Stochastic phase-space simulation of multimode cat states via the positive-P representation

TL;DR

This paper introduces a positive-P phase-space method for simulating the transient dynamics of multimode Schrödinger cat states in dissipative resonator arrays, enabling larger system simulations than traditional approaches.

Contribution

The paper develops an exact stochastic differential equation approach using the positive-P representation for large-scale open quantum systems with non-Gaussian states.

Findings

Simulated networks up to 21 sites.

Identified computational instability in parity estimation.

Provided scalable simulation pathway for large quantum systems.

Abstract

We present a comprehensive study of the transient dynamics of multimode Schr\"odinger cat states in dissipatively coupled resonator arrays using the positive-P phase-space method. By employing the positive-P representation, we derive the exact stochastic differential equations governing the system's dynamics, enabling the simulation of system sizes significantly larger than those accessible via direct master equation simulation. We demonstrate the utility of this method by simulating transient dynamics for networks up to N=21 sites. Furthermore, we critically examine the method's usefulness and limitations, specifically highlighting the computational instability encountered when estimating the state parity in the systems. Our results provide a pathway for scalable simulations of non-Gaussian states in large open quantum systems.