The role of diagonalization within a diagonalization/Monte Carlo scheme

TL;DR

This paper introduces a versatile computational method combining diagonalization and Monte Carlo techniques to efficiently identify key basis vectors of low energy quantum states across various basis types and Hamiltonian properties.

Contribution

It presents a novel quasi-sparse eigenvector diagonalization method that works with any basis and Hamiltonian, integrating diagonalization with Monte Carlo for quantum computations.

Findings

Applicable to any basis type

Works with Hermitian and non-Hermitian Hamiltonians

Effective for finite and infinite-dimensional systems

Abstract

We discuss a method called quasi-sparse eigenvector diagonalization which finds the most important basis vectors of the low energy eigenstates of a quantum Hamiltonian. It can operate using any basis, either orthogonal or non-orthogonal, and any sparse Hamiltonian, either Hermitian, non-Hermitian, finite-dimensional, or infinite-dimensional. The method is part of a new computational approach which combines both diagonalization and Monte Carlo techniques.