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

• Published in: Journal of chemical theory and computation Vol. 19; no. 21; pp. 7617 - 7625
• Main Author: Sugisaki, Kenji
• Format: Journal Article
• Language: English
• Published: Washington American Chemical Society 14.11.2023
• Subjects: Algorithms; Bayesian analysis; Electron states; Fourier transforms; Mathematical analysis; Phase shift; Quantum computers; Quantum Electronic Structure; Qubits (quantum computing); Statistical inference; Wave functions
• ISSN: 1549-9618; 1549-9626; 1549-9626
• DOI: 10.1021/acs.jctc.3c00784

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).