发表机构
Seoul National University; Korea Institute for Advanced Study（首尔大学; 韩国高等科学研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种结合克利福德和与准概率稳定子模拟的框架，通过自适应方差估计终止模拟，将低方差区域样本复杂度从二次降为线性，并在随机电路和T掺杂电路中验证优势。
AI 中文摘要
量子电路的经典可模拟性在表征和量化量子计算优势中起着核心作用。通常，非克利福德门的存在会给经典估计可观测量期望值带来指数级的运行时间开销。在本工作中，我们引入了一个高效的模拟框架，该框架将基于克利福德和（sum-over-Clifford）方法与基于准概率的稳定子模拟相结合，以直接估计期望值。为了优化效率，我们加入了一种通过方差估计协议进行的电路自适应缩减，一旦经验置信界足以保证规定的误差容限，该协议即终止模拟。我们的方法规避了过于保守的霍夫丁不等式，从而在低方差区域将逐门稳定子程度的依赖性从二次降低为线性，同时保持与先前方法相同的空间复杂度。我们明确证明了随机量子电路和T掺杂克利福德电路的样本复杂度降低，并在量子近似优化算法和量子核方法中实证验证了这些优势。
英文摘要
Classical simulability of quantum circuits plays a central role in characterizing and quantifying quantum computational advantage. Typically, the presence of non-Clifford gates introduces an exponential runtime overhead for classically estimating expectation values of observables. In this work, we introduce an efficient simulation framework that integrates the sum-over-Clifford method with quasi-probability-based stabilizer simulation to directly estimate expectation values. To optimize efficiency, we incorporate a circuit-adaptive reduction via variance estimation protocol, which terminates simulations once an empirical confidence bound is sufficient to guarantee the prescribed error tolerance. Our method circumvents overly conservative Hoeffding's inequality, thereby reducing the dependence on the gate-wise stabilizer extent from quadratic to linear in the low-variance regime, while maintaining the same space complexity as previous approaches. We explicitly prove the sample-complexity reduction for random quantum circuits and T-doped Clifford circuits and also empirically validate these advantages in the quantum approximate optimization algorithm and quantum kernel method.
