Optimizing quantum phase estimation for the simulation of Hamiltonian eigenstates

TL;DR

This paper improves quantum phase estimation techniques for Hamiltonian eigenstate simulation by introducing a new statistical estimator, demonstrating enhanced accuracy and efficiency, and validating methods on IBM Q hardware with noisy quantum models.

Contribution

It introduces the mean phase direction as a new estimator, enabling more accurate and shallower quantum algorithms for Hamiltonian eigenstate estimation.

Findings

The mean phase direction outperforms the standard majority rule in accuracy.

The method allows for shallower algorithms when the state is an eigenstate.

Successful implementation of algorithms on IBM Q hardware with noisy models.

Abstract

We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the parent distribution associated with eigenstate inputs as a new post-processing tool. By connecting it with the unknown phase, we find that if used as its direct estimator, it exceeds the accuracy of the standard majority rule using one less bit of resolution, making evident that it can also be inverted to provide unbiased estimation. Moreover, we show how to directly use this quantity to accurately find the energy levels when the initialized state is an eigenstate of the simulated propagator during the whole time evolution, which allows for shallower algorithms. We then use IBM Q hardware to carry out the digital quantum simulation of three toy models: a two-level system, a two-spin Ising model and a two-site Hubbard model at half-filling. Methodologies are provided to implement Trotterization and reduce the variability of results in noisy intermediate scale quantum computers.