  The accumulation of noise in quantum computers is the dominant issue
stymieing the push of quantum algorithms beyond their classical counterparts.
We do not expect to be able to afford the overhead required for quantum error
correction in the next decade, so in the meantime we must rely on low-cost,
unscalable error mitigation techniques to bring quantum computing to its full
potential. 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 refer to this technique as "verified phase estimation"
(VPE) and show that it can be adapted to function without the use of control
qubits in order to simplify the control circuitry for near-term
implementations. Using VPE, we demonstrate the estimation of expectation values
on numerical simulations of intermediate scale quantum circuits with multiple
orders of magnitude improvement over unmitigated estimation at near-term error
rates (even after accounting for the additional complexity of phase
estimation). Our numerical results suggest that VPE can mitigate against any
single errors that might occur; i.e., 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 reveal VPE as a practical technique for mitigating errors in
near-term quantum experiments.
