Application of Weighted Chebyshev Approximation in Pulse Design for Quantum Gates

Chebyshev approximation problems are fundamen-tal in approximation theory and are integral to various engi-neering applications. In this study, we suggest that weighted Chebyshev approximation (WCA) can be effectively applied to designing quantum gates. Specifically, we examine a class of two-qubit gates in superconducting qubits known as controlled-phase (CPHASE) gates, which leverage interactions between higher levels controlled by baseband flux pulses. We frame the design of CPHASE gates as a pulse design problem and propose Chebyshev pulses, generated through WCA, as an alternative solution. We utilize an illustrative example to demonstrate our process of designing a Chebyshev pulse with WCA, then contrast it with a benchmark Slepian pulse for comparison. We find that Chebyshev pulses can facilitate faster CPHASE gates while ensuring leakage errors remain below the desired threshold.