Discrete-Time Quantum Random Walk for Epidemiological Modeling

Fuente: arXiv
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Autori principali: Manna, Sayan, Kowshik, Nikhil, Pal, Sudebkumar Prasant
Natura: Preprint
Pubblicazione: 2025
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author Manna, Sayan
Kowshik, Nikhil
Pal, Sudebkumar Prasant
author_facet Manna, Sayan
Kowshik, Nikhil
Pal, Sudebkumar Prasant
contents We introduce a discrete-time quantum random walk (QRW) framework for spatial epidemic modelling on a two-dimensional square lattice and compare its dynamics to classical random-walk SIR models. In our model, each infected site spawns a quantum walker whose coherent evolution (controlled by an amplitude-splitting coin and conditional shifts) can infect visited susceptible sites with probability $p$ and persists for a lifetime of $τ$ steps. We perform extensive quantum simulations on finite lattices and compute the basic reproduction number $R_0$ across a broad grid of $(p,τ)$ values. Results show that QRW dynamics interpolate between diffusive and super-diffusive regimes: at low $p$ the QRW reproduces classical-like $R_0$, while at higher $p$ and $τ$ ballistic propagation and interference produce markedly larger $R_0$ and non-Gaussian spatial profiles. We compare the QRW $R_0$ range to empirical estimates from historical outbreaks and discuss parameter regimes where QRW offers a closer qualitative match than classical diffusion. We conclude that QRWs provide a flexible, conceptually novel toy model for exploring rapid or heavy-tailed epidemic spread.
format Preprint
id arxiv_https___arxiv_org_abs_2509_05795
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Discrete-Time Quantum Random Walk for Epidemiological Modeling
Manna, Sayan
Kowshik, Nikhil
Pal, Sudebkumar Prasant
Quantum Physics
We introduce a discrete-time quantum random walk (QRW) framework for spatial epidemic modelling on a two-dimensional square lattice and compare its dynamics to classical random-walk SIR models. In our model, each infected site spawns a quantum walker whose coherent evolution (controlled by an amplitude-splitting coin and conditional shifts) can infect visited susceptible sites with probability $p$ and persists for a lifetime of $τ$ steps. We perform extensive quantum simulations on finite lattices and compute the basic reproduction number $R_0$ across a broad grid of $(p,τ)$ values. Results show that QRW dynamics interpolate between diffusive and super-diffusive regimes: at low $p$ the QRW reproduces classical-like $R_0$, while at higher $p$ and $τ$ ballistic propagation and interference produce markedly larger $R_0$ and non-Gaussian spatial profiles. We compare the QRW $R_0$ range to empirical estimates from historical outbreaks and discuss parameter regimes where QRW offers a closer qualitative match than classical diffusion. We conclude that QRWs provide a flexible, conceptually novel toy model for exploring rapid or heavy-tailed epidemic spread.
title Discrete-Time Quantum Random Walk for Epidemiological Modeling
topic Quantum Physics
url https://arxiv.org/abs/2509.05795