Unifying variational methods for simulating quantum many-body systems

TL;DR

This paper presents a unified variational framework for simulating quantum many-body systems, enabling efficient variation over diverse state classes like MERA and matrix-product states, with demonstrated numerical results.

Contribution

It introduces a novel variational method over quantum circuits using infinitesimal unitary transformations, unifying various existing approaches and enabling new hybrid methods.

Findings

Successfully implemented variational algorithms for MERA and matrix-product states

Demonstrated flexibility in hybridizing different variational classes

Achieved numerical benchmarks showing the method's effectiveness

Abstract

We introduce a unified formulation of variational methods for simulating ground state properties of quantum many-body systems. The key feature is a novel variational method over quantum circuits via infinitesimal unitary transformations, inspired by flow equation methods. Variational classes are represented as efficiently contractible unitary networks, including the matrix-product states of density matrix renormalization, multiscale entanglement renormalization (MERA) states, weighted graph states, and quantum cellular automata. In particular, this provides a tool for varying over classes of states, such as MERA, for which so far no efficient way of variation has been known. The scheme is flexible when it comes to hybridizing methods or formulating new ones. We demonstrate the functioning by numerical implementations of MERA, matrix-product states, and a new variational set on benchmarks.