Symmetry-guided quantum state preparation: Branched-Subspaces Adiabatic Preparation (B-SAP)

TL;DR

This paper introduces a hybrid quantum state preparation algorithm combining variational and adiabatic methods, utilizing group theory to efficiently approximate ground and excited states in many-body systems, demonstrated on the XYZ Heisenberg model.

Contribution

A novel hybrid algorithm that leverages group-theoretic structures and classical post-processing to improve quantum state preparation efficiency.

Findings

Accurately prepares low-energy eigenstates of the XYZ model.

Achieves polynomial scaling circuit depths with system size.

Demonstrates effectiveness across various parameters and sizes.

Abstract

Quantum state preparation lies at the heart of quantum computation and quantum simulations, enabling the investigation of complex manybody systems across physics, chemistry, and data science. While existing methods such as Variational Quantum Algorithms (VQAs) and Adiabatic Preparation (AP) offer viable pathways, both face substantial limitations. Here we introduce a hybrid algorithm that integrates the conceptual strengths of both VQAs and AP, enhanced via the use of group-theoretic structures and classical post-processing to approximate ground and excited states of many-body Hamiltonian models. We validate our approach by applying it to the one-dimensional XYZ Heisenberg model with periodic boundary conditions, evaluating its performance across a broad range of parameters and system sizes. Our results show accurate preparation of low-energy eigenstates, achieved with circuit depths with polynomial scaling versus system size.