In this contribution, we investigate the structure of short-range correlations in many-body states. We obtain the highly correlated many-body states with an explicitly correlated basis which enables us to get a precise solution of a many-body Schrödinger equation for a realistic interaction. We show two-body density distributions calculated from three- and four-body states to investigate the short-range correlations between nucleon pairs. At distances below 1 fm a universal behavior is found which does not depend on the many-body states. The universality is also seen in the high momentum components of the two-body momentum distributions.In this contribution, we investigate the structure of short-range correlations in many-body states. We obtain the highly correlated many-body states with an explicitly correlated basis which enables us to get a precise solution of a many-body Schrödinger equation for a realistic interaction. We show two-body density distributions calculated from three- and four-body states to investigate the short-range correlations between nucleon pairs. At distances below 1 fm a universal behavior is found which does not depend on the many-body states. The universality is also seen in the high momentum components of the two-body momentum distributions.

Journal of Physics Conference SeriesSep 16, 20110 citations

Verifiably exact solution of the electronic Schrödinger equation on quantum devices

Scott E. Smart, David A. Mazziotti

Quantum computers have the potential for a significant speedup of molecular computations. However, existing algorithms have limitations; quantum phase estimation (QPE) is intractable on current hardware while variational quantum eigensolvers (VQE) are dependent upon approximate wave functions without guaranteed convergence. In this paper we present an algorithm that yields verifiably exact solutions of the many-electron Schr\"odinger equation. Rather than solve the Schr\"odinger equation directly, we solve its contraction over all electrons except two, known as the contracted Schr\"odinger equation (CSE). The CSE generates a wave-function Ansatz, constructed from an iterative product of nonunitary two-body transformations, whose energy gradient with respect to the two-body operator of the current iteration vanishes if and only if the CSE is satisfied. Because the CSE implies the Schr\"odinger equation, the two-electron Ansatz provides a verifiably exact Ansatz for solving the many-electron Schr\"odinger equation. The exactness property contrasts with that of Ans\"atze built from the product of unitary two-body transformations where the gradient---the residual of the anti-Hermitian part of the CSE (ACSE)---can vanish without implying a solution of the Schr\"odinger equation. We demonstrate the algorithm on both simulators and noisy quantum computers with ${\mathrm{H}}_{2}$ dissociation and the rectangle-to-square transition in ${\mathrm{H}}_{4}$ .Quantum computers have the potential for a significant speedup of molecular computations. However, existing algorithms have limitations; quantum phase estimation (QPE) is intractable on current hardware while variational quantum eigensolvers (VQE) are dependent upon approximate wave functions without guaranteed convergence. In this paper we present an algorithm that yields verifiably exact solutions of the many-electron Schr\"odinger equation. Rather than solve the Schr\"odinger equation directly, we solve its contraction over all electrons except two, known as the contracted Schr\"odinger equation (CSE). The CSE generates a wave-function Ansatz, constructed from an iterative product of nonunitary two-body transformations, whose energy gradient with respect to the two-body operator of the current iteration vanishes if and only if the CSE is satisfied. Because the CSE implies the Schr\"odinger equation, the two-electron Ansatz provides a verifiably exact Ansatz for solving the many-electron Schr\"odinger equation. The exactness property contrasts with that of Ans\"atze built from the product of unitary two-body transformations where the gradient---the residual of the anti-Hermitian part of the CSE (ACSE)---can vanish without implying a solution of the Schr\"odinger equation. We demonstrate the algorithm on both simulators and noisy quantum computers with ${\mathrm{H}}_{2}$ dissociation and the rectangle-to-square transition in ${\mathrm{H}}_{4}$.

arXiv:2303.00758Physical Review AFeb 5, 202418 citations

Many-Body Schrödinger Equation

Hiroshi Isozaki

Mathematical physics studiesJan 1, 20236 citations

Many-body Schroedinger equation in the collective variables

A.K. Petrauskas, L.Yu. Sabalyauskas

Oct 1, 19740 citations

{\mathrm{H}}_{2}

dissociation and the rectangle-to-square transition in

{\mathrm{H}}_{4}