Bang-bang preparation of a quantum many-body ground state in a finite lattice: optimization of the algorithm with a tensor network

TL;DR

This paper presents an optimized bang-bang algorithm using tensor networks to efficiently prepare ground states of lattice quantum many-body systems, focusing on boundary effects and scalability in 1D and 2D models.

Contribution

It introduces a two-stage optimization method for bang-bang algorithms with tensor networks, enhancing ground state preparation in finite lattices by focusing on boundary modifications.

Findings

The optimized algorithm improves ground state accuracy near quantum critical points.

Boundary-only optimization reduces computational complexity.

The method is effective in 1D and 2D quantum Ising models.

Abstract

A bang-bang (BB) algorithm prepares the ground state of a lattice quantum many-body Hamiltonian $H=H_1+H_2$ by evolving an initial product state alternating between $H_1$ and $H_2$. We optimize the algorithm with tensor networks in one and two dimensions. The optimization has two stages. In stage one, a shallow translationally-invariant circuit is optimized in an infinite lattice. In stage two, the infinite-lattice gate sequence is used as a starting point for a finite lattice where it remains optimal in the bulk. The prepared state requires optimization only at its boundary, within a healing length from lattice edges, and the gate sequence needs to be modified only within the causal cone of the boundary. We test the procedure in the 1D and 2D quantum Ising model near its quantum critical point employing, respectively, the matrix product state (MPS) and the pair-entangled projected state (PEPS). At the boundary already the infinite-lattice sequence turns out to provide a more accurate state than in the bulk.