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The rapid development of noisy intermediate-scale quantum (NISQ) devices hasraised the question of whether or not these devices will find commercial use.Unfortunately, a major shortcoming of many proposed NISQ-amenable algorithms,such as the variational quantum eigensolver (VQE), is coming into view: thealgorithms require too many independent quantum measurements to solve practicalproblems in a reasonable amount of time. This motivates the central question ofour work: how might we speed up such algorithms in spite of the impact of erroron NISQ computations? We demonstrate on quantum hardware that the estimation ofexpectation values, a core subroutine of many quantum algorithms including VQE,can be improved in terms of precision and accuracy by using a technique we callRobust Amplitude Estimation. Consequently, this method reduces the runtime toachieve the same mean-squared error compared to the standardprepare-and-measure estimation method. The surprising result is that by usingdeeper, and therefore more error-prone, quantum circuits, we realize moreaccurate quantum computations in less time. As the quality of quantum devicesimproves, this method will provide a proportional reduction in estimationruntime. This technique may be used to speed up quantum computations into theregime of early fault-tolerant quantum computation and aid in the realizationof quantum advantage.

Reducing runtime and error in VQE using deeper and noisier quantum circuits