Evaluating energy differences on a quantum computer with robust phase estimation

TL;DR

This paper presents a robust quantum algorithm for evaluating energy differences between eigenstates, demonstrated on a hydrogen molecule, with high tolerance to errors and no need for controlled unitaries.

Contribution

The authors adapt the robust phase estimation algorithm for energy difference evaluation without controlled unitaries, enabling practical quantum chemistry calculations on cloud quantum computers.

Findings

Successfully calculated hydrogen molecule energy differences on a cloud quantum computer.

Demonstrated high robustness to coherent errors in state preparation and measurement.

Showed that all quantum phase estimation algorithms evaluate eigenvalue differences.

Abstract

We adapt the robust phase estimation algorithm to the evaluation of energy differences between two eigenstates using a quantum computer. This approach does not require controlled unitaries between auxiliary and system registers or even a single auxiliary qubit. As a proof of concept, we calculate the energies of the ground state and low-lying electronic excitations of a hydrogen molecule in a minimal basis on a cloud quantum computer. The denominative robustness of our approach is then quantified in terms of a high tolerance to coherent errors in the state preparation and measurement. Conceptually, we note that all quantum phase estimation algorithms ultimately evaluate eigenvalue differences.