We consider the problem of jointly estimating expectation values of many Pauli observables, a crucial subroutine in variational quantum algorithms. Starting with randomized measurements, we propose an efficient derandomization procedure that iteratively replaces random single-qubit measurements with fixed Pauli measurements; the resulting deterministic measurement procedure is guaranteed to perform at least as well as the randomized one. In particular, for estimating any $L$ low-weight Pauli observables, a deterministic measurement on only of order $\log(L)$ copies of a quantum state suffices. In some cases, for example when some of the Pauli observables have a high weight, the derandomized procedure is substantially better than the randomized one. Specifically, numerical experiments highlight the advantages of our derandomized protocol over various previous methods for estimating the ground-state energies of small molecules.
翻译:我们考虑了共同估计许多保利可观测物的预期值的问题,这是量子算法中关键的次常规。从随机测量开始,我们建议一种高效的去随机化程序,以固定的保利测量物取代随机的单方位测量物;由此产生的确定性测量程序保证至少和随机地进行。特别是,对于估算任何低重量的保利可观测物,仅对量子值的顺序($log(L))副本进行确定性测量。在某些情况下,例如,某些保利可观测物的重量较高,取消性程序大大优于随机性测量物。具体地说,数字实验凸显了我们解禁协议相对于以往估算小分子地面能量的各种方法的优势。