Noise-Aware Variational Eigensolvers: A Dissipative Route for Lattice Gauge Theories

We propose a novel variational ansatz for the ground state preparation of the $\mathbb{Z}_2$ lattice gauge theory (LGT) in quantum simulators (QSs). It combines dissipative and unitary operations in a completely deterministic scheme with a circuit complexity that does not scale with the size of the considered lattice. We find that, with very few variational parameters, the ansatz is able to achieve $>\!99\%$ fidelity with the true ground state in both the confined and deconfined phase of the $\mathbb{Z}_2$ LGT. We benchmark our proposal against the unitary Hamiltonian variational ansatz (HVA), and find a clear advantage of our scheme, especially for few variational parameters as well as for large system sizes. After performing a finite-size scaling analysis, we show that our dissipative variational ansatz is able to predict critical exponents with accuracies that surpass the capabilities of the HVA. Furthermore, we investigate the ground-state preparation algorithm in the presence of circuit-level noise and determine variational error thresholds, which determine error rates $p_{L}$, below which it would be beneficial to increase the number of layers $L \mapsto L+1$. Comparing those values to quantum gate errors $p$ of state-of-the-art quantum processors, we provide a detailed assessment of the prospects of our scheme to explore the $\mathbb{Z}_2$ LGT on near-term devices.