Obtaining the expectation value of an observable on a quantum computer is a crucial step in the variational quantum algorithms. For complicated observables such as molecular electronic Hamiltonians, a common strategy is to present the observable as a linear combination of measurable fragments. The main problem of this approach is a large number of measurements required for accurate sampling of the observable's expectation value. We consider several partitioning schemes based on grouping of commuting multi-qubit Pauli products with the goal of minimizing the number of measurements. Three main directions are explored: 1) grouping commuting operators using the greedy approach, 2) involving non-local unitary transformations for measuring, and 3) taking advantage of compatibility of some Pauli products with several measurable groups. The last direction gives rise to a general framework that not only provides improvements over previous methods but also connects measurement grouping approaches with recent advances in techniques of shadow tomography. Following this direction, we develop two new measurement schemes that achieve a severalfold reduction in the number of measurements for a set of model molecules compared to previous state-of-the-art methods.
Direct fidelity estimation through joint fiducial grouping
ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology（光子科学研究所，巴塞罗那科技研究院）；Centre for Quantum Technologies, National University of Singapore（量子技术中心，新加坡国立大学）
Mean-State Entropy Hierarchies and Classical Communication through Quantum Convolutions
Central South University（中南大学）；Harbin Engineering University（哈尔滨工程大学）；Changsha University of Science and Technology（长沙理工大学）；Capital Normal University（首都师范大学）；Zhejiang University（浙江大学）
