Optimizing digital quantum simulation of open quantum lattice models

• URL: http://arxiv.org/abs/2509.02268v2
• Date: Sun, 07 Sep 2025 10:21:38 GMT
• Title: Optimizing digital quantum simulation of open quantum lattice models
• Authors: Xie-Hang Yu, Hongchao Li, J. Ignacio Cirac, Rahul Trivedi,
• Abstract summary: We address the problem of simulating geometrically local many-body open quantum systems interacting with a stationary Gaussian environment.<n>We develop near-optimal algorithms that attain a simulation error $delta$ in the system-state with $mathcalO(Nt(Nt/delta)o(1))$ gates, $mathcalO(t(Nt/delta)o(1))$ ancillas.
• Score: 3.761360709981958
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Many-body systems arising in condensed matter physics and quantum optics inevitably couple to the environment and need to be modelled as open quantum systems. While near-optimal algorithms have been developed for simulating many-body quantum dynamics, algorithms for their open system counterparts remain less well investigated. We address the problem of simulating geometrically local many-body open quantum systems interacting with a stationary Gaussian environment. Under a smoothness assumption on the system-environment interaction, we develop near-optimal algorithms that, for a model with $N$ spins and evolution time $t$, attain a simulation error $\delta$ in the system-state with $\mathcal{O}(Nt(Nt/\delta)^{o(1)})$ gates, $\mathcal{O}(t(Nt/\delta)^{o(1)})$ parallelized circuit depth and $\tilde{\mathcal{O}}(N(Nt/\delta)^{o(1)})$ ancillas. We additionally show that, if only simulating local observables is of interest, then the circuit depth of the digital algorithm can be chosen to be independent of the system size $N$. This provides theoretical evidence for the utility of these algorithms for simulating physically relevant models, where typically local observables are of interest, on pre-fault tolerant devices. Finally, for the limiting case of Markovian dynamics with commuting jump operators, we propose two algorithms based on sampling a Wiener process and on a locally dilated Hamiltonian construction, respectively. These algorithms reduce the asymptotic gate complexity on $N$ compared to currently available algorithms in terms of the required number of geometrically local gates.

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