Entangling fixed-frequency transmon qubits with fast non-Abelian non-adiabatic geometric gates

Fixed frequency qubits and resonators are promising candidates to build a universal quantum computer because of their stability and long coherence times. However, the lack of energy tunability reduces controllability which may introduce an operational overhead. Additionally, two-qubit gates using microwave drives only are slow and impose conditions on the qubit frequencies. Our experimental results show how to use fast non-Abelian geometric phases to create entanglement between qubits. We entangle two fixed-frequency transmon qubits connected via a resonator by creating a lambda system where we simultaneously drive both transitions. Various two qubit states can be created by changing the amplitudes and phases of the two drives. The SWAP like nature of this geometric operation makes it well suited for variational quantum algorithms that compute molecular energies by exploring the part of Hilbert space with a fixed number of electrons.