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：本文提出一种针对复合开放量子系统模拟的数值方法。该方法基于林德布拉德主方程与绝热消去技术。假设每个子系统在部分退相干通道的轻微影响及与其他子系统的弱耦合作用下，能够指数收敛至一个稳态子空间。本数值方法基于摄动分析与渐进展开技术，利用降维后的慢速动力学形式，并依赖于每个子系统局域标称耗散动力学的不变算子。二阶展开仅需局域数值计算即可完成，从而避免了在全系统张量积希尔伯特空间上的计算。该方法特别适用于自主量子纠错方案。对于作用在单量子比特和双猫量子比特上的典型量子门（Z门、ZZ门及CNOT门），当每个猫量子比特的平均光子数小于8时，该约化模型的模拟结果与全模型完整模拟结果一致。对于更大平均光子数及涉及三猫量子比特的量子门（ZZZ门及CCNOT门），全模型模拟几乎不可行，而约化模型模拟仍可进行。该模型尤其能够捕捉主导的相位翻转误差率以及随平均光子数呈指数抑制的极小比特翻转误差率。