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The Quantum-Mechanical Model of an Atom02:45

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Efficient Energy Measurement of Chemical Systems via One-Particle Reduced Density Matrix: A NOF-VQE Approach for

Juan Felipe Huan Lew-Yee1, Mario Piris1,2,3

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|February 21, 2025
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This study introduces a method using the one-particle reduced density matrix (1RDM) to optimize quantum computing energy measurements. This approach significantly reduces quantum resource usage for chemical system calculations within the variational quantum eigensolver (VQE) framework.

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Area of Science:

  • Quantum Computing
  • Computational Chemistry
  • Quantum Information Science

Background:

  • Variational Quantum Eigensolver (VQE) is a leading algorithm for quantum chemistry simulations.
  • Calculating molecular energies on quantum computers requires significant computational resources.
  • The one-particle reduced density matrix (1RDM) offers a reduced representation of quantum states.

Purpose of the Study:

  • To streamline energy measurements of chemical systems on quantum computers using the 1RDM.
  • To reduce the number of quantum circuits and measurements needed in VQE.
  • To explore the application of Natural Orbital Functional (NOF) theory within a quantum computing context.

Main Methods:

  • Leveraging the exact energy functional of the 1RDM.
  • Measuring only the necessary elements of the 1RDM instead of the full Hamiltonian.
  • Utilizing NOF theory with natural orbitals and occupation numbers derived from measured 1RDM.
  • Validating accuracy by comparing NOF-derived energies with standard VQE results.
  • Optimizing gate parameters by minimizing energy using NOF approximations.

Main Results:

  • The 1RDM approach requires measuring significantly fewer elements compared to standard VQE.
  • NOF approximations applied to quantum-derived 1RDM yield accurate energies for systems like H2.
  • The NOF-VQE method achieved approximately 90% savings in circuit executions for tested chemical systems (LiH, Li2, OH-, FH, NeH+, F2).
  • Demonstrated viability of NOF approximations for accurate quantum energy calculations.

Conclusions:

  • The 1RDM-based NOF-VQE method offers a significant reduction in quantum resource requirements.
  • This approach provides accurate energy estimations crucial for the noisy intermediate-scale quantum (NISQ) era.
  • The study highlights the potential for developing novel quantum-tailored functionals for advanced quantum computing applications.