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Determining the Ensemble N-Representability of Reduced Density Matrices.

Ofelia B Oña1, Gustavo E Massaccesi2,3, Pablo Capuzzi4,5

  • 1Instituto de Investigaciones Fisicoquímicas Teóricas Y Aplicadas, Universidad Nacional de La Plata, Consejo Nacional de Investigaciones Científicas Y Técnicas, Diag. 113 Y 64 (S/N), Sucursal 4, CC 16, La Plata 1900, Argentina.

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This study presents a new quantum algorithm for ensemble N-representability, purifying ensemble states into pure states for accurate density matrix calculations.

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Area of Science:

  • Quantum Computing
  • Electronic Structure Theory
  • Quantum Chemistry

Background:

  • The N-representability problem for reduced density matrices is a key challenge in electronic structure theory.
  • Previous work explored pure-state N-representability using variational quantum algorithms.

Purpose of the Study:

  • To develop a practical framework for determining the ensemble N-representability of a p-body matrix.
  • To enable error correction of defective ensemble reduced density matrices and quantum-state reconstruction.

Main Methods:

  • A purification strategy embeds an ensemble state into a pure state in an extended Hilbert space.
  • Iterative application of variational unitaries minimizes the Hilbert-Schmidt distance to a target p-body matrix.

Main Results:

  • The algorithm successfully determines ensemble N-representability by reproducing reduced density matrices of the original ensemble.
  • Numerical simulations validated the algorithm's robustness on systems with two to four electrons, including molecular systems at finite temperatures.

Conclusions:

  • The proposed framework offers a robust method for density-matrix refinement and N-representability determination.
  • This work advances the application of quantum algorithms in electronic structure calculations.