噪声诱导的经典相：在最优解纠缠随机量子电路中的表现

中文摘要 AI 辅助

我们研究了开放量子动力学的经典可模拟性，使用掺杂非克利福德相位旋转并受局部噪声影响的随机克利福德电路。我们将动力学解纠缠为随机量子轨迹，并使用克利福德增强的矩阵乘积态进行模拟，引入了一种量化所需经典资源的模拟成本。通过对随机解纠缠方式优化该成本，我们识别出噪声诱导的经典相：在这些扩展的参数区域内，动力学可以在任意电路深度下被克利福德操作完全解纠缠。它们的存在取决于噪声模型和具体的解纠缠方式。利用量子通道的几何表示，我们解析地确定了一类广泛噪声模型的最优解纠缠方式，数值模拟证实了预测的相边界。我们进一步将最优成本与通道的与解纠缠无关的非稳定子资源联系起来，并表明，连同轨迹分辨的纠缠和非稳定子资源，它可以区分不同的动力学区域。最后，我们证明这些经典相在平均密度矩阵描述中消失，因为那里不再有解纠缠自由度。我们的结果表明，噪声随机电路中经典性的出现取决于用于探测它的测量方案，并为驱动-耗散动力学经典可模拟性的进一步研究铺平了道路。

英文摘要

We study the classical simulability of open quantum dynamics using random Clifford circuits doped with non-Clifford phase rotations and subject to local noise. We unravel the dynamics into stochastic quantum trajectories simulated with Clifford-augmented matrix product states, and introduce a simulation cost that quantifies the classical resources required. Optimizing this cost over stochastic unravelings, we identify noise-induced classical phases: extended parameter regions in which the dynamics can be fully disentangled by Clifford operations at arbitrary circuit depth. Their existence depends on both the noise model \emph{and} the unraveling. Using a geometric representation of quantum channels, we analytically determine optimal unravelings for a broad class of noise models, with numerical simulations confirming the predicted phase boundaries. We further relate the optimal cost to the unraveling-independent nonstabilizerness of the channel and show that, together with trajectory-resolved entanglement and nonstabilizerness, it classifies distinct dynamical regimes. Finally, we show that these classical phases disappear in the averaged density-matrix description, where no unraveling freedom remains. Our results show that the emergence of classicality in noisy random circuits depends on the measurement scheme adopted to probe it, and paves the way to further studies on the classical simulability of driven-dissipative dynamics.

发表机构

• Institute of Physics and Center for Quantum Science and Engineering, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理研究所与量子科学与工程中心）

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