Quantum Krylov-Subspace Method Based Linear Solver

• URL: http://arxiv.org/abs/2405.06359v1
• Date: Fri, 10 May 2024 09:50:06 GMT
• Title: Quantum Krylov-Subspace Method Based Linear Solver
• Authors: Rui-Bin Xu, Zhu-Jun Zheng, Zheng Zheng,
• Abstract summary: Quantum Krylov-subspace method (QKSM) is a hybrid classical-quantum algorithm. We introduce the quantum Krylov-subspace method based linear solver that not only reduces computational redundancy but also enhances efficiency and accuracy.
• Score: 1.689689700250852
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Despite the successful enhancement to the Harrow-Hassidim-Lloyd algorithm by Childs et al., who introduced the Fourier approach leveraging linear combinations of unitary operators, our research has identified non-trivial redundancies within this method. This finding points to a considerable potential for refinement. In this paper, we propose the quantum Krylov-subspace method (QKSM), which is a hybrid classical-quantum algorithm, to mitigate such redundancies. By integrating QKSM as a subroutine, we introduce the quantum Krylov-subspace method based linear solver that not only reduces computational redundancy but also enhances efficiency and accuracy. Extensive numerical experiments, conducted on systems with dimensions up to $2^{10} \times 2^{10}$, have demonstrated a significant reduction in computational resources and have led to more precise approximations.

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