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

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 with0(1) qumodes and totally performs 0(1) operations,which significantly reduces the space and runtime consumption.