发表机构
University of Maryland, College Park; Electrical & Computer Engineering Department, UCLA; Department of Electrical and Computer Engineering, Princeton University; QuEra Computing Inc.; Department of Physics, Stanford University（马里兰大学帕克分校; 加州大学洛杉矶分校电气与计算机工程系; 普林斯顿大学电气与计算机工程系; QuEra计算公司; 斯坦福大学物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明，几何局部 noisy 量子电路在深度独立于系统尺寸时即可被经典计算机多项式时间近似采样，通过聚合物模型和簇展开实现。
AI 中文摘要
开发 noisy 量子电路的经典模拟算法对于界定量子优势的极限至关重要。现有的针对一般电路的经典采样方法要求电路深度随系统尺寸对数增长，以便噪声将全局输出态驱动到接近平凡态。在这里，我们证明噪声在独立于系统尺寸的深度上的局部累积已经足够。具体来说，我们证明任何由幺正操作组成并穿插强度为 $p$ 的单量子比特去极化噪声的几何局部电路，在 $\Omega(p^{-1} \log p^{-1})$ 深度之后，可以从多项式时间的经典计算机上近似采样。我们的证明将电路的输出态映射到统计力学中的聚合物模型，并将收敛的簇展开与去极化信道的超收缩性相结合。
英文摘要
Developing classical simulation algorithms for noisy quantum circuits is essential to delineating the limits of quantum advantage. Existing classical sampling approaches for general circuits require circuit depths to grow logarithmically with system size, so that noise drives the global output state close to a trivial state. Here we show that local accumulation of noise at a depth independent of system size is already sufficient. Specifically, we prove that any geometrically local circuit composed of unital operations and interspersed with single-qubit depolarizing noise of strength $p$ after $Θ(p^{-1} \log p^{-1})$ depth can be approximately sampled from a polynomial-time classical computer. This generalizes existing results that impose anticoncentration assumptions or non-universal gate sets in order to obtain a classical sampler at such shallow depths. Our proof maps the output state of the circuit to a polymer model in statistical mechanics, and combines a convergent cluster expansion with hypercontractivity of the depolarizing channel.
