Stochastic simulation of quantum systems

Mohan Sarovar, Matthew Grace

Thomas J. Elliott, Mile Gu

By exploiting the complexity intrinsic to quantum dynamics, quantum technologies promise a host of computational advantages. One such advantage lies in the field of stochastic modeling, where it has been shown that quantum stochastic simulators can operate with a lower memory overhead than their best classical counterparts. This advantage is particularly pronounced for continuous-time stochastic processes; however, the corresponding quantum stochastic simulators heretofore prescribed operate only on a quasi-continuous-time basis and suffer an ever-increasing circuit complexity with increasing temporal resolution. Here, by establishing a correspondence with quantum trajectories (a method for modeling open quantum systems), we show how truly continuous-time quantum stochastic simulators can be embedded in such open quantum systems, bridging this gap and obviating previous constraints. We further show how such an embedding can be made for discrete-time stochastic processes, which manifest as jump-only trajectories, and discuss how viewing the correspondence in the reverse direction provides a means of studying structural complexity in quantum systems themselves. Published by the American Physical Society 2024

C. V. Heer

Radim Filip

The stochastic simulations of quantum evolution are introduced, alternatively to the Ito-stochastic simulations, for the normal, symmetrical and antinormal ordering in the double dimensional phase-space. The nonclassical effects in the linearized parametric amplifier can be very well simulated in contrast to the collapses-revivals effect in the nonlinear version of amplifier. It is illustrated that the stochastic simulation method using the continuous variables cannot be used if the discreteness of light has pronounced influence on the dynamics.

Radim Filip

The stochastic simulations of quantum evolution are introduced, alternatively, to the Ito-stochastic simulations, for the normal, symmetrical and antinormal ordering in the double-dimensional phase space. The nonclassical effects in the linearized parametric amplifier can be very well simulated in contrast to the collapses-revivals effect in a nonlinear version, which is stimulated by the discreteness of light. The reason is that the stochastic simulations use the continuous variables, whereas the quantum noise in nonlinear systems cannot generally be treated continuously.

N. G. van Kampen