Work

Lower bounds to variational problems with guarantees

Year: 2026

Type: article

Abstract: Variational methods play an important role in the study of quantum many-body problems, both in the flavor of classical variational principles based on tensor networks as well as of quantum variational principles in near-term quantum computing. This work stresses that for translationally invariant lattice Hamiltonians with periodic boundary conditions, one can easily derive efficiently computable lower bounds to ground state energies that can and should be compared with variational principles providing upper bounds. As small technical results, it is shown that (i) the Anderson bound and a (ii) common hierarchy of semidefinite relaxations both provide approximations with performance guarantees that scale as a constant in the energy density for cubic lattices. (iii) Also, the Anderson bound is systematically improved as a hierarchy of semidefinite relaxations inspired by the quantum marginal problem.

Source: Physical Review A

DOI: 10.1103/cz6k-y46r

Author: J. Eisert

Institutions: Helmholtz-Zentrum Berlin für Materialien und Energie, Freie Universität Berlin

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,675

Funders: Bundesministerium für Wirtschaft und Klimaschutz, Deutsche Forschungsgemeinschaft, QuantERA, H2020 European Research Council