Good and Bad News for Noisy Variational Quantum Algorithms – Part I

Variational quantum algorithms (VQAs) have been regarded as the most promising route towards useful, near-term quantum advantage. The hope has been that the variational quantum eigensolver and the quantum approximate optimisation algorithm could solve classically intractable problems in chemistry and binary classification, respectively. Recent years have seen the development of shallow quantum circuits for these purposes. In this talk, we present a thorough analysis of how noise affect these algorithms' performances. We show that for leading algorithms for variational quantum chemistry, low levels of gate noise preclude useful quantum simulations of even the smallest molecules. For VQAs to output chemically-accurate eigen-energy estimates, noise levels must be significantly lower than fault-tolerance thresholds. The same unfortunate conclusions hold for VQAs targeted towards binary classification. We evaluate possible remedies. We show that simple error-mitigation methods can boost the noise resilience by a factor of 10 to 100. Further, we provide additional tricks to boost noise resilience. Using knowledge of the algorithmic properties of VQAs, we show that it is possible to dynamically tweak algorithms to avoid computational regions that incur significant noise.