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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.
Journal of Chemical Theory and Computation
|December 26, 2025
Summary
This study presents a new quantum algorithm for ensemble N-representability, purifying ensemble states into pure states for accurate density matrix calculations.
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.
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