Symplectic Engineering of Drive-Mediated Interactions in Superconducting Circuits

Implementing fast and reliable multi-qubit control is a key functionality for all quantum information platforms. Nonetheless, there can be an insidious interplay of strong nonlinearities and strong driving leading to undesirable effects, such as crosstalk, leakage and correlated noise, that lead to loss of fidelity. Here we present a new method based on symplectic transformations that allows an analytical derivation of effective two-qubit couplings achievable via driving of nonlinear Hamiltonians. Crucially, this method can incorporate the effect of strong non-local flux or local charge drives non-perturbatively and deconvolve the desired interaction from the spurious terms, as validated by both numerical simulations and experimental verification. Our approach provides a systematic route to derive and deconstruct several well-known modalities of drive-mediated interactions, such as cross-resonance Rabi and parametric SWAP, while informing optimal operating regimes for suppression of errors due to higher-order nonlinearities.