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arXiv:2507.19203 · Physical review. D/Physical review. D.

Barren-plateau free variational quantum simulation of Z 2 lattice gauge theories

Fariha Azad, Matteo Antonio Inajetovic, Stefan Kühn, Anna Pappa

Published Jul 23, 2026• 0 citations
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Abstract

In this work, we implement a variational quantum eigensolver (VQE) suitable for investigating ground states and static string breaking in a Z 2 lattice gauge theory (LGT). We consider a two-leg ladder lattice with Kogut-Susskind staggered fermions and verify the results of the VQE simulations using tensor network methods. We find that for varying Hamiltonian parameter regimes and in the presence of external charges, the VQE is able to arrive at the gauge-invariant ground state without explicitly enforcing gauge invariance through penalty terms. Additionally, experiments showing string breaking are performed on IBM’s quantum platform. Thus, VQEs are seen to be a promising tool for Z 2 LGTs, and could serve as a stepping stone toward studies of other gauge groups. We find that the scaling of gradients with the number of qubits is favorable for avoiding barren plateaus. Furthermore, strategies that avoid barren plateaus arise naturally as features of LGTs, such as choosing the initialization by setting the Gauss law sector and restricting the Hilbert space to the gauge-invariant subspace.

DOI
10.1103/rvrq-1scy

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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.
We introduce the Cyclic Variational Quantum Eigensolver (CVQE), a hardware-efficient framework for accurate ground-state quantum simulation on noisy intermediate-scale quantum (NISQ) devices. CVQE departs from conventional VQE by incorporating a measurement-driven feedback cycle: Slater determinants with significant sampling probability are iteratively added to the reference superposition, while a fixed entangler (e.g., single-layer UCCSD) is reused throughout. This adaptive reference growth systematically enlarges the variational space in most promising directions, avoiding manual ansatz or operator-pool design, costly searches, and preserving compile-once circuits. The strategy parallels multi-reference methods in quantum chemistry, while remaining fully automated on quantum hardware. Remarkably, CVQE exhibits a distinctive staircase-like descent pattern, where successive energy drops sharply signal efficient escape from barren plateaus. Benchmarks show that CVQE consistently maintains chemical precision across correlation regimes, outperforms fixed UCCSD by several orders of magnitude, and achieves favorable accuracy-cost trade-offs compared to the Selected Configuration Interaction. These results position CVQE as a scalable, interpretable, and resource-efficient paradigm for near-term quantum simulation.