Entanglement Generation in Superconducting Qubits Using Holonomic Operations

We investigate a nonadiabatic holonomic operation that enables us to entangle two fixed-frequency superconducting transmon qubits attached to a common bus resonator. Two coherent microwave tones are applied simultaneously to the two qubits and drive transitions between the first excited resonator state and the second excited state of each qubit. The cyclic evolution within this effective three-level Lambda-type system gives rise to a holonomic operation entangling the two qubits. Two-qubit states with 95% fidelity, limited mainly by charge noise of the current device, are created within 213 ns. This scheme is a step toward implementation of a SWAP-type gate directly in an all-microwave controlled hardware platform. By extending the available set of two-qubit operations in the fixed-frequency qubit architecture, the proposed scheme may find applications in near-term quantum applications using variational algorithms to efficiently create problem-specific trial states. We illustrate this point by computing the ground state of molecular hydrogen using the holonomic operation.