Decoherence Limits the Cost to Simulate an Anharmonic Oscillator

TL;DR

Decoherence can simplify the simulation of an anharmonic oscillator's quantum dynamics by suppressing quantum interference, effectively recovering semiclassical behavior and impacting quantum advantage in noisy systems.

Contribution

This work demonstrates how decoherence enhances simulation efficiency by aligning open quantum dynamics with semiclassical approximations, revealing complex interactions between quantum and open system effects.

Findings

Decoherence suppresses quantum interference in phase space.

Open dynamics approximate semiclassical truncated Wigner dynamics.

Regression to semiclassical behavior increases with initial amplitude.

Abstract

We study how decoherence increases the efficiency with which we can simulate the quantum dynamics of an anharmonic oscillator, governed by the Kerr effect. As decoherence washes out the fine-grained subPlanck structure associated with phase-space quantum interference in the closed quantum system, open quantum dynamics can be more efficiently simulated using a coarse-grained finite-difference numerical integration. We tie this to the way in which decoherence recovers the semiclassical truncated Wigner approximation (TWA), which strongly differs from the exact closed-system dynamics at times when quantum interference leads to cat states and more general superpositions of coherent states. The regression in quadrature measurement statistics to semiclassical dynamics becomes more pronounced as the initial amplitude of the oscillator grows, with implications for the quantum advantage that might be accessible as system size grows in noisy quantum devices. Lastly, we show that this regression does not have the form of a convex noise model, such as for a depolarizing noise channel. Instead, closed quantum system effects interact with the open system effects, giving rise to distinct open system behavior.