Projective Quantum Phase Difference Estimation Algorithm for the Direct Computation of Eigenenergy Gaps on a Quantum Computer

TL;DR

This paper introduces a projective quantum phase difference estimation algorithm that enables direct, single-shot measurement of eigenenergy gaps on quantum computers, improving accuracy over previous Bayesian methods.

Contribution

The authors propose an inverse quantum Fourier transform-based QPDE algorithm that allows for projective measurement of energy differences with fewer assumptions about input states.

Findings

Successfully demonstrated on hydrogen molecule's energy gap

Accurately computed excitation energies of halogen-substituted methylenes

Validated the method with formaldehyde energy gap calculations

Abstract

Quantum computers are capable of calculating the energy gap of two electronic states by using the quantum phase difference estimation (QPDE) algorithm. The Bayesian inference based implementations for the QPDE have been reported so far, but this approach is not projective, and the quality of the calculated energy gap depends on the input wave functions being used. Here, we report the inverse quantum Fourier transformation based QPDE with $N_a$ of ancillary qubits, which allows us to compute the difference of eigenenergies based on the single-shot projective measurement. As a proof-of-concept demonstrations, we report numerical experiments for the singlet--triplet energy gap of hydrogen molecule and the vertical excitation energies of halogen-substituted methylenes (CHF, CHCl, CF$_2$, CFCl and CCl$_2$) and formaldehyde (HCHO).