Determining the Ensemble N‑Representability of Reduced Density Matrices
Ofelia B. Oña, Gustavo E. Massaccesi, Pablo Capuzzi, Luis Lain, Alicia Torre, Juan E. Peralta, Diego R. Alcoba, Gustavo E. Scuseria
TL;DR
This paper introduces a new method to determine if a reduced density matrix can represent an ensemble of quantum states, using purification and variational algorithms.
Contribution
A practical framework for ensemble N-representability using purification and variational quantum algorithms.
Findings
The purification strategy successfully embeds ensemble states into pure states for N-representability analysis.
The algorithm effectively minimizes the Hilbert-Schmidt distance to determine N-representability.
Numerical simulations on multi-electron systems confirm the method's robustness and applicability.
Abstract
The N-representability problem for reduced density matrices remains a fundamental challenge in electronic structure theory. Following our previous work that employs a unitary-evolution algorithm based on an adaptive derivative-assembled pseudo-Trotter variational quantum algorithm to probe pure-state N-representability of reduced density matrices [J. Chem. Theory Comput. 2024, 20, 9968], in this work we propose a practical framework for determining the ensemble N-representability of a p-body matrix. This is accomplished using a purification strategy that embeds an ensemble state into a pure state defined on an extended Hilbert space, such that the reduced density matrices of the purified state reproduce those of the original ensemble. By iteratively applying variational unitaries to an initial purified state, the proposed algorithm minimizes the Hilbert-Schmidt distance between its…
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum many-body systems · Spectroscopy and Quantum Chemical Studies