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Current implementations of the Variational Quantum Eigensolver (VQE)technique for solving the electronic structure problem involve splitting thesystem qubit Hamiltonian into parts whose elements commute within their singlequbit subspaces. The number of such parts rapidly grows with the size of themolecule, this increases the uncertainty in the measurement of the energyexpectation value because elements from different parts need to be measuredindependently. To address this problem we introduce a more efficientpartitioning of the qubit Hamiltonian using fewer parts that need to bemeasured separately. The new partitioning scheme is based on two ideas: 1)grouping terms into parts whose eigenstates have a single-qubit productstructure, and 2) devising multi-qubit unitary transformations for theHamiltonian or its parts to produce less entangled operators. The firstcondition allows the new parts to be measured in the number of involved qubitconsequential one-particle measurements. Advantages of the new partitioningscheme resulting in several-fold reduction of separately measured terms areillustrated on the H2 and LiH problems.

Revising measurement process in the variational quantum eigensolver: Is it possible to reduce the number of separately measured operators?