Characterizing non-Markovian and Coherent Errors in Quantum Simulators

Error characterization and error correction are imperative to obtain practical advantages in all quantum technologies including quantum sensing, simulation, and computation. Errors in quantum control can be divided into three categories 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, etc. and (iii) non-Markovian errors originating from fluctuations of control parameters such as laser power and frequency, heating of motional modes of the trapped quantum systems or leakage into other quantum levels. Here we develop a technique to characterize such errors.

The technique is based on symmetries of the system and is suitable for quantum simulators, where a multi-qubit quantum system is evolved under a fixed Hamiltonian. We show that the dynamics of the expectation value of the target Hamiltonian itself, which is ideally constant 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 it 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.