Reducing the cost of energy estimation in the Variational Quantum Eigensolver through robust amplitude estimation

Quantum computers promise to solve previously intractable problems in chemistry and materials. Recent work proposes to use noisy intermediate-scale quantum devices to achieve quantum advantage in the near future. However, a critical subroutine known as expectation value estimation have proven to be a bottleneck in these approaches. Traditional expectation value estimation in the Variational Quantum Eigensolver (VQE) algorithm proceeds by averaging and is thus plagued by an inverse square dependence on the desired absolute precision. This is a considerable obstacle to quantum chemistry applications, which require a fixed absolute precision regardless of the size of the molecular system considered. Previous work has shown that even with measurement reduction techniques such as grouping and Hamiltonian factorization, the runtime to obtain accurate energies with VQE on idealized devices were impractical, thus compromising near-terms prospects of quantum advantage in quantum chemistry. Here, we investigate how robust amplitude estimation can mitigate this issue by extracting more information with each measurement. We estimate minimum hardware parameters needed to achieve quantum advantage and show numerically a reduction in total runtime as device fidelities improve.