Variational quantum chemistry requires gate-error probabilities below the fault-tolerance threshold

The variational quantum eigensolver (VQE) is a leading contender for useful quantum advantages in the NISQ era. The interplay between quantum processors and classical optimisers is believed to make the VQE noise resilient. In this talk, we probe this hypothesis in two ways. First, we present full density-matrix simulations to rank the noise resilience of leading VQE algorithms. Second, we show that, for a wide range of small molecules, even the best-performing VQE algorithms require gate-error probabilities on the order of 10^-5 to reach chemical accuracy. This is significantly below the fault-tolerance threshold of most error-correction protocols. Therefore, our results indicate that useful implementation of gate-based VQEs on pre-error-correction hardware is unlikely.