Lattice stitching by eigenvector continuation for Holstein polaron

TL;DR

This paper introduces a lattice stitching algorithm using eigenvector continuation that significantly reduces computational complexity, enabling large-scale simulations of the Holstein polaron with quantum algorithms.

Contribution

The authors develop a novel method to construct eigenstates of large lattice systems from small segments, facilitating quantum simulations of particle-phonon interactions.

Findings

Reduces Hilbert space exponentially for large lattices

Allows calculation of Holstein polaron ground state in large systems

Enables quantum algorithms to simulate 100-site lattices with minimal qubits

Abstract

Simulations of lattice particle - phonon systems are fundamentally restricted by the exponential growth of the number of quantum states with the lattice size. Here, we demonstrate an algorithm that constructs the lowest eigenvalue and eigenvector for the Holstein model in extended lattices from eigenvalue problems for small, independent lattice segments. This leads to exponential reduction of the computational Hilbert space and allows applications of variational quantum algorithms to particle - phonon interactions in large lattices. We illustrate that the ground state of the Holstein polaron in the entire range of electron - phonon coupling, from weak to strong, and the lowest phonon frequency ($\omega/t = 0.1$) considered by numerical calculations to date can be obtained from a sequence of up to four-site problems. When combined with quantum algorithms, the present approach leads to a dramatic reduction of required quantum resources. We show that the ground state of the Holstein polaron in a lattice with 100 sites and 32 site phonons can be computed by a variational quantum eigensolver with 11 qubits.