Fast, high-fidelity single and two-qubit gates are essential to building aviable quantum information processor, but achieving both in the same system hasproved challenging for spin qubits. We propose and analyze an approach toperform a long-distance two-qubit controlled phase (CPHASE) gate between twosinglet-triplet qubits using an electromagnetic resonator to mediate theirinteraction. The qubits couple longitudinally to the resonator, and by drivingthe qubits near the resonator's frequency they can be made to acquire astate-dependent geometric phase that leads to a CPHASE gate independent of theinitial state of the resonator. Using high impedance resonators enables gatetimes of order 10 ns while maintaining long coherence times. Simulations showaverage gate fidelities of over 96% using currently achievable experimentalparameters and over 99% using state-of-the-art resonator technology. Afteroptimizing the gate fidelity in terms of parameters tuneable in-situ, we findit takes a simple power-law form in terms of the resonator's impedance andquality and the qubits' noise bath.
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