Although gauge invariance is a postulate in fundamental theories of nature such as quantum electrodynamics, in quantum-simulation implementations of gauge theories it is compromised by experimental imperfections. In a recent paper [Halimeh and Hauke, Phys. Rev. Lett. 125, 030503 (2020)], it has been shown in finite-size spin-
1/2 quantum link lattice gauge theories that upon introducing an energy-penalty term of sufficiently large strength
V, unitary gauge-breaking errors at strength $\ensuremath{\lambda}$ are suppressed $\ensuremath{\propto}{\ensuremath{\lambda}}^{2}/{V}^{2}$ up to all accessible evolution times. Here, we show numerically that this result extends to quantum link models in the thermodynamic limit and with larger spin
S. As we show analytically, the dynamics at short times is described by an adjusted gauge theory up to a timescale that is at earliest ${\ensuremath{\tau}}_{\text{adj}}\ensuremath{\propto}\sqrt{V/{V}_{0}^{3}}$, with
V0 an energy factor. Moreover, our analytics predicts that a renormalized gauge theory dominates at intermediate times up to a timescale ${\ensuremath{\tau}}_{\text{ren}}\ensuremath{\propto}exp(V/{V}_{0})/{V}_{0}$. In both emergent gauge theories,
V is volume independent and scales at worst $\ensuremath{\sim}{S}^{2}$. Furthermore, we numerically demonstrate that robust gauge invariance is also retained through a single-body gauge-protection term, which is experimentally straightforward to implement in ultracold-atom setups and NISQ devices.
Recent years have seen strong progress in quantum simulation of gauge-theory dynamics using ultracold-atom experiments. A principal challenge in these efforts is the certification of gauge invariance, which has recently been realized in [B.~Yang et al., arXiv:2003.08945]. One major but poorly investigated experimental source of gauge-invariance violation is an imperfect preparation of the initial state. Using the time-dependent density-matrix renormalization group, we analyze the robustness of gauge-invariant dynamics against potential preparation defects in the above ultracold-atom implementation of a
U(1) gauge theory. We find defects related to an erroneous initialization of matter fields to be innocuous, as the associated gauge-invariance violation remains strongly localized throughout the time evolution. A defect due to faulty initialization of the gauge field leads to a mild proliferation of the associated violation. Furthermore, we characterize the influence of immobile and mobile defects by monitoring the spread of entanglement entropy. Overall, our results indicate that the aforementioned experimental realization exhibits a high level of fidelity in the gauge invariance of its dynamics at all evolution times. Our work provides strong evidence that ultracold-atom setups can serve as an extremely reliable framework for the quantum simulation of gauge-theory dynamics.
Abstract Protection of gauge invariance in experimental realizations of lattice gauge theories based on energy-penalty schemes has recently stimulated impressive efforts both theoretically and in setups of quantum synthetic matter. A major challenge is the reliability of such schemes in non-abelian gauge theories where local conservation laws do not commute. Here, we show through exact diagonalization (ED) that non-abelian gauge invariance can be reliably controlled using gauge-protection terms that energetically stabilize the target gauge sector in Hilbert space, suppressing gauge violations due to unitary gauge-breaking errors. We present analytic arguments that predict a volume-independent protection strength V, which when sufficiently large leads to the emergence of an adjusted gauge theory with the same local gauge symmetry up to least a timescale ∝ V / V 0 3 . Thereafter, a renormalized gauge theory dominates up to a timescale ∝exp(V/V 0)/V 0 with V 0 a volume-independent energy factor, similar to the case of faulty abelian gauge theories. Moreover, we show for certain experimentally relevant errors that single-body protection terms robustly suppress gauge violations up to all accessible evolution times in ED, and demonstrate that the adjusted gauge theory emerges in this case as well. These single-body protection terms can be readily implemented with fewer engineering requirements than the ideal gauge theory itself in current ultracold-atom setups and noisy intermediate-scale quantum (NISQ) devices.
A major test of the capabilities of modern quantum simulators and NISQ devices is the reliable realization of gauge theories, which constitute a gold standard of implementational efficacy. In addition to unavoidable unitary errors, realistic experiments suffer from decoherence, which compromises gauge invariance and, therefore, the gauge theory itself. Here, we study the effect of decoherence on the quench dynamics of a lattice gauge theory. Rigorously identifying the gauge violation as a divergence measure in the gauge sectors, we find at short times that it first grows diffusively
∼γt due to decoherence at environment-coupling strength
γ, before unitary errors at strength
λ dominate and the violation grows ballistically
∼λ2t2. We further introduce multiple quantum coherences in the context of gauge theories to quantify decoherence effects. Both experimentally accessible measures will be of independent interest beyond the immediate context of this work.
Simulations of lattice gauge theories on noisy quantum hardware inherently suffer from violations of the gauge symmetry due to coherent and incoherent errors of the underlying physical system that implements the simulation. These gauge violations cause the simulations to become unphysical requiring the result of the simulation to be discarded. We investigate an active correction scheme that relies on detecting gauge violations locally and subsequently correcting them by dissipatively driving the system back into the physical gauge sector. We show that the correction scheme not only ensures the protection of the gauge symmetry, but it also leads to a longer validity of the simulation results even within the gauge-invariant sector. Finally, we discuss further applications of the scheme such as preparation of the many-body ground state of the simulated system. Published by the American Physical Society 2024
Simulations of lattice gauge theories on noisy quantum hardware inherently suffer from violations of the gauge symmetry due to coherent and incoherent errors of the underlying physical system that implements the simulation. These gauge violations cause the simulations to become unphysical requiring the result of the simulation to be discarded. We investigate an active correction scheme that relies on detecting gauge violations locally and subsequently correcting them by dissipatively driving the system back into the physical gauge sector. We show that the correction scheme not only ensures the protection of the gauge symmetry, but it also leads to a longer validity of the simulation results even within the gauge-invariant sector. Finally, we discuss further applications of the scheme such as preparation of the many-body ground state of the simulated system.