Theory Seminar: Optimizing digital quantum simulation of open quantum lattice models

Xiehang Yu
Theory Seminar at the Herbert-Walther Hörsaal, MPQ
Wednesday November 5th, 11:00 (MEZ)

Abstract: Many-body systems arising in condensed matter physics and quantum optics inevitably couple to the environment and need to be modeled 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.