Year: 2025
Type: preprint
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 δ in the system-state with O(N t(N t/δ) o( 1)) gates, O(t(N t/δ) o( 1)) parallelized circuit depth and Õ(N (N t/δ) 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.
Source: MPG.PuRe (Max Planck Society)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7140258564