Analysis of Frequency Collisions in Parametrically Modulated Superconducting Circuits

TL;DR

This paper introduces a numerical and analytical framework based on Floquet theory to analyze and mitigate frequency collisions caused by parametric modulation in superconducting quantum circuits, enhancing scalability.

Contribution

It develops a comprehensive method combining numerical Floquet analysis and analytical models to identify and avoid parasitic frequency collisions in superconducting circuits.

Findings

Framework effectively predicts parasitic interactions.

Optimization identifies parameter regimes avoiding collisions.

Application to quantum gate design improves fidelity.

Abstract

Superconducting circuits are a leading platform for scalable quantum computing, where parametric modulation is a widely used technique for implementing high-fidelity multi-qubit operations. A critical challenge, however, is that this modulation can induce a dense landscape of parasitic couplings, leading to detrimental frequency collisions that constrain processor performance. In this work, we develop a comprehensive numerical framework, grounded in Floquet theory, to systematically analyze and mitigate these collisions. Our approach integrates this numerical analysis with newly derived analytical models for both qubit-modulated and coupler-modulated schemes, allowing us to characterize the complete map of parasitic sideband interactions and their distinct error budgets. This analysis forms the basis of a constraint-based optimization methodology designed to identify parameter configurations that satisfy the derived physical constraints, thereby avoiding detrimental parasitic interactions. We illustrate the utility of this framework with applications to analog quantum simulation and gate design. Our work provides a predictive tool for co-engineering device parameters and control protocols, enabling the systematic suppression of crosstalk and paving the way for large-scale, high-performance quantum processors.