Quantum Metropolis-Hastings via Penalised Qubitized Walks: Spectral Filtering and Circuit Implementation

• URL: http://arxiv.org/abs/2604.15179v1
• Date: Thu, 16 Apr 2026 15:59:50 GMT
• Title: Quantum Metropolis-Hastings via Penalised Qubitized Walks: Spectral Filtering and Circuit Implementation
• Abstract summary: We construct and simulate an explicit circuit level implementation of a quantum Metropolis-Hastings algorithm based on the framework introduced by Claudon emphet al..<n>We present the full quantum workflow required to prepare a stationary distribution, including a number of modifications required to make the algorithm implementable in a realistic quantum circuit model.
• Score: 0.45880283710344066
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Metropolis-Hastings algorithm is a cornerstone of Markov Chain Monte Carlo methods, underpinning a wide range of applications in computational physics, Bayesian inference, and machine learning. Quantum variants of Metropolis-Hastings promise accelerated mixing through quantum walks, but their practical realisation remains challenging. In this work, we construct and simulate an explicit circuit level implementation of a quantum Metropolis-Hastings algorithm based on the framework introduced by Claudon \emph{et al.} (arXiv:2506.11576). We present the full quantum workflow required to prepare a stationary distribution, including a number of modifications required to make the algorithm implementable in a realistic quantum circuit model. Our results demonstrate that these modifications are essential to recover the correct stationary behaviour and highlight both the potential and current limitations of quantum Metropolis-Hastings algorithms, which are expected to become practically relevant in the fault tolerant quantum computing regime.

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