南京信息工程大学主页平台管理系统王友乐--中文主页-- Variational Quantum Singular Value Decomposition

论文成果

Variational Quantum Singular Value Decomposition

发布时间：2023-09-08点击次数：

发表刊物：Quantum
关键字：Variational quantum algorithm, singular value decomposition
摘要：Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed to determine the singular values and their associated singular vectors of a given matrix. Although these algorithms are promising, the required quantum subroutines and resources are too costly on near-term quantum devices. In this work, we propose a variational quantum algorithm for singular value decomposition (VQSVD). By exploiting the variational principles for singular values and the Ky Fan Theorem, we design a novel loss function such that two quantum neural networks (or parameterized quantum circuits) could be trained to learn the singular vectors and output the corresponding singular values. Furthermore, we conduct numerical simulations of VQSVD for random matrices as well as its applications in image compression of handwritten digits. Finally, we discuss the applications of our algorithm in recommendation systems and polar decomposition.
Our work explores new avenues for quantum information processing beyond the conventional protocols that only works for Hermitian data, and reveals the capability of matrix decomposition on near-term quantum devices.
论文类型：期刊论文
是否译文：否
收录刊物：SCI
发布刊物链接：https://arxiv.org/pdf/2006.02336

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