Characterizing non-Markovian off-resonant errors in quantum gates

As quantum gates improve, it becomes increasingly difficult to characterize the remaining errors. Here we describe a class of coherent non-Markovian errors---excitations due to an off-resonant drive---that occur naturally in quantum devices that use time-dependent fields to generate gate operations. We show how these errors are mischaracterized using standard quantum computer verification and validation techniques that rely on Markovianity and are therefore often overlooked or assumed to be incoherent. We first demonstrate off-resonant errors within a simple toy model of Z gates created by the ac Stark effect, then show how off-resonant errors manifest in all gates driven on a fixed-frequency transmon architecture, a prominent example being incidental cross-resonance interaction driven during single-qubit gates. Furthermore, the same methodology can access the errors caused by two-level systems, showing evidence of coherent, off-resonant interactions with subsystems that are not intentional qubits. While we explore these results and their impact on gate error for fixed-frequency devices, we note that off-resonant excitations potentially limit any architectures that use frequency selectivity.