Projective Measurement-Based Quantum Phase Difference Estimation Algorithm for the Direct Computation of Eigenenergy Differences on a Quantum Computer

Kenji Sugisaki

doi:10.1021/acs.jctc.3c00784

Projective Measurement-Based Quantum Phase Difference Estimation Algorithm for the Direct Computation of Eigenenergy Differences on a Quantum Computer

J Chem Theory Comput. 2023 Nov 14;19(21):7617-7625. doi: 10.1021/acs.jctc.3c00784. Epub 2023 Oct 24.

Author

Kenji Sugisaki^{1

2

3}

Affiliations

¹ Graduate School of Science and Technology, Keio University, 7-1 Shinkawasaki, Saiwai-ku, Kawasaki, Kanagawa 212-0032, Japan.
² Quantum Computing Center, Keio University, 3-14-1 Hiyoshi, Kohoku-ku Yokohama, Kanagawa 223-8522, Japan.
³ Centre for Quantum Engineering, Research and Education TCG Centres for Research and Education in Science and Technology, Sector V, Salt Lake, Kolkata 700091, India.

Abstract

Quantum computers are capable of calculating the energy difference of two electronic states using the quantum phase difference estimation (QPDE) algorithm. The Bayesian inference-based implementations for the QPDE have been reported so far, but in this approach, the quality of the calculated energy difference 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 proof-of-concept demonstrations, we report numerical experiments for the singlet-triplet energy difference of the hydrogen molecule and the vertical excitation energies of halogen-substituted methylenes (CHF, CHCl, CF₂, CFCl, and CCl₂) and formaldehyde (HCHO).