论文标题
用砖瓦电路进行阴影估算的封闭式分析表达式
Closed-form analytic expressions for shadow estimation with brickwork circuits
论文作者
论文摘要
可以使用经典阴影估算量子系统的属性，该阴影基于一务工的随机组合实现测量值。实际实现最初是为全球Clifford Unitaries和单Qubit Clifford Gates的产品而得出的，仅限于中等数量的Qubits的后者方案。除了本地门外，在实验上，具有两个局部门的非常短的随机电路的准确实现仍然是可行的，因此，对于在近期应用中实施测量值而言，这很有趣。在这项工作中，我们使用具有两层平行的两层HAAR-RANDOM（或Clifford）单位的砖瓦电路来得出封闭形式的分析表达式，以进行阴影估计。除了构建经典影子外，我们的结果还产生了样本复杂性保证，以估算Pauli可观察到。然后，我们将阴影估计的性能与砖砌电路与使用本地Clifford统一的方法进行比较，并在足够多的量子器上支持可观察到的可观察结果时发现了改善的样本复杂性。
Properties of quantum systems can be estimated using classical shadows, which implement measurements based on random ensembles of unitaries. Originally derived for global Clifford unitaries and products of single-qubit Clifford gates, practical implementations are limited to the latter scheme for moderate numbers of qubits. Beyond local gates, the accurate implementation of very short random circuits with two-local gates is still experimentally feasible and, therefore, interesting for implementing measurements in near-term applications. In this work, we derive closed-form analytical expressions for shadow estimation using brickwork circuits with two layers of parallel two-local Haar-random (or Clifford) unitaries. Besides the construction of the classical shadow, our results give rise to sample-complexity guarantees for estimating Pauli observables. We then compare the performance of shadow estimation with brickwork circuits to the established approach using local Clifford unitaries and find improved sample complexity in the estimation of observables supported on sufficiently many qubits.
