Gate Error Analysis of Tunable Coupling Architecture in the Large-scale Superconducting Quantum System

Abstract

In this paper, we examine various software and hardware strategies for implementing high-fidelity controlled-Z gate in the large-scale quantum system by solving the system's Hamiltonian with the Lindblad master equation. First, we show that the optimal single-parameter pulse achieved the gate error on the order of $10^{-4}$ for the 40 ns controlled-Z gate in the 4-qubit system. Second, we illustrate that the pulse optimized in the isolated 2-qubit system must be further optimized in the larger-scale system to achieve errors lower than the fault-tolerant threshold. Lastly, we explain that the hardware parameter regions with low gate fidelities are characterized by resonances in the large-scale quantum system. Our study provides software-oriented and hardware-level guidelines for building a large-scale fault-tolerant quantum system.