Preconditioning for a Variational Quantum Linear Solver

• Main Authors: Hosaka, Aruto, Yanagisawa, Koichi, Koshikawa, Shota, Kudo, Isamu, Alifu, Xiafukaiti, Yoshida, Tsuyoshi
• Format: Journal Article
• Language: English
• Published: 25-12-2023
• Subjects: Physics - Quantum Physics
• DOI: 10.48550/arxiv.2312.15657

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.