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

TL;DR

This work tackles the challenge of simulating the ground state of the 1D Heisenberg spin-1/2 chain on NISQ hardware by comparing hardware-efficient and symmetry-preserving, physics-informed variational circuits within VQE. Hamiltonian encoding uses Pauli-string decompositions and a batched measurement strategy, while the symmetry-preserving ansatz employs a spin-exchange unitary that commutes with $S^2_{\,tot}$ and $S^z_{\,tot}$ to stay within the correct symmetry sector. Results show that the symmetry-preserving approach yields lower variational energies and greater robustness to hardware noise, both in noiseless simulations and on the IQM Garnet processor, with a systematic energy offset observed on hardware due to noise. The findings demonstrate that incorporating physical symmetries into circuit design substantially improves reliability and interpretability of near-term quantum simulations, informing scalable strategies for many-body quantum problems on NISQ devices.

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.

Figures (4)

• Figure 1: Ground-state energy estimates obtained via noiseless simulation for the Heisenberg model using hardware-efficient ansatz and Exact diagonalization.
• Figure 2: Ground-state energy as a function of system size $N$ for the one-dimensional Heisenberg spin chain. Exact diagonalization results are shown alongside variational quantum eigensolver (VQE) simulation results using a generic expressive ansatz and a symmetry-preserving physics-informed ansatz. The increasing separation between the restricted variational energy and the exact ground state reflects the expressibility limitations imposed by symmetry constraints.
• Figure 3: Energy landscape obtained on IQM Garnet hardware using the physics-informed symmetry-preserving ansatz. A clear minimum indicates successful preparation of an entangled antiferromagnetic state despite hardware noise.
• Figure 4: Comparison of hardware-efficient and physics-informed ansatz on IQM Garnet hardware. The physics-informed ansatz consistently achieves lower energies under identical resource constraints.