Issue 36, 2021

Bayesian phase difference estimation: a general quantum algorithm for the direct calculation of energy gaps

Abstract

Quantum computers can perform full configuration interaction (full-CI) calculations by utilising the quantum phase estimation (QPE) algorithms including Bayesian phase estimation (BPE) and iterative quantum phase estimation (IQPE). In these quantum algorithms, the time evolution of wave functions for atoms and molecules is simulated conditionally with an ancillary qubit as the control, which make implementation to real quantum devices difficult. Also, most of the problems in chemistry discuss energy differences between two electronic states rather than total energies themselves, and thus direct calculations of energy gaps are promising for future applications of quantum computers to real chemistry problems. In the race of finding efficient quantum algorithms to solve quantum chemistry problems, we test a Bayesian phase difference estimation (BPDE) algorithm, which is a general algorithm to calculate the difference of two eigenphases of unitary operators in the several cases of the direct calculations of energy gaps between two electronic states on quantum computers, including vertical ionisation energies, singlet–triplet energy gaps, and vertical excitation energies. In the BPDE algorithm, state preparation is carried out conditionally on the ancillary qubit, and the time evolution of the wave functions in superposition of two electronic states are executed unconditionally. Based on our test, we conclude that BPDE is capable of computing the energy gap with an accuracy similar to BPE without controlled-time evolution simulations and with the smaller number of iterations in Bayesian optimisations.

Graphical abstract: Bayesian phase difference estimation: a general quantum algorithm for the direct calculation of energy gaps

Supplementary files

Article information

Article type
Paper
Submitted
12 Jul 2021
Accepted
09 Aug 2021
First published
02 Sep 2021
This article is Open Access
Creative Commons BY license

Phys. Chem. Chem. Phys., 2021,23, 20152-20162

Bayesian phase difference estimation: a general quantum algorithm for the direct calculation of energy gaps

K. Sugisaki, C. Sakai, K. Toyota, K. Sato, D. Shiomi and T. Takui, Phys. Chem. Chem. Phys., 2021, 23, 20152 DOI: 10.1039/D1CP03156B

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