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.Th...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.展开更多
In this paper,an efficient algorithm is proposed for Toeplitz matrix recovery via hybrid thresh-olding operator.The algorithm is based on the mean-value augmented Lagrangian multiplier algorithm and the singular value...In this paper,an efficient algorithm is proposed for Toeplitz matrix recovery via hybrid thresh-olding operator.The algorithm is based on the mean-value augmented Lagrangian multiplier algorithm and the singular values processed by hybrid singular value threshold operator.The new algorithm ensures that the matrix generated by the iteration has a Toeplitz structure,which reduces the calculation time and obtains a more accurate Toeplitz matrix.The convergence of the new algorithm is discussed under certain assumptions.Numerical experiments show that the new algorithm achieves less CPU time than the mean-value augmented Lagrangian multiplier algorithm,smooth augmented Lagrangian multiplier algorithm,and augmented Lagrangian multiplier algorithm.展开更多
基金Project supported by the Key Research and Development Program of Guangdong Province,China(Grant No.2018B030326001)the National Natural Science Foundation of China(Grant Nos.61521001,12074179,and 11890704)。
文摘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.
基金supported by National Natural Science Foundation of China(No.12371381)the special fund for Science and Technology Innovation Team of Shanxi Province(No.202204051002018)。
文摘In this paper,an efficient algorithm is proposed for Toeplitz matrix recovery via hybrid thresh-olding operator.The algorithm is based on the mean-value augmented Lagrangian multiplier algorithm and the singular values processed by hybrid singular value threshold operator.The new algorithm ensures that the matrix generated by the iteration has a Toeplitz structure,which reduces the calculation time and obtains a more accurate Toeplitz matrix.The convergence of the new algorithm is discussed under certain assumptions.Numerical experiments show that the new algorithm achieves less CPU time than the mean-value augmented Lagrangian multiplier algorithm,smooth augmented Lagrangian multiplier algorithm,and augmented Lagrangian multiplier algorithm.
