Characterizing Unwanted Motional Coupling in Mølmer-Sørensen Gates

Mølmer–Sørensen gates constitute an integral hardware component of an ion trap quantum computer. These gates entangle qubits to motional modes of the ions, generating phonons that manifest in errors on future gates. As a result, the analysis of fault tolerant quantum computation schemes becomes challenging. In this work, we quantify the impact of ignoring non-Markovian features in the noise model for Mølmer–Sørensen gates by developing numerical tools to compute the fidelity of a sequence of N Mølmer–Sørensen gates. Although completely ignoring non-Markovianity results in an overestimation of this fidelity, we present Markovian models that can reproduce the same scaling of fidelity as the true noise process. These accurate Markovian models rely on a heuristic assumption that the displacements of the motional modes resemble a random walk.