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Luis Lain

Publications and source records attributed to Luis Lain.

6 recordsLinked to original sources
arXiv2026

Is the matrix completion of reduced density matrices unique?

Reduced density matrices are central to describing observables in many-body quantum systems. In electronic structure theory, the two-particle reduced density matrix (2-RDM) suffices to determine the energy and other key properties. Recent work has used matrix completion, leveraging the low-rank structure of RDMs and approximate theoretical models, to reconstruct the 2-RDM from partial data and thus reduce computational cost. However, matrix completion is, in general, an under-determined problem. Revisiting Rosina's theorem [M. Rosina, Queen's Papers on Pure and Applied Mathematics No. 11, 369 (1968)], we here show that the matrix completion is unique under certain conditions, identifying the subset of 2-RDM elements that enables its exact reconstruction from incomplete information. Building on this, we introduce a hybrid quantum-stochastic algorithm that achieves exact matrix completion, demonstrated through applications to the Fermi-Hubbard model.

quant-ph↗
arXiv2026

Determining the ensemble N-representability of Reduced Density Matrices

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 consisting of embedding 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 p-body reduced density matrix and a specified target p-body matrix, which serves as a measure of the N-representability of the target. This methodology facilitates both error correction of defective ensemble reduced density matrices, and quantum-state reconstruction on a quantum computer, offering a route for density-matrix refinement. We validate the algorithm with numerical simulations on systems of two, three, and four electrons in both, simple models as well as molecular systems at finite temperature, demonstrating its robustness.

quant-ph↗
arXiv2025

Determining the N-representability of a reduced density matrix via unitary evolution and stochastic sampling

The N-representability problem consists in determining whether, for a given p-body matrix, there exists at least one N-body density matrix from which the p-body matrix can be obtained by contraction, that is, if the given matrix is a p-body reduced density matrix (p-RDM). The knowledge of all necessary and sufficient conditions for a p-body matrix to be N-representable allows the constrained minimization of a many-body Hamiltonian expectation value with respect to the p-body density matrix and, thus, the determination of its exact ground state. However, the number of constraints that complete the N-representability conditions grows exponentially with system size, and hence the procedure quickly becomes intractable in practice. This work introduces a hybrid quantum-stochastic algorithm to effectively replace the N-representability conditions. The algorithm consists of applying to an initial N-body density matrix a sequence of unitary evolution operators constructed from a stochastic process that successively approaches the reduced state of the density matrix on a p-body subsystem, represented by a p-RDM, to a target p-body matrix, potentially a p-RDM. The generators of the evolution operators follow the adaptive derivative-assembled pseudo-Trotter method (ADAPT), while the stochastic component is implemented using a simulated annealing process. The resulting algorithm is independent of any underlying Hamiltonian, and it can be used to decide if a given p-body matrix is N-representable, establishing a criterion to determine its quality and correcting it. We apply this hybrid ADAPT algorithm to alleged reduced density matrices from a quantum chemistry electronic Hamiltonian, the reduced BCS model with constant pairing, and the Heisenberg XXZ spin model. In all cases, the proposed method behaves as expected for 1-RDMs and 2-RDMs, evolving the initial matrices towards different targets.

quant-ph↗
arXiv2013

Symmetry-adapted formulation of the combined G-particle-hole Hypervirial equation and Hermitian Operator method

High accuracy energies of low-lying excited states, in molecular systems, have been determined by means of a procedure which combines the G-particle-hole Hypervirial (GHV) equation method [Alcoba et al. Int. J. Quantum Chem. 109:3178 (2009)] and the Hermitian Operator (HO) one [Bouten et al. Nucl. Phys. A 202:127 (1973)]. This paper reports a suitable strategy to introduce the point group symmetry within the framework of the combined GHV-HO method, what leads to an improvement of the computational efficiency. The resulting symmetry-adapted formulation has been applied to illustrate the computer timings and the hardware requirements in selected chemical systems of several geometries.

physics.chem-ph↗
arXiv2008

Domain-averaged Fermi hole versus regional reduced density matrices: a critical comparison

In their recent work Cooper and Ponec [Phys. Chem. Chem. Phys., 2008, 10, 1319-1329] proposed a ``one-electron approximation to domain-averaged Fermi hole (DAFH)" used in electronic population studies. The goal of this comment is to note that the proposal had been already published within the framework of domain-restricted reduced density matrices ($\mathrmΩ$-RDM) and to show that it cannot conceptually be considered as an approximation to DAFH as the authors invoke.

quant-ph↗