ gates, in order to define optimal chip architecture. The algorithm operation is simulated considering directional coupler imperfection influence on the scheme parameters. We also determined tolerance boundaries for distortions of the coupler dimensions.

DOI
10.1088/1402-4896/ab6523

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Abstract This paper introduces a model of Grover’s algorithm suitable for implementation in a linear photonic chip. We compare two known realizations of its main components, two-qubit CZ gates, in order to define optimal chip architecture. The algorithm operation is simulated considering directional coupler imperfection influence on the scheme parameters. We also determined tolerance boundaries for distortions of the coupler dimensions.
Subject of Research. The paper presents a quantum search algorithm model, suitable for integration into a linear optical chip. Error impact caused by two-qubit operator implementation and directional coupler manufacture imperfection on the algorithm output is studied. Method. Analytical calculation of the algorithm scheme was performed to assess error impact caused by two-qubit operator optical implementation. Numerical simulation of the algorithm was executed for taking into account distortions caused by directional coupler imperfections. The simulation was completed using Qutip library on Python programming language. Main Results. Two well-known implementations of the algorithm scheme main component, a two-qubit CZ gate, are compared in order to select the most optimal chip architecture. It was shown that one of two-qubit gate implementations introduces an error critical for the algorithm work. Another implementation based on projection measurements does not introduce an error, but has a lower efficiency. We have performed simulation of the proposed scheme, taking into account the imperfections of its components in the framework of unitary dynamics. We have shown that the algorithm error probability does not exceed 0.011. Two-qubit Grover’s algorithm оptical implementation with regard to directional coupler imperfections has a low error rate, but it is limited by the low two-qubit operator efficiency. Practical Relevance. The study carried out can be useful for the physical implementation of the algorithm. Creation of an integrated optical scheme that implements Grover’s algorithm will make it possible to build a quantum router for the optimal route search in quantum networks with complex topology.
We present recursive multiport schemes for implementing quantum Fourier transforms and the inversion step in Grover's algorithm on an integrated linear optics device. In particular, each scheme shows how to execute a quantum operation on 2d2d2d modes using a pair of circuits for the same operation on ddd modes. The circuits operate on path-encoded qudits and realize ddd-dimensional unitary transformations on these states using linear optical networks with O(d2)O\left({d}^{2}\right)O(d2) optical elements. To evaluate the schemes against realistic errors, we ran simulations of proof-of-principle experiments using a simple fabrication model of silicon-based photonic integrated devices that employ directional couplers and thermo-optic modulators for beam splitters and phase shifters, respectively. We find that high-fidelity performance is achievable with our multiport circuits for 2-qubit and 3-qubit quantum Fourier transforms, and for quantum search on four-item and eight-item databases.
Linear Optics Quantum Computing can be achieved by implementing a complete Silicon Photonic Integrated Circuit. This involves optimizing the layout and fabrication of photonic circuits tailored for quantum computing applications using linear optics principles. A prototype of this kind of circuit is the universal two-qubit Controlled-NOT gate. This scheme makes use of linear, coincidence basis gate that performs all the operations of a controlled-NOT gate and requires only single photons at the input. The key components in the photonic quantum circuit using the CNOT gate scheme are designed and simulated. Subsequently, the layouts for the chips incorporating the optimal parameters identified in simulations of all the components are designed.
Photonic crystal is a sort of artificial material,which has special characteristics.Recently,the application of photonic crystal in quantum computation has been introduced by Angelakis et al.In the paper,the implementation of the Grover search algorithm in two-dimensional planar photonic crystals for two-qubit system is proposed.By using the concepts of qubit and conditional quantum phase gate proposed by Angelakis et al,a more efficient and easily operated simulation of Grover algorithm is achieved.The details of scheme are given and related issues are discussed.