Fast and Robust Geometric Two-Qubit Gates for Superconducting Qubits and beyond

Quantum protocols based on adiabatic evolution are remarkably robust against imperfections of control pulses and system uncertainties. While adiabatic protocols have been successfully implemented for quantum operations such as quantum state transfer and single-qubit gates, their use for geometric two-qubit gates remains a challenge. In this paper, we propose a general scheme to realize robust geometric two-qubit gates in multilevel qubit systems where the interaction between the qubits is mediated by an auxiliary system (such as a bus or coupler). While our scheme utilizes stimulated Raman adiabatic passage (STIRAP), it is substantially simpler than STIRAP-based gates that have been proposed for atomic platforms, requiring fewer control tones and ancillary states, as well as utilizing only a generic dispersive interaction. We also show how our gate can be accelerated using a shortcuts-to-adiabaticity approach, allowing one to achieve a gate that is both fast and relatively robust. We present a comprehensive theoretical analysis of the performance of our two-qubit gate in parametrically modulated superconducting circuits comprising two fluxonium qubits coupled to an auxiliary system.