Gate-error analysis in simulations of quantum computers with transmon qubits

TL;DR

This paper analyzes various metrics for gate errors in superconducting transmon qubits, revealing their limitations in predicting gate performance in quantum algorithms.

Contribution

It provides a numerical analysis of gate fidelity, diamond distance, and unitarity for transmon qubits, highlighting their systematic errors and predictive limitations.

Findings

Metrics reflect systematic errors in gate implementation.

Echoed cross-resonance gates show pronounced errors.

Metrics cannot reliably predict repeated gate performance.

Abstract

In the model of gate-based quantum computation, the qubits are controlled by a sequence of quantum gates. In superconducting qubit systems, these gates can be implemented by voltage pulses. The success of implementing a particular gate can be expressed by various metrics such as the average gate fidelity, the diamond distance, and the unitarity. We analyze these metrics of gate pulses for a system of two superconducting transmon qubits coupled by a resonator, a system inspired by the architecture of the IBM Quantum Experience. The metrics are obtained by numerical solution of the time-dependent Schr\"odinger equation of the transmon system. We find that the metrics reflect systematic errors that are most pronounced for echoed cross-resonance gates, but that none of the studied metrics can reliably predict the performance of a gate when used repeatedly in a quantum algorithm.