A randomized quantum algorithm for statistical phase estimation

TL;DR

This paper introduces a randomized quantum phase estimation algorithm that achieves complexity independent of the Hamiltonian's term count and allows error suppression through data sampling without increasing circuit depth.

Contribution

The paper presents a novel randomized phase estimation method with complexity independent of the number of Hamiltonian terms and error suppression via data sampling.

Findings

Complexity is independent of the number of Hamiltonian terms.

Errors can be suppressed by collecting more data samples.

The approach does not increase circuit depth for error correction.

Abstract

Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent of the number of terms L in the Hamiltonian. Second, unlike previous L-independent approaches, such as those based on qDRIFT, all sources of error in our algorithm can be suppressed by collecting more data samples, without increasing the circuit depth.