Efficient Z-Gates for Quantum Computing

For superconducting qubits, microwave pulses drive rotations around the Bloch sphere. Here we show that the phase of these drives can be used to generate zero-duration arbitrary Z-gates which, combined with two Xπ/2 gates, can generate any SU(2) gate. We perform randomized benchmarking using a Clifford set of Hadamard and Z-gates and show that the error per Clifford is reduced versus a set consisting of standard finite-duration X and Y gates. Z-gates can also correct unitary rotation errors for weakly anharmonic qubits as an alternative to pulse shaping techniques such as DRAG. We investigate leakage and show that a combination of DRAG pulse shaping to minimize leakage and Z-gates to correct rotation errors (DRAGZ) realizes a 13.3ns Xπ/2 gate characterized by low error (1.95[3]×10−4) and low leakage (3.1[6]×10−6). Ultimately leakage is limited by the finite temperature of the qubit, but this limit is two orders-of-magnitude smaller than pulse errors due to decoherence.