Comprehensive explanation of ZZ coupling in superconducting qubits

TL;DR

This paper introduces analytical and numerical methods to understand and control unwanted ZZ couplings in superconducting qubits, aiding the design of scalable quantum computers with high gate fidelity.

Contribution

It provides a comprehensive framework with multiple pictures to explain ZZ coupling mechanisms, enabling identification of parameter regions for weak or strong coupling.

Findings

Identified parameter regions with near-zero ZZ coupling using current technology

Developed diagrammatic perturbation theory and a state-assignment algorithm

Demonstrated potential for implementing adiabatic controlled-phase gates

Abstract

A major challenge for scaling up superconducting quantum computers is unwanted couplings between qubits, which lead to always-on ZZ couplings that impact gate fidelities by shifting energy levels conditional on qubit states. To tackle this challenge, we introduce analytical and numerical techniques, including a diagrammatic perturbation theory and a state-assignment algorithm. Together, these tools enable us to explain the emergence of ZZ coupling in three linked pictures, where each picture tells us more about the underlying mechanisms creating the ZZ coupling. These pictures generalize previous efforts, which focused on specific setups and a single mechanism. The deeper understanding that we provide of the mechanisms behind the ZZ coupling facilitate finding parameter regions of weak and strong ZZ coupling. We showcase our techniques for a system consisting of two fixed-frequency transmon qubits connected by a flux-tunable transmon coupler. There, we find three types of parameter regions with zero or near-zero ZZ coupling, all of which are accessible with current technology. We furthermore find regions of strong ZZ coupling nearby, which may be used to implement adiabatic controlled-phase gates and quantum simulations. Our framework is applicable to many types of qubits and opens up for the design of large-scale quantum computers with improved gate fidelities.