Effect of chaos on gate fidelity in coupled transmon systems

Multi-qubit architectures in the superconducting platform mostly use coupled transmon devices. Recent studies have shown that these many-body coupled nonlinear oscillator systems display chaotic behaviour in certain regimes of the inter-qubit coupling strength. In this work, we characterize the dynamical effects of chaos on the quantum gates applied to the transmons. We apply OTOCs as a possible measure of chaos in a system of 1D transmon chains and compare it to spectral statistics used in earlier works. Further, we construct a model for practical gate implementation in this system, and through numerical simulations explore the effect of chaos on the gate fidelity while varying the inter-qubit coupling strength, local Hilbert space dimension and gate support. Finally, we compare our numerical calculations with analytical calculations to explain the results.