Efficient Z-Gates for Quantum Computing

Abstract

For superconducting qubits, microwave pulses drive rotations around the Bloch sphere. The phase of these drives can be used to generate zero-duration arbitrary "virtual" Z-gates which, combined with two $X_{\pi /2}$ gates, can generate any SU(2) gate. Here we show how to best utilize these virtual Z-gates to both improve algorithms and correct pulse errors. 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 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 13.3~ns $X_{\pi /2}$ gate characterized by low error ($1.95[3]\times 10^{-4}$) and low leakage ($3.1[6]\times 10^{-6}$). 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.

8 pages, 6 figures. V2: Small changes to improve clarity. Added a section on z-gates in multiqubit systems

References in corpus (7)

• Charge insensitive qubit design derived from the Cooper pair box
• Demonstration of Two-Qubit Algorithms with a Superconducting Quantum Processor
• Randomized Benchmarking of Quantum Gates
• Simple pulses for elimination of leakage in weakly nonlinear qubits
• Robust randomized benchmarking of quantum processes
• Analytic control methods for high fidelity unitary operations in a weakly nonlinear oscillator
• Quantification and Characterization of Leakage Errors

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