Predicting Noise in a Trapped-ion Quantum Simulation of a Lattice Gauge Theory

A recent trapped-ion experiment realised a lattice gauge theory in which the internal states of the ions carry the gauge field and their vibrations carry bosonic matter. In that experiment, a charge moving around a loop was frozen in place by Aharonov--Bohm interference. The noise of such a device is usually simulated after the measurements have been made. Here we show that it can be predicted before the machine is run. For each quantity that the experiment measures, we derive, from the reported noise rates alone, a formula for how it decays together with a bound it can never exceed. The results reveal a simple pattern. The local conservation law of the theory is a parity of the vibrational mode, so heating violates it at a rate that grows as the mode warms, and the violation accelerates rather than accumulating steadily. At zero electric field, each of the three noise processes of the device leaves its own fingerprint. Heating affects only the conservation law, motional dephasing only the interference, and qubit errors only the stored flux and the frozen state. Once the electric field is switched on, the frozen state begins to leak, and we write an exact formula and a guaranteed bound for that leak.