发表机构
Ecole Polytechnique Fédérale de Lausanne; Institute of Physics, Ecole Polytechnique Fédérale de Lausanne; Centre for Quantum Science and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院; 洛桑联邦理工学院物理研究所; 洛桑联邦理工学院量子科学与工程中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明耗散（如泡利噪声）可指数抑制高权重可观测量分量，从而加速开放量子系统的量子和经典模拟，实现与系统大小无关的Trotter步长，并展示弱耗散下潜在的多项式量子优势。
AI 中文摘要
模拟开放量子系统揭示了环境耦合如何影响弛豫、激发输运以及量子关联的动力学。在量子硬件上，耗散通道增加了操作，似乎会增加成本。然而，我们表明，包括退极化在内的一类广泛的泡利噪声，可以通过指数级抑制海森堡演化的可观测量中的高权重分量，来简化量子和经典模拟。对于有界度的林德布拉德动力学，这允许在估计局部可观测量时采用与系统大小无关的Trotter步长。将这种压缩与Richardson外推相结合，我们提供了相对于传播可观测量的2-范数的经典和量子误差界。这些界为随机输入态或作用于固定态和受控（超时序）关联函数的随机哈密顿量提供了高概率的期望值保证。具体而言，我们表明，在时间$t$时，局部可观测量的期望值可以使用最大深度为$O\\!\left(\left[1+\left(t/\gamma\right)^{3/2}\right]\log^2(1/\varepsilon)\right)$的电路估计到精度$\varepsilon$，该深度与系统大小$n$无关。在经典方面，我们表明，对于每个固定的$\gamma>0$，稀疏泡利传播在$n$、$t$和$1/\varepsilon$的多项式时间内运行，在弱耗散极限中多项式次数为$O(1/\gamma)$。我们的量子与经典上界之间的差距为随着耗散减弱而出现的实质性多项式量子优势留下了空间，这一观察也得到了我们数值结果的进一步支持。
英文摘要
Simulating open quantum systems reveals how environmental coupling shapes relaxation, excitation transport, and the dynamics of quantum correlations. On quantum hardware, dissipative channels add operations and might seem to increase cost. However, we show that a broad class of Pauli noise, including depolarization, can ease quantum and classical simulation by exponentially suppressing high-weight components of Heisenberg-evolved observables. For bounded-degree Lindblad dynamics, this permits system-size-independent Trotter steps when estimating local observables. Combining this compression with Richardson extrapolation, we provide classical and quantum error bounds with respect to the 2-norm of the propagated observable. These give high-probability expectation-value guarantees for random input states or random Hamiltonians acting on a fixed state and control (out-of-time-order) correlators. Concretely, we show that expectation values of local observables at time $t$ can be estimated to accuracy $\varepsilon$ using circuits of maximum depth $O\!\left(\left[1+\left(t/γ\right)^{3/2}\right]\log^2(1/\varepsilon)\right)$, independent of the system size $n$. Classically, we show that sparse Pauli propagation runs in time polynomial in $n$, $t$ and $1/\varepsilon$ for every fixed $γ>0$, with polynomial degree $O(1/γ)$ in the weak dissipation limit. The gap between our quantum and classical upper bounds leaves room for a substantial polynomial quantum advantage as dissipation weakens, an observation further supported by our numerical results.
Comments10 + 64 pages, 2 figures
