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arXiv:2512.22950

Effective Kinetic Monte Carlo for a Quantum Epidemic Process

Alexander Sturges, Hugo Smith, Matteo Marcuzzi

cond-mat.stat-mechquant-phSubmitted Dec 28, 2025• Announced Dec 30, 2025• 0 citations
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Abstract

Inspired by previous works on epidemic-like processes in open quantum systems, we derive an elementary quantum epidemic model that is simple enough to be studied via Quantum Jump Monte Carlo simulations at reasonably large system sizes. We show how some weak symmetries of the Lindblad equation allow us to map the dynamics onto a classical Kinetic Monte Carlo; this simplified, effective dynamics can be described via local stochastic jumps coupled with a local deterministic component. Simulations are then used to reconstruct a phase diagram which displays stationary features completely equivalent to those of completely classical epidemic processes, but richer dynamics with multiple, recurrent waves of infection.

Comments
38 paages (62 including Appendices and Bibliography); 25 figures (28 counting the three in the Appendices)

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Abstract The formulation of the dynamics of open quantum systems by means of stochastic processes in Hilbert space leads to efficient Monte–Carlo simulation techniques which are introduced and examined in this chapter. Depending on whether the stochastic process is a piecewise deterministic process or a diffusion process, the corresponding individual realizations consist of intervals of deterministic evolution periods interrupted by instantaneous quantum jumps, or of continuous, nowhere differentiable paths. Various Monte Carlo algorithms for both types of processes are described in detail, and their convergence behaviour and their numerical performance is investigated for a number of applications, such as the damped harmonic oscillator, the driven two-level system, and the damped driven Morse oscillator.
We develop an extension of the Monte Carlo wave function approach that unambiguously identifies dynamical entanglement in general composite, open systems. Our algorithm performs tangential projections onto the set of separable states, leading to classically correlated quantum trajectories. By comparing this restricted evolution with the unrestricted one, we can characterize the entangling capabilities of quantum channels without making use of input-output relations. Moreover, applying this method is equivalent to solving the nonlinear master equation in Lindblad form introduced in \cite{PAH24} for two-qubit systems. We here extend these equations to multipartite systems of qudits, describing non-entangling dynamics in terms of a stochastic differential equation. We identify the impact of dynamical entanglement in open systems by applying our approach to several correlated decay processes. Therefore, our methodology provides a complete and ready-to-use framework to characterize dynamical quantum correlations caused by arbitrary open-system processes.