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Projective Measurement-Based Quantum Phase Difference Estimation Algorithm for the Direct Computation of Eigenenergy

Kenji Sugisaki1,2,3

  • 1Graduate School of Science and Technology, Keio University, 7-1 Shinkawasaki, Saiwai-ku, Kawasaki, Kanagawa 212-0032, Japan.

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This study introduces an improved quantum phase difference estimation (QPDE) algorithm using inverse quantum Fourier transformation. This method enhances accuracy for calculating electronic energy differences, crucial for quantum chemistry simulations.

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Area of Science:

  • Quantum computing
  • Computational chemistry
  • Quantum algorithms

Background:

  • Quantum computers can calculate electronic energy differences via the quantum phase difference estimation (QPDE) algorithm.
  • Previous Bayesian inference-based QPDE methods showed dependency on input wave function quality.

Purpose of the Study:

  • To develop an improved QPDE algorithm for accurate eigenenergy difference computation.
  • To overcome the limitations of existing Bayesian inference-based QPDE approaches.

Main Methods:

  • Implementation of an inverse quantum Fourier transformation-based QPDE algorithm.
  • Utilizing ancillary qubits (Na) for enhanced computation.
  • Employing single-shot projective measurement for eigenenergy difference determination.

Main Results:

  • Successful computation of singlet-triplet energy difference for the hydrogen molecule.
  • Accurate calculation of vertical excitation energies for halogen-substituted methylenes (CHF, CHCl, CF2, CFCl, CCl2) and formaldehyde (HCHO).

Conclusions:

  • The inverse quantum Fourier transformation-based QPDE offers a robust method for calculating electronic energy differences.
  • This approach provides accurate results independent of input wave function quality, demonstrated through various molecular systems.