Investigating Different Barren Plateaus Mitigation Strategies in Variational Quantum Eigensolver

TL;DR

This paper systematically benchmarks four barren plateau mitigation strategies in VQE across various molecular systems, revealing that optimal mitigation depends on system size and iteration budget rather than gradient variance alone.

Contribution

It provides a comprehensive comparison of mitigation techniques, highlighting their performance dependencies on system size and computational resources.

Findings

Pretrained VQE outperforms SEA at 100 iterations in 14-qubit systems.

SEA achieves near-exact energies with high fidelity in smaller systems.

Mitigation effectiveness depends on iteration budget and system size, not just gradient variance.

Abstract

Variational Quantum Eigensolver (VQE) algorithms suffer from barren plateaus, where gradients vanish with system size and circuit depth. Although many mitigation strategies exist, their connection to convergence performance under different iteration budgets remains unclear. Moreover, a systematic analysis identifying which state-of-the-art mitigation techniques perform best under specific scenarios is also lacking. We benchmark four approaches, Local-Global, Adiabatic, State Efficient Ansatz (SEA), and Pretrained VQE, against standard VQE on molecular systems from 4 to 14 qubits, analyzing gradient variance up to 50 layers and convergence over 1000 iterations. Our results show that the impact of gradient preservation is iteration-dependent. In the 14-qubit BeH2 system, Pretrained VQE outperforms SEA at 100 iterations despite lower gradient variance, but SEA becomes 2.2x more accurate at 1000 iterations. For smaller systems, SEA achieves near-exact energies (H2: 10^-5 Ha, LiH: 2x10^-4 Ha) with fidelities 0.999, while standard methods plateau early. The results demonstrate that robust barren plateau mitigation depends on aligning the chosen strategy with both system size and available computational budget, rather than treating gradient variance as the sole predictor of performance.