Randomized gap and amplitude estimation

TL;DR

This paper introduces a novel spectral gap estimation method that uses approximate Haar-random unitaries, eliminating the need for ancillary qubits and well-characterized gates, with applications in amplitude estimation and device calibration.

Contribution

It presents a new approach for spectral gap estimation that simplifies implementation by removing the need for ancillary qubits and precise gate characterization.

Findings

Effective spectral gap estimation without ancillary qubits

Applicable to in-place amplitude estimation

Useful for quantum device calibration

Abstract

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.