Systematic frequency-collision analysis of the cross-resonance gate outside the straddling regime

TL;DR

This paper proposes operating the cross-resonance gate outside the traditional straddling regime to reduce frequency collisions in large-scale fixed-frequency transmon quantum processors.

Contribution

It introduces a systematic analysis and optimization method for frequency allocation in the far-detuned regime, improving collision-free qubit frequency assignment.

Findings

Far-detuned CR gate design reduces frequency collisions.

Systematic parameter sweeps identify collision-free frequency regions.

Linear programming optimizes qubit frequency allocation for large lattices.

Abstract

Frequency crowding remains a major obstacle to scaling fixed-frequency transmon processors. Among the widely used all-microwave two-qubit gates, the cross-resonance (CR) gate is particularly sensitive to qubit-frequency spread because the conventional straddling regime condition constrains assignable qubit frequencies tightly and makes the system susceptible to frequency collisions. Here, we propose and analyze the CR gate outside the straddling regime, which we refer to as the far-detuned regime, and evaluate frequency collisions using a numerical method that remains accurate under high-intensity, smoothly ramped microwave drives. Based on this analysis, we perform systematic parameter sweeps and provide collision-free conditions that define designable frequency regions in which qubit frequencies can be assigned consistently with surrounding qubit frequencies. Furthermore, we formulate frequency allocation as a linear programming optimization on a unit-cell lattice with periodic boundary conditions to obtain an optimal allocation. We demonstrate that far-detuned designs significantly reduce collisions compared with designs in the straddling regime. Monte Carlo yield analysis indicates that 10% collision-free yield for a 1024-qubit square lattice at a 0.1% two-qubit-gate error threshold requires $\sigma_{\mathrm{f}}/2\pi \le 6.8~\mathrm{MHz}$. Our findings suggest that this is feasible with an approximately twofold reduction in the state-of-the-art qubit-frequency spread.