Optimized quantum singular value thresholding algorithm based on a hybrid quantum computer

doi:10.1088/1674-1056/ac40fb

Abstract Quantum singular value thresholding (QSVT) algorithm, as a core module of many mathematical models, seeks the singular values of a sparse and low rank matrix exceeding a threshold and their associated singular vectors. The existing all-qubit QSVT algorithm demands lots of ancillary qubits, remaining a huge challenge for realization on nearterm intermediate-scale quantum computers. In this paper, we propose a hybrid QSVT (HQSVT) algorithm utilizing both discrete variables (DVs) and continuous variables (CVs). In our algorithm, raw data vectors are encoded into a qubit system and the following data processing is fulfilled by hybrid quantum operations. Our algorithm requires O[log(MN)] qubits with O(1) qumodes and totally performs O(1) operations, which significantly reduces the space and runtime consumption.

Keywords: singular value thresholding algorithm hybrid quantum computation

Received: 31 October 2021
Revised: 23 November 2021
Accepted manuscript online: 08 December 2021

PACS:	87.55.kd	(Algorithms)
	03.67.Ac	(Quantum algorithms, protocols, and simulations)

Fund: Project supported by the Key Research and Development Program of Guangdong Province, China (Grant No. 2018B030326001) and the National Natural Science Foundation of China (Grant Nos. 61521001, 12074179, and 11890704).

Corresponding Authors: Shaoxiong Li, Yang Yu
E-mail: shaoxiong.li@nju.edu.cn;yuyang@nju.edu.cn

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Yangyang Ge(葛阳阳), Zhimin Wang(王治旻), Wen Zheng(郑文), Yu Zhang(张钰), Xiangmin Yu(喻祥敏), Renjie Kang(康人杰), Wei Xin(辛蔚), Dong Lan(兰栋), Jie Zhao(赵杰), Xinsheng Tan(谭新生), Shaoxiong Li(李邵雄), and Yang Yu(于扬) Optimized quantum singular value thresholding algorithm based on a hybrid quantum computer 2022 Chin. Phys. B 31 048704

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