Efficient simulation of quantum evolution using dynamical coarse-graining

TL;DR

This paper introduces a new method for efficiently simulating the evolution of specific quantum observables by leveraging a time-scale separation in open-system dynamics, using stochastic nonlinear Schrödinger equations.

Contribution

It proposes a novel coarse-graining scheme that exploits time-scale separation to simulate quantum evolution of observables via open-system dynamics and stochastic equations.

Findings

Time-scale separation enables efficient simulation of quantum observables.

GCS are stable solutions of the stochastic nonlinear Schrödinger equation.

The method applies to Hamiltonians linear in algebra elements.

Abstract

A novel scheme to simulate the evolution of a restricted set of observables of a quantum system is proposed. The set comprises the spectrum-generating algebra of the Hamiltonian. The idea is to consider a certain open-system evolution, which can be interpreted as a process of weak measurement of the distinguished observables performed on the evolving system of interest. Given that the observables are "classical" and the Hamiltonian is moderately nonlinear, the open system dynamics displays a large time-scales separation between the dephasing of the observables and the decoherence of the evolving state in the basis of the generalized coherent states (GCS), associated with the spectrum-generating algebra. The time scale separation allows the unitary dynamics of the observables to be efficiently simulated by the open-system dynamics on the intermediate time-scale.The simulation employs unraveling of the corresponding master equations into pure state evolutions, governed by the stochastic nonlinear Schroedinger equantion (sNLSE). It is proved that GCS are globally stable solutions of the sNLSE, if the Hamilonian is linear in the algebra elements.