发表机构
The University of Tokyo; University of Manchester（东京大学; 曼彻斯特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明在量子信道学习中，访问Stinespring膨胀酉算子及其逆算子相比黑盒访问，能以指数级更少的查询次数估计最优平均门保真度，并排除通用模拟器的存在。
AI 中文摘要
我们提出一个量子信道学习任务，该任务在两种访问模型之间展现出查询复杂度（以量子比特数量计）的指数级分离：i) 黑盒信道访问，以及 ii) 访问信道的Stinespring膨胀酉算子及其逆算子。我们考虑学习未知信道与酉信道集合的接近程度这一任务。该接近程度由最优平均门保真度（OAGF）刻画，其定义为在所有酉信道上最大化的平均门保真度。对于常数Kraus秩和维度为polylog(d)的膨胀环境，我们提供一种算法，该算法使用对Stinespring膨胀酉算子及其逆算子的polylog(d)次查询，即可将OAGF估计到固定的加性精度。与此相反，在黑盒访问模型下，即使对于常数Kraus秩和常数加性精度的信道，该估计也需要至少Ω(√d)次查询。作为推论，我们排除了一个通用模拟器的存在，该模拟器仅使用对未知信道的poly(log d, q)次查询，就能近似任意q次查询算法在访问随机采样的Stinespring膨胀酉算子及其逆算子时的输出，即使误差小到足够小的常数。这些结果表明，访问系统-环境联合演化及其逆算子可以在估计量子信道的内在属性时提供指数级优势。
英文摘要
We present a learning task for quantum channels that exhibits an exponential separation in query complexity (in terms of the number of qubits) between two access models: i) black-box channel access and ii) access to a Stinespring dilation unitary of the channel along with its inverse. We consider the task of learning how close the unknown channel is to the set of unitary channels. This is characterized by the \textit{optimal average gate fidelity (OAGF)}, defined as the average gate fidelity maximized over all unitary channels. For constant Kraus rank and a dilation environment of dimension $\operatorname{polylog}(d)$, we provide an algorithm that estimates the OAGF to fixed additive accuracy using $\operatorname{polylog}(d)$ queries to the Stinespring dilation unitary and its inverse. In contradistinction, under the black-box access model, this estimation requires at least $Ω(\sqrt{d})$ queries, even for channels of constant Kraus rank and constant additive accuracy. As a corollary, we rule out a universal simulator that uses only $\operatorname{poly}(\log d,q)$ queries to the unknown channel to approximate the output of arbitrary $q$-query algorithms with access to a randomly-sampled Stinespring dilation unitary and its inverse, even to sufficiently small constant error. These results demonstrate that access to the system-environment joint evolution and its inverse can provide an exponential advantage in estimating an intrinsic property of a quantum channel.
Comments42 pages, 3 figures
