Symmetry-Preserving Variational Quantum Simulation of the Heisenberg Spin Chain on Noisy Quantum Hardware

TL;DR

This paper demonstrates that embedding physical symmetries into variational quantum circuits improves the accuracy and robustness of simulating the Heisenberg spin chain on noisy quantum hardware, advancing practical quantum simulation methods.

Contribution

It introduces symmetry-preserving variational circuits for the Heisenberg model, showing improved performance over generic ansatz on noisy quantum hardware.

Findings

Symmetry-preserving circuits yield more accurate energy estimates.

Enhanced robustness against hardware noise with symmetry incorporation.

Clearer convergence behavior compared to hardware-efficient ansatz.

Abstract

Variational quantum algorithms are among the most promising approaches for simulating interacting quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. However, the practical success of variational quantum eigensolvers (VQE) critically depends on the structure of the chosen variational ansatz. In this work, we investigate the ground-state properties of the one-dimensional antiferromagnetic Heisenberg spin-1/2 chain using both generic hardware-efficient ansatz and physics-informed, symmetry-preserving variational circuits. We benchmark variational results against exact diagonalization and noiseless simulations, and subsequently validate the approach on real IQM Garnet quantum hardware. Our results demonstrate that incorporating physical symmetries into the circuit design leads to significantly improved energy estimates, enhanced robustness against hardware noise, and clearer convergence behavior when compared to hardware-efficient ansatz under identical resource constraints. These findings highlight the importance of problem specific ansatz construction for reliable quantum simulations in the NISQ era.