Randomized gap and amplitude estimation

We provide a new method for estimating spectral gaps in low-dimensional systems. Unlike traditional phase estimation, our approach does not require ancillary qubits nor does it require well characterised gates. Instead, it only requires the ability to perform approximate Haar–random unitary operations, applying the unitary whose eigenspectrum is sought out and performing measurements in the computational basis. We discuss application of these ideas to in-place amplitude estimation and quantum device calibration.