Preconditioning for a Variational Quantum Linear Solver

• URL: http://arxiv.org/abs/2312.15657v3
• Date: Tue, 23 Apr 2024 15:09:29 GMT
• Title: Preconditioning for a Variational Quantum Linear Solver
• Authors: Aruto Hosaka, Koichi Yanagisawa, Shota Koshikawa, Isamu Kudo, Xiafukaiti Alifu, Tsuyoshi Yoshida,
• Abstract summary: We numerically demonstrate a notable reduction in the required ansatz depth, demonstrating that preconditioning is useful for quantum algorithms. Our findings suggest that combining classical computing techniques, such as preconditioning, with quantum algorithms can significantly enhance the performance of NISQ algorithms.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We apply preconditioning, which is widely used in classical solvers for linear systems $A\textbf{x}=\textbf{b}$, to the variational quantum linear solver. By utilizing incomplete LU factorization as a preconditioner for linear equations formed by $128\times128$ random sparse matrices, we numerically demonstrate a notable reduction in the required ansatz depth, demonstrating that preconditioning is useful for quantum algorithms. This reduction in circuit depth is crucial to improving the efficiency and accuracy of Noisy Intermediate-Scale Quantum (NISQ) algorithms. Our findings suggest that combining classical computing techniques, such as preconditioning, with quantum algorithms can significantly enhance the performance of NISQ algorithms.

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