Faster Phase Estimation

TL;DR

This paper introduces new quantum phase estimation algorithms that optimize measurement efficiency and circuit complexity, achieving near-minimal measurement counts with reduced circuit depth and qubit requirements.

Contribution

It presents a quantum algorithm for phase estimation with asymptotic runtime improvements and minimal classical post-processing, along with a review of measurement-based methods.

Findings

Purely random measurements are measurement-efficient but require exponential classical post-processing.

The proposed quantum algorithm approaches the theoretical minimum number of measurements.

The quantum circuit for the new method has lower depth and fewer qubits than traditional quantum phase estimation.

Abstract

We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing. We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine its scaling in circuit depth and width. We show that the use of purely random measurements requires a number of measurements that is optimal up to constant factors, albeit at the cost of exponential classical post-processing; the method can also be used to improve classical signal processing. We then develop a quantum algorithm for phase estimation that yields an asymptotic improvement in runtime, coming within a factor of log* of the minimum number of measurements required while still requiring only minimal classical post-processing. The corresponding quantum circuit requires asymptotically lower depth and width (number of qubits) than quantum phase estimation.