Scalable Quantum Ground State Preparation of the Heisenberg Model: A Variational Quantum Eigensolver Approach

TL;DR

This paper demonstrates the use of the Variational Quantum Eigensolver (VQE) to efficiently prepare ground states of the 1D generalized Heisenberg model on NISQ devices, advancing quantum simulation methods for many-body systems.

Contribution

It introduces a scalable ansatz for VQE that can handle all coupling values, including critical states, and analyzes the precision and efficiency of classical and quantum sampling methods.

Findings

Successful ground state preparation for all coupling regimes.

Insights into sampling precision and time efficiency.

Potential for improved quantum algorithms in condensed matter physics.

Abstract

Quantum systems have historically been formidable to simulate using classical computational methods, particularly as the system size grows. In recent years, advancements in quantum computing technology have offered new opportunities for tackling complex quantum systems, potentially enabling the study and preparation of quantum states directly on quantum processors themselves. The Variational Quantum Eigensolver (VQE) algorithm is a system composed of a quantum circuit as well as a classical optimizer that can be used to efficiently prepare interesting many-body states on the current noisy intermediate-scale quantum (NISQ) devices. We assess the efficacy and scalability of VQE by preparing the ground states of the 1D generalized Heisenberg model, a pivotal model in understanding magnetic materials. We present an ansatz capable of preparing the ground states for all possible values of the coupling, including the critical states for the anisotropic XXZ model. This paper also aims to provide insights into the precision and time consumption involved in classical and optimized sampling approaches in the calculation of expectation values. In preparing the ground state for the Heisenberg models, this paper paves the way for more efficient quantum algorithms and contributes to the broader field of condensed matter physics.