A Physics-Informed Measurement Protocol for Expectation Values of Fermionic Observables

Abstract

A central roadblock in the realization of Variational Quantum Eigensolvers on quantum hardware is the high overhead associated with measurement repetitions, which hampers the simulation of complex systems, such as mid- and large-sized molecules. We propose a novel measurement proto- col which relies on computing an approximation of the Hamiltonian expectation value. It involves measuring cheap grouped operators directly and estimating the residual elements through iterative measurements of new grouped operators in different bases, with the process being truncated at a certain stage. The measured elements are defined by the Hard-Core Bosonic approximation, which encode electron-pair annihilation and creation operators. These can be decomposed into three self- commuting groups to measure simultaneously. Applied to molecular systems, the method achieves a reduction of 30% to 80% in the number of measurement and gates depth in the measuring circuits compared to state-of-the-art methods. This provides a scalable and cheap measurement protocol, advancing the application of variational approaches for simulating physical systems