Quantum Metropolis-Hastings via Penalised Qubitized Walks: Spectral Filtering and Circuit Implementation
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915983258550272 |
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| author | Carrasco-Arango, Miguel Badia, Rosa M. Garcia-Saez, Artur |
| author_facet | Carrasco-Arango, Miguel Badia, Rosa M. Garcia-Saez, Artur |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15179 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum Metropolis-Hastings via Penalised Qubitized Walks: Spectral Filtering and Circuit Implementation Carrasco-Arango, Miguel Badia, Rosa M. Garcia-Saez, Artur Quantum Physics 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. |
| title | Quantum Metropolis-Hastings via Penalised Qubitized Walks: Spectral Filtering and Circuit Implementation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2604.15179 |