Quantum chemistry on a budget: resource estimation and measurement optimization for near-term VQE

Finding molecular groundstates using the variational quantum eigensolver (VQE) is one of the main proposed use-cases of NISQ devices. Yet significant hurdles remain to develop practical, useful implementations for existing quantum computing hardware. In particular, the number of electronic excitations varies quadratically with the number of active electrons, leading to deep quantum circuits even for simple molecules. Canonical VQE have been extended to schemes that adaptively select the excitations most contributing to the final groundstate. However, even given an effective scheme for finding these excitations, optimizing their parameters remains computationally expensive and noisy due to the large measurement overhead required to compute the expectation value of realistic target Hamiltonians.

A variety of schemes have been proposed to try to lower the number of measurements needed to perform this optimization. In this work, we use finite-shots simulation to estimate the benefit of each of these and their feasibility for a variety of “benchmark” molecular systems.