Frustration-Induced Expressibility Limitations in Variational Quantum Algorithms

TL;DR

This paper analyzes how geometric frustration in quantum systems limits the expressibility of variational quantum algorithms, leading to increased circuit depth and proposing bond-resolved parameters to improve performance.

Contribution

It identifies the fundamental expressibility limitations caused by frustration and introduces bond-resolved variational parameters as a solution.

Findings

Frustration causes inhomogeneous correlations hard to capture with standard ansatz.

Circuit depth increases significantly in the frustrated regime.

Bond-resolved parameters improve accuracy at lower circuit depth.

Abstract

Geometric frustration, arising from competing interactions that prevent simultaneous energy minimization, presents a fundamental challenge for variational quantum algorithms applied to quantum many-body systems. We investigate the transverse-field Ising model on a square lattice with frustrated diagonal coupling and show that geometric frustration leads to strongly inhomogeneous correlations that are difficult to capture using standard Hamiltonian-inspired ans\"atze with global parameters. As a result, the required circuit depth increases significantly in the intermediate-field regime. We demonstrate that this limitation is not caused by optimization difficulties such as barren plateaus, but instead arises from insufficient expressibility of the ansatz. By introducing bond-resolved variational parameters, we recover accurate results at reduced circuit depth. We also study low-energy excitations and find that near-degenerate spectra in the frustrated regime further challenge variational methods. Our results provide a clear physical explanation for the limitations of variational quantum algorithms in frustrated systems and suggest improved ansatz design strategies for quantum simulation.