Error mitigation via verified phase estimation

The accumulation of noise in quantum computers is the dominant issue stymieing the push of quantum algorithms beyond their classical counterparts. This paper presents a new error mitigation technique based on quantum phase estimation that can also reduce errors in expectation value estimation (e.g., for variational algorithms). The general idea is to apply phase estimation while effectively post-selecting for the system register to be in the starting state, which allows us to catch and discard errors which knock us away from there. We show that this "verified phase estimation" (VPE) technique can be adapted to function without the use of control qubits in order to simplify the control circuitry for near-term implementations. We apply this technique to simulations of intermediate scale quantum circuits wand show multiple orders of magnitude improvement over unmitigated estimation at near-term error rates. Our results suggest that VPE can mitigate against single errors that occur --- the error in the estimated expectation values often scale as O(p^2), where p is the probability of an error occurring at any point in the circuit. This property, combined with robustness to sampling noise, shows VPE a practical technique for mitigating errors in near-term quantum experiments.