We provide a 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-characterized gates. Instead, it only requires the ability to perform approximate Haar random unitary operations, applying the unitary whose eigenspectrum is sought and performing measurements in the computational basis. We discuss application of these ideas to in-place amplitude estimation and quantum device calibration.

• Received 28 March 2016

DOI:https://doi.org/10.1103/PhysRevA.93.062306