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arXiv · 2508.06611

Matrix Inversion by Quantum Walk

Alastair Kay·Christino Tamon
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Abstract

The HHL algorithm for matrix inversion is a landmark algorithm in quantum computation. Its ability to produce a state $|x\rangle$ that is the solution of $Ax=b$, given the input state $|b\rangle$, is envisaged to have diverse applications. In this paper, we substantially simplify the algorithm, originally formed of a complex sequence of phase estimations, amplitude amplifications and Hamiltonian simulations, by replacing the phase estimations with a continuous time quantum walk. The key technique is the use of weak couplings to access the matrix inversion embedded in perturbation theory.

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Alastair Kay, Christino Tamon. 2025-08-08. Matrix Inversion by Quantum Walk. https://arxiv.org/abs/2508.06611

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