School of Mathematical & Statistical Sciences Faculty Publications
Document Type
Article
Publication Date
9-15-2026
Abstract
Continuous-time quantum walks (CTQWs) are a fundamental tool in the development of quantum algorithms. Recently, it was shown that discretizations of p-adic Schrödinger equations give rise to continuous-time quantum Markov chains (CTQMCs); this type of Markov chain includes the CTQWs constructed using adjacency matrices of graphs as a particular case. Unlike classical continuous-time Markov chains (CTMCs), the CTQMCs studied here do not satisfy the classical Chapman–Kolmogorov equation; this is a genuine quantum effect, due to the fact that the underlying unitary evolution composes at the level of probability amplitudes rather than probabilities, and we make precise the sense in which the term ‘quantum Markov chain’ is used. In this paper, we study a large class of p-adic Schrödinger equations and the associated CTQMCs by comparing them with p-adic heat equations and the associated CTMCs. The comparison is done by a mathematical study of the mentioned equations, which requires, for instance, solving the initial value problems attached to the mentioned equations, and through numerical simulations. We conducted multiple simulations, including numerical approximations of the limiting distribution. Our simulations show that the limiting distribution of quantum Markov chains is greater than the stationary probability of their classical counterparts, for a large class of CTQMCs.
Recommended Citation
Zúñiga-Galindo, W. A., and L. F. Chacón-Cortés. "Continuous-time quantum Markov chains and discretizations of p-adic Schrödinger equations: comparisons and simulations." Journal of Statistical Mechanics: Theory and Experiment 2026, no. 9 (2026): 093401. https://doi.org/10.1088/1742-5468/ae9fd4
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication Title
Journal of Statistical Mechanics: Theory and Experiment
DOI
10.1088/1742-5468/ae9fd4
Comments
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