  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 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.
