Spectral Gap Optimization for Enhanced Adiabatic State Preparation

TL;DR

This paper introduces an efficient method to optimize the spectral gap in adiabatic quantum algorithms, enabling improved preparation of tensor network states such as AKLT and GHZ states, by leveraging Hamiltonian construction and symmetries.

Contribution

It proposes a novel spectral gap optimization technique for adiabatic state preparation of tensor network states, applicable to both injective and non-injective tensors with symmetry considerations.

Findings

Successfully prepared various tensor network states using the optimized adiabatic method

Demonstrated the method's effectiveness on random TNS, AKLT, and GHZ states

Enhanced spectral gap leads to more efficient adiabatic state preparation

Abstract

The preparation of non-trivial states is crucial to the study of quantum many-body physics. Such states can be prepared with adiabatic quantum algorithms, which are restricted by the minimum spectral gap along the path. In this letter, we propose an efficient method to adiabatically prepare tensor networks states (TNSs). We maximize the spectral gap leveraging degrees of freedom in the parent Hamiltonian construction. We demonstrate this efficient adiabatic algorithm for preparing TNS, through examples of random TNS in one dimension, AKLT, and GHZ states. The Hamiltonian optimization applies to both injective and non-injective tensors, in the latter case by exploiting symmetries present in the tensors.