How to really measure operator gradients in ADAPT-VQE

Abstract

ADAPT-VQE is a leading variational quantum algorithm as it circumvents the choice-of-ansatz conundrum by iteratively growing compact and arbitrarily accurate problem-tailored ansätze. However, for molecular Hamiltonians and hardware-efficient operator pools, the gradient-measurement step of the algorithm requires the estimation of $\mathcal{O}(N^8)$ observables, which may represent a bottleneck for relevant system sizes on real devices. We present an efficient strategy for measuring the gradients of the three best-performing hardware-efficient operator pools by partitioning the required observables into $\mathcal{O}(N^3)$-sized sets of commuting Paulis that can be simultaneously measured with an at most $N-3$ CNOT overhead. We argue that our approach is robust to shot-noise effects and show that measuring the pool gradients is, in fact, not $\mathcal{O}(N^4)$, but only about $4N$ times as expensive as measuring the energy once. Our proposed measurement strategy significantly ameliorates the measurement overhead of ADAPT-VQE and brings us one step closer to practical implementations on real devices.