A symmetry-based error characterization protocol for neutral atom quantum simulators*

Errors in quantum control of neutral atoms can be divided into three classes based on their physical origin: (i) Unitary or coherent errors originating e.g, from miscalibration of time, frequency, or power of lasers or microwaves, (ii) Markovian errors originating from coupling to the environment, e.g., spontaneous decay, light assisted loss of atoms, etc. and (iii) non-Markovian errors originating from fluctuations of control parameters such as laser power and frequency, heating of motional modes or leakage into other quantum levels. Here we develop a new technique based on the symmetries of the system to characterize such errors. The technique is suitable for quantum simulators, where a multi-qubit quantum system is time-evolved under a fixed Hamiltonian, typically an interacting many-body Hamiltonian. We show that the dynamics of the expectation value of the target Hamiltonian itself, which is ideally conserved in time, can be used to characterize these errors [1]. In the presence of errors, the expectation value of the target Hamiltonian shows characteristic thermalization dynamics, when the latter satisfies the operator thermalization hypothesis (OTH). That is, an oscillation in the short time followed by relaxation to a steady-state value in the long time limit. We show that while the steady-state value can be used to characterize the coherent errors, the amplitude of the oscillations can be used to estimate the non-Markovian errors. Using these results, we develop experimental protocols to characterize the unitary and non-Markovian errors. Furthermore, we extend these results to include Markovian errors, in the presence of which the expectation value of the Hamiltonian shows a characteristic exponential decay. We show that by varying the initial state, the Markovian decay dynamics can be completely characterized and efficiently so if they are generated by independent loss events for each atom. Finally, we develop analogs of some of these results for evolution under time-dependent Hamiltonians, including the important case of adiabatic quantum dynamics.