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

TL;DR

This paper analyzes the error sources in implementing high-fidelity controlled-Z gates in large-scale superconducting quantum systems, providing insights for software and hardware optimization to achieve fault tolerance.

Contribution

It demonstrates the need for system-specific pulse optimization and characterizes hardware parameter regions affecting gate fidelity in large-scale quantum systems.

Findings

Optimal single-parameter pulse achieves ~10^{-4} error in 40 ns in 4-qubit system.

Pulse optimization in small systems is insufficient for larger systems.

Low-fidelity regions are linked to resonances in the 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.