Feynman Formula for Discrete-time Quantum Walks
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909846789423104 |
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| author | Fouque, Jean-Pierre Ichiba, Tomoyuki Lam, Ka Lok |
| author_facet | Fouque, Jean-Pierre Ichiba, Tomoyuki Lam, Ka Lok |
| contents | We explicitly connect (discrete-time) quantum walks on Z with a four-state Markov additive process via a Feynman-type formula (2.5). Using this representation, we derive a relation between the spectral decomposition of the Markov additive process and the limiting density of the homogeneous quantum walk. In addition, we consider a space-time rescaling of quantum walks, which leads to a system of quantum transport PDEs in continuous time and space with a phase interaction term. Our probabilistic representation for this type of PDE offers an efficient Monte Carlo computational technique. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_12038 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Feynman Formula for Discrete-time Quantum Walks Fouque, Jean-Pierre Ichiba, Tomoyuki Lam, Ka Lok Probability Mathematical Physics 60F05, 60J10, 81-10, 81Q05 We explicitly connect (discrete-time) quantum walks on Z with a four-state Markov additive process via a Feynman-type formula (2.5). Using this representation, we derive a relation between the spectral decomposition of the Markov additive process and the limiting density of the homogeneous quantum walk. In addition, we consider a space-time rescaling of quantum walks, which leads to a system of quantum transport PDEs in continuous time and space with a phase interaction term. Our probabilistic representation for this type of PDE offers an efficient Monte Carlo computational technique. |
| title | Feynman Formula for Discrete-time Quantum Walks |
| topic | Probability Mathematical Physics 60F05, 60J10, 81-10, 81Q05 |
| url | https://arxiv.org/abs/2510.12038 |