Saved in:
| Main Authors: | , , , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.17303 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912286350770176 |
|---|---|
| author | Massaccesi, Gustavo. E. Oña, Ofelia. B. Capuzzi, Pablo Melo, Juan I. Lain, Luis Torre, Alicia Peralta, Juan E. Alcoba, Diego R. Scuseria, Gustavo E. |
| author_facet | Massaccesi, Gustavo. E. Oña, Ofelia. B. Capuzzi, Pablo Melo, Juan I. Lain, Luis Torre, Alicia Peralta, Juan E. Alcoba, Diego R. Scuseria, Gustavo E. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17303 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Determining the N-representability of a reduced density matrix via unitary evolution and stochastic sampling Massaccesi, Gustavo. E. Oña, Ofelia. B. Capuzzi, Pablo Melo, Juan I. Lain, Luis Torre, Alicia Peralta, Juan E. Alcoba, Diego R. Scuseria, Gustavo E. Quantum Physics 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. |
| title | Determining the N-representability of a reduced density matrix via unitary evolution and stochastic sampling |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2503.17303 |