Disentangling Expressibility, Symmetry Protection, and Hardware Noise in Variational Quantum Simulation of the Two-Flavor Schwinger Model

Abstract:Existing quantum simulations of the two-flavor Schwinger model have run at a single lattice size, and it is not known how far the variational approach can be pushed or which weakness stops it first. Following the model from N = 2 to 6 staggered lattice sites, we find that the binding constraint at reachable sizes is hardware noise rather than circuit expressibility or trainability, and identify N = 3 as the immediately viable extension of existing trapped-ion experiments. The energy error of a charge-conserving ansatz collapses onto one function of p/d, the ratio of variational parameters to physical-sector dimension, and falls by more than two orders of magnitude as p/d rises through order unity, giving the expressibility condition L(4N - 1) >= binom(2N,N) for L circuit layers. The condition is local in chemical potential: at N = 3 the layer count sufficient at zero chemical potential leaves a 74.38% error near the first-order boundary, while one further layer reaches 0.08%. Charge conservation also protects trainability and prevents charge-sector leakage: as the qubit count doubles from 4 to 8, the normalized gradient variance falls to 1/3.56 of its starting value for the constrained ansatz, versus 1/13.57 for an unconstrained circuit. Comparing a global contraction with per-gate local noise, a fixed-parameter control shows that the noise model, not whether the optimizer runs inside the noisy loop, sets how strongly noise degrades the first-order transition. At N = 4, a noiseless control reaches 0.12% mean error, whereas the same circuit at 1.00% depolarizing noise reaches 25.69 to 52.81%.

arXiv:2609.30496 [quant-ph]

(or arXiv:2609.30496v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.30496 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.