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Quantum Information and Measurement (QIM)

Modeling two-qubit Grovers algorithm implementation in a linear optical chip

E.O. Samsonov, Fedor Dmitrievich Kiselev

Published Jan 1, 2019• 0 citations
Publisher

Abstract

We introduce a model of Grovers algorithm suitable for implementation in a linear photonic chip. We compared two known realizations of two-qubit CZ gates and determined tolerance boundaries for distortions of the coupler dimensions.
DOI
10.1364/qim.2019.f5a.24

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Acta Physica Sinica•Jan 1, 2025•0 citations
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.
The field of linear optical quantum computation (LOQC) will soon need a repertoire of experimental milestones. We make progress in this direction by describing several experiments based on Grover's algorithm. These experiments range from a relatively simple implementation using only a single nonscalable controlled-NOT (CNOT) gate to the most complex, requiring two concatenated scalable CNOT gates, and thus form a useful set of early milestones for LOQC. We also give a complete description of basic LOQC using polarization-encoded qubits, making use of many simplifications to the original scheme of Knill, Laflamme, and Milburn [E. Knill, R. Laflamme, and G. J. Milburn, Nature (London) 409, 46 (2001)].
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.
Efficient and high-fidelity two-qubit gates are crucial to achieving fault-tolerant quantum computing and have become one of the key research topics in the quantum computing field. The fidelity of quantum gate is affected by many factors, such as quantum chip parameters and control waveforms. In theory, the chip paramters and waveforms can be precisely designed. However, in practice, the actual chip parameters and waveforms may deviate from the theoretical values. It is necessary to systematically study the effects of chip parameters, control waveforms, and other factors on the fidelity of two-qubit gate, and determine the magnitude and direction of the each factor’s effect. Here, we systematically study the effects of chip parameters, control waveforms, coupler start frequency, qubit frequency, etc. on the fidelity of CZ gate. On this basis, the response of gate fidelity to deviations in control parameters is further studied. At the chip design level, quantum chips based on CBQ parameters can achieve higher-fidelity CZ gate in shorter gate operation time. In terms of controlling waveforms, the three-level Fourier series wave is superior to the square wave and rounded trapezoidal wave in achieving lower gate error rate and shorter gate operation time, and can better meet the requirements for efficient implementation of high-fidelity quantum gates. Factors such as the coupler starting frequency and qubit frequency have relatively little effect on the fidelity of the CZ gate. In a wide frequency range, high-fidelity CZ gate can always be achieved by optimizing the control waveform parameters. It should be pointed out that slight deviations of control parameters will lead to a significant increase in gate error. This study is of great significance for clarifying the effects of various factors on the fidelity of the CZ gate. It can provide theoretical and technical support for designing superconducting quantum chips and realizing high-fidelity CZ gate, thereby promoting the engineering development of quantum computing.