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Chinese Physics B

Comparison of differential evolution, particle swarm optimization, quantum-behaved particle swarm optimization, and quantum evolutionary algorithm for preparation of quantum states

Xin Cheng, Xiujuan Lu, Yanan Liu, Sen Kuang

Published Apr 11, 2022• 6 citations
Publisher

Abstract

Four intelligent optimization algorithms are compared by searching for control pulses to achieve the preparation of target quantum states for closed and open quantum systems, which include differential evolution (DE), particle swarm optimization (PSO), quantum-behaved particle swarm optimization (QPSO), and quantum evolutionary algorithm (QEA). We compare their control performance and point out their differences. By sampling and learning for uncertain quantum systems, the robustness of control pulses found by these four algorithms is also demonstrated and compared. The resulting research shows that the QPSO nearly outperforms the other three algorithms for all the performance criteria considered. This conclusion provides an important reference for solving complex quantum control problems by optimization algorithms and makes the QPSO be a powerful optimization tool.

DOI
10.1088/1674-1056/ac65ee

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Inspired by the idea of hybrid optimization algorithms, this paper proposes two hybrid quantum evolutionary algorithms (QEA) based on combining QEA with particle swarm optimization (PSO) to improve the performance of QEA . The main idea of the first method called PSEQEA is to embed the evolutionary equation of PSO in the evolutionary operator of QEA; while the main idea of the second method called PSSQEA is to replace the evolutionary operator of QEA using the evolutionary equation of PSO which is redefined the meanings of the original evolutionary equations. The experiment results of the knapsack problem, the function optimization problems and multiuser detection problem show that the both of the proposed methods not only have simpler algorithm structure, but also perform better than conventional QEA and PSO in terms of ability of global optimum
Designing a high-quality control is crucial for reliable quantum computation. Among the existing approaches, closed-loop leaning control is an effective choice. Its efficiency depends on the learning algorithm employed, thus deserving algorithmic comparisons for its practical applications. Here we assess three representative learning algorithms, including GRadient Ascent Pulse Engineering (GRAPE), improved Nelder-Mead (NMplus), and Differential Evolution (DE), by searching for high-quality control pulses to prepare the Bell state. We first implement each algorithm experimentally in a nuclear magnetic resonance system and then conduct a numerical study considering the impact of some possible significant experimental uncertainties. The experiments report the successful preparation of the high-fidelity target state by the three algorithms, while NMplus converges fastest, and these results coincide with the numerical simulations when potential uncertainties are negligible. However, under certain significant uncertainties, these algorithms possess distinct performance with respect to their resulting precision and efficiency, and DE shows the best robustness. This study provides insight to aid in the practical application of different closed-loop learning algorithms in realistic physical scenarios.
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