Statistical Approach to Quantum Phase Estimation

TL;DR

The paper presents a new statistical and variational method for quantum phase estimation that can identify eigenstate-eigenphase pairs more comprehensively than traditional methods, using a simplified hardware approach and simulation results.

Contribution

It introduces a novel variational approach to quantum phase estimation that can determine any eigenstate-eigenphase pair from a unitary matrix, extending beyond traditional iterative methods.

Findings

Successfully simulated the method with Qiskit on IBM Q platform.

Can search for eigenphases within specified ranges.

Uses a probabilistic metric to estimate proximity to eigenstates.

Abstract

We introduce a new statistical and variational approach to the phase estimation algorithm (PEA). Unlike the traditional and iterative PEAs which return only an eigenphase estimate, the proposed method can determine any unknown eigenstate-eigenphase pair from a given unitary matrix utilizing a simplified version of the hardware intended for the Iterative PEA (IPEA). This is achieved by treating the probabilistic output of an IPEA-like circuit as an eigenstate-eigenphase proximity metric, using this metric to estimate the proximity of the input state and input phase to the nearest eigenstate-eigenphase pair and approaching this pair via a variational process on the input state and phase. This method may search over the entire computational space, or can efficiently search for eigenphases (eigenstates) within some specified range (directions), allowing those with some prior knowledge of their system to search for particular solutions. We show the simulation results of the method with the Qiskit package on the IBM Q platform and on a local computer.