细粒度量子计算霸权
Fine-grained quantum computational supremacy
摘要：
几个次通用量子计算模型的输出概率分布不能被经典有效地采样，除非在经典复杂性理论中出现一些不太可能的结果，例如多项式时间层次的崩溃。然而，这些被称为量子霸权的结果并不排除超多项式时间经典模拟的可能性。在本文中，我们研究了“细粒度”版本的量子霸权，排除了一些指数时间的经典模拟。首先，我们关注两个亚普适模型，即一个干净的量子比特模型（或DQC 1模型）和HC 1 Q模型。假设在细粒度的复杂性理论的某些结构，我们表明，对于任何$a>0$输出概率分布的这些模型不能被经典的采样在一个恒定的乘法误差和在$2^{(1-a)N+o(N)}$的时间，其中$N$是量子比特的数量。接下来，我们考虑通用量子计算。例如，我们考虑Clifford和$T$门上的量子计算，并表明在另一个细粒度复杂性猜想下，Clifford- $T$量子计算的输出概率分布不能在恒定乘法误差内在$2^{o(t)}$时间内经典采样，其中$t$是$T$门的数量。
英文摘要：
Output probability distributions of several sub-universal quantum computing models cannot be classically efficiently sampled unless some unlikely consequences occur in classical complexity theory, such as the collapse of the polynomial-time hierarchy. These results, so called quantum supremacy, however, do not rule out possibilities of super-polynomial-time classical simulations. In this paper, we study "fine-grained" version of quantum supremacy that excludes some exponential-time classical simulations. First, we focus on two sub-universal models, namely, the one-clean-qubit model (or the DQC1 model) and the HC1Q model. Assuming certain conjectures in fine-grained complexity theory, we show that for any $a>0$ output probability distributions of these models cannot be classically sampled within a constant multiplicative error and in $2^{(1-a)N+o(N)}$ time, where $N$ is the number of qubits. Next, we consider universal quantum computing. For example, we consider quantum computing over Clifford and $T$ gates, and show that under another fine-grained complexity conjecture, output probability distributions of Clifford-$T$ quantum computing cannot be classically sampled in $2^{o(t)}$ time within a constant multiplicative error, where $t$ is the number of $T$ gates.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
