Pure quantum gradient descent algorithm and full quantum variational eigensolver

IF 6.5 2区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY Frontiers of Physics Pub Date : 2023-12-02 DOI:10.1007/s11467-023-1346-7
Ronghang Chen, Zhou Guang, Cong Guo, Guanru Feng, Shi-Yao Hou
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引用次数: 1

Abstract

Optimization problems are prevalent in various fields, and the gradient-based gradient descent algorithm is a widely adopted optimization method. However, in classical computing, computing the numerical gradient for a function with d variables necessitates at least d + 1 function evaluations, resulting in a computational complexity of O(d). As the number of variables increases, the classical gradient estimation methods require substantial resources, ultimately surpassing the capabilities of classical computers. Fortunately, leveraging the principles of superposition and entanglement in quantum mechanics, quantum computers can achieve genuine parallel computing, leading to exponential acceleration over classical algorithms in some cases. In this paper, we propose a novel quantum-based gradient calculation method that requires only a single oracle calculation to obtain the numerical gradient result for a multivariate function. The complexity of this algorithm is just O(1). Building upon this approach, we successfully implemented the quantum gradient descent algorithm and applied it to the variational quantum eigensolver (VQE), creating a pure quantum variational optimization algorithm. Compared with classical gradient-based optimization algorithm, this quantum optimization algorithm has remarkable complexity advantages, providing an efficient solution to optimization problems. The proposed quantum-based method shows promise in enhancing the performance of optimization algorithms, highlighting the potential of quantum computing in this field.

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纯量子梯度下降算法和全量子变分特征求解器
优化问题普遍存在于各个领域,基于梯度下降算法是一种被广泛采用的优化方法。然而,在经典计算中,计算具有d个变量的函数的数值梯度至少需要d + 1次函数求值,导致计算复杂度为O(d)。随着变量数量的增加,经典的梯度估计方法需要大量的资源,最终超出了经典计算机的能力。幸运的是,利用量子力学中的叠加和纠缠原理,量子计算机可以实现真正的并行计算,在某些情况下导致经典算法的指数加速。在本文中,我们提出了一种新的基于量子的梯度计算方法,它只需要一次oracle计算就可以获得多元函数的数值梯度结果。该算法的复杂度为0(1)。在此基础上,我们成功地实现了量子梯度下降算法,并将其应用于变分量子特征求解器(VQE),创建了一个纯量子变分优化算法。与经典的基于梯度的优化算法相比,量子优化算法具有显著的复杂度优势,能够有效地解决优化问题。提出的基于量子的方法有望提高优化算法的性能,突出了量子计算在该领域的潜力。
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来源期刊
Frontiers of Physics
Frontiers of Physics PHYSICS, MULTIDISCIPLINARY-
CiteScore
9.20
自引率
9.30%
发文量
898
审稿时长
6-12 weeks
期刊介绍: Frontiers of Physics is an international peer-reviewed journal dedicated to showcasing the latest advancements and significant progress in various research areas within the field of physics. The journal's scope is broad, covering a range of topics that include: Quantum computation and quantum information Atomic, molecular, and optical physics Condensed matter physics, material sciences, and interdisciplinary research Particle, nuclear physics, astrophysics, and cosmology The journal's mission is to highlight frontier achievements, hot topics, and cross-disciplinary points in physics, facilitating communication and idea exchange among physicists both in China and internationally. It serves as a platform for researchers to share their findings and insights, fostering collaboration and innovation across different areas of physics.
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