A numerical method is proposed for simulation of composite open quantum systems. It is based on Lindblad master equations and adiabatic elimination. Each subsystem is assumed to converge exponentially towards a stationary subspace, slightly impacted by some decoherence channels and weakly coupled to the other subsystems. This numerical method is based on a perturbation analysis with an asymptotic expansion. It exploits the formulation of the slow dynamics with reduced dimension. It relies on the invariant operators of the local and nominal dissipative dynamics attached to each subsystem. Second-order expansion can be computed only with local numerical calculations. It avoids computations on the tensor-product Hilbert space attached to the full system. This numerical method is particularly well suited for autonomous quantum error correction schemes. Simulations of such reduced models agree with complete full model simulations for typical gates acting on one and two cat-qubits (Z, ZZ and CNOT) when the mean photon number of each cat-qubit is less than 8. For larger mean photon numbers and gates with three cat-qubits (ZZZ and CCNOT), full model simulations are almost impossible whereas reduced model simulations remain accessible. In particular, they capture both the dominant phase-flip error-rate and the very small bit-flip error-rate with its exponential suppression versus the mean photon number.

翻译：提出了一种用于模拟复合开放量子系统的数值方法，该方法基于林德布拉德主方程和绝热消除。假设每个子系统在受退相干通道轻微影响且与其他子系统弱耦合的情况下，指数收敛至驻留子空间。该数值方法基于含渐近展开的摄动分析，利用降维形式的慢动力学，并依赖于每个子系统局部标称耗散动力学的不变算子。二阶展开仅通过局部数值计算即可实现，避免了在全系统张量积希尔伯特空间上的计算。此方法特别适用于自主量子纠错方案。当每个猫量子比特的平均光子数小于8时，针对单比特和双比特门（Z、ZZ和CNOT）的降阶模型模拟与完整全模型模拟结果一致。对于更大平均光子数及三比特门（ZZZ和CCNOT），全模型模拟几乎不可行，而降阶模型模拟仍可进行。特别地，降阶模型能同时捕获主导的相位翻转错误率和极小的比特翻转错误率，其中比特翻转错误率随平均光子数呈指数抑制。