标题： 基于维度最优误差界的快速量子测量层析术 显示英文标题

标题： Fast quantum measurement tomography with dimension-optimal error bounds

摘要： 我们提出了一种两步协议用于量子测量层析，该协议在经典计算处理成本上较为轻量，并且在系统维度上仍能达到最优样本复杂度。 给定来自已知探测态集合的测量数据，我们首先应用最小二乘估计来生成一个不受约束的POVM近似，然后将该估计投影到有效量子测量的集合上。 对于作用于$d$维系统的具有$L$个结果的POVM，我们证明该协议在最坏情况距离下达到误差$\epsilon$需要$\mathcal{O}(d^3 L \ln(d)/\epsilon^2)$个样本，在平均情况距离下需要$\mathcal{O}(d^2 L^2 \ln(dL)/\epsilon^2)$个样本。 我们进一步建立了任何非自适应、单拷贝POVM层析协议的两个几乎匹配的样本复杂度下界，分别为$\Omega(d^3/\epsilon^2)$和$\Omega(d^2 L/\epsilon^2)$。 因此，我们的投影最小二乘POVM层析技术在维度$d$上至对数因子是样本最优的。 当使用全局或局部2设计作为探测集合时，我们的方法具有解析形式，并且能够提供严格的非渐近误差保证。 最后，我们还在一个带有通量可调transmon量子比特的噪声超导量子计算机上进行了经验性能研究，以补充我们的发现。 显示英文摘要

摘要： We present a two-step protocol for quantum measurement tomography that is light on classical co-processing cost and still achieves optimal sample complexity in the system dimension. Given measurement data from a known probe state ensemble, we first apply least-squares estimation to produce an unconstrained approximation of the POVM, and then project this estimate onto the set of valid quantum measurements. For a POVM with $L$ outcomes acting on a $d$-dimensional system, we show that the protocol requires $\mathcal{O}(d^3 L \ln(d)/\epsilon^2)$ samples to achieve error $\epsilon$ in worst-case distance, and $\mathcal{O}(d^2 L^2 \ln(dL)/\epsilon^2)$ samples in average-case distance. We further establish two almost matching sample complexity lower bounds of $\Omega(d^3/\epsilon^2)$ and $\Omega(d^2 L/\epsilon^2)$ for any non-adaptive, single-copy POVM tomography protocol. Hence, our projected least squares POVM tomography is sample-optimal in dimension $d$ up to logarithmic factors. Our method admits an analytic form when using global or local 2-designs as probe ensembles and enables rigorous non-asymptotic error guarantees. Finally, we also complement our findings with empirical performance studies carried out on a noisy superconducting quantum computer with flux-tunable transmon qubits.