Optimization of Two-Qubit Gates in Tunable-Coupler Architectures Using Single-Flux-Quantum Control

We present a gradient-based method for constructing high-fidelity, two-qubit quantum gates in a system consisting of two transmon qubits coupled via a tunable coupler. In particular, we focus on single-flux-quantum [1, 2] pulses as a promising and scalable alternative to traditional control schemes that use microwave electronics. We develop a continuous embedding scheme and use it to optimize these discrete pulses, taking advantage of autodifferentiation in our model. This approach allows us to achieve fSim-type gates with average gate fidelities on the order of 99.99% and controlled-Z and controlled-NOT gates with fidelities above 99.9%. Furthermore, we provide an alternative semianalytical construction of these gates via an exact decomposition [3] using a pair of fSim gates, which leads to the reduction in memory required to store the associated pulse sequences.

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[2] Cesar A Mancini and Mark F Bocko. Phase-locked operation of rsfq ring oscillators. Superconductor Science and Technology, 12(11):789, 1999.

[3] Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando GSL Brandao, David A Buell, et al. Quantum supremacy using a programmable superconducting processor. Nature, 574(7779):505–510, 2019.