Model Order Reduction for Open Quantum Systems Based on Measurement-adapted Time-coarse Graining

TL;DR

This paper introduces a measurement-adapted time-coarse graining method for model order reduction in open quantum systems, enabling efficient long-time simulations while maintaining essential dynamics.

Contribution

The authors develop a novel reduction technique based on measurement resolution, providing a rigorous effective quantum master equation with analytical parameters for complex quantum systems.

Findings

Derived the fourth-order effective quantum master equation for a superconducting qubit.

Higher-order corrections reveal potential new phenomena beyond previous models.

Method improves computational efficiency for long-time quantum system simulations.

Abstract

Model order reduction encompasses mathematical techniques aimed at reducing the complexity of mathematical models in simulations while retaining the essential characteristics and behaviors of the original model. This is particularly useful in the context of large-scale dynamical systems, which can be computationally expensive to analyze and simulate. Here, we present a model order reduction technique to reduce the time complexity of open quantum systems, grounded in the principle of measurement-adapted coarse-graining. This method, governed by a coarse-graining time scale $\tau$ and the spectral band center $\omega_0$, organizes corrections to the lowest-order model which aligns with the RWA Hamiltonian in certain limits, and rigorously justifies the resulting effective quantum master equation (EQME). The focus on calculating to a high degree of accuracy only what can be resolved by the measurement introduces a principled regularization procedure to address singularities and generates low-stiffness models suitable for efficient long-time integration. Furthermore, the availability of the analytical form of the EQME parameters significantly boosts the interpretive capabilities of the method. As a demonstration, we derive the fourth-order EQME for a challenging problem related to the dynamics of a superconducting qubit under high-power dispersive readout in the presence of a continuum of dissipative waveguide modes. This derivation shows that the lowest-order terms align with previous results, while higher-order corrections suggest new phenomena.