Renormalization algorithm with graph enhancement

TL;DR

This paper introduces a new variational state class combining matrix product states with weighted graph states, enabling efficient simulation of quantum many-body systems with long-range correlations and entanglement.

Contribution

It presents a novel variational class and a renormalization algorithm with graph enhancement (RAGE), improving upon density-matrix renormalization group methods for quantum simulations.

Findings

Enhanced simulation accuracy for ground states.

Ability to handle long-range correlations.

Efficient computation of local properties.

Abstract

We introduce a class of variational states to describe quantum many-body systems. This class generalizes matrix product states which underly the density-matrix renormalization group approach by combining them with weighted graph states. States within this class may (i) possess arbitrarily long-ranged two-point correlations, (ii) exhibit an arbitrary degree of block entanglement entropy up to a volume law, (iii) may be taken translationally invariant, while at the same time (iv) local properties and two-point correlations can be computed efficiently. This new variational class of states can be thought of as being prepared from matrix product states, followed by commuting unitaries on arbitrary constituents, hence truly generalizing both matrix product and weighted graph states. We use this class of states to formulate a renormalization algorithm with graph enhancement (RAGE) and present numerical examples demonstrating that improvements over density-matrix renormalization group simulations can be achieved in the simulation of ground states and quantum algorithms. Further generalizations, e.g., to higher spatial dimensions, are outlined.