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Frequency- and Amplitude-Modulated Gates for Universal Quantum Control

Qi Ding1,2,*, Shoumik D. Chowdhury1,2, Agustin Di Paolo3, Réouven Assouly2, Alan V. Oppenheim1,2, Jeffrey A. Grover2, and William D. Oliver1,2,4,†

  • *Contact author: qding@mit.edu
  • †Contact author: william.oliver@mit.edu
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PRX Quantum 7, 033066 – Published 24 September, 2026

DOI: https://doi.org/10.1103/zhk6-vxnn

Abstract

Achieving high-fidelity single- and two-qubit gates is essential for executing arbitrary digital quantum algorithms and for building error-corrected quantum computers. We propose a theoretical framework for implementing quantum gates using frequency- and amplitude-modulated microwave control, enabling the systematic analysis and design of frequency modulation alongside conventional amplitude modulation. Our approach operates on fixed-frequency qubits, converting the need for qubit frequency tunability into drive frequency modulation. Using Floquet theory, we analyze and design these drives for optimal fidelity within specified criteria. Our framework spans adiabatic to nonadiabatic gates within the Floquet framework, ensuring broad applicability across gate types and control schemes. Using typical transmon qubit parameters in numerical simulations, we demonstrate a universal gate set—including the X, Hadamard, phase, and cz gates—with control error well below 0.1% and gate times of 25–40 ns for single-qubit operations and 125–135 ns for two-qubit operations. Furthermore, we show an always-on cz gate tailored for driven qubits, which has gate times of 80–90 ns.

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Popular Summary

High-fidelity quantum gates are essential for running quantum algorithms and building error-corrected quantum computers. In superconducting qubits, microwave control on fixed-frequency devices offers hardware simplicity and reduced flux-noise sensitivity, but can suffer from frequency crowding. Flux control enables faster and more tunable gates, but adds calibration complexity and noise sensitivity. Here, we propose an all-microwave framework for designing gates using both amplitude and frequency modulation of the drive. By treating the microwave drive frequency as an additional control knob, our approach brings tunability to fixed-frequency qubits without requiring direct qubit-frequency tuning. This approach can help alleviate frequency-crowding constraints while preserving the reduced flux-noise sensitivity and coherence advantages associated with fixed-frequency qubits. Numerical simulations with typical transmon parameters demonstrate a universal set of single- and two-qubit gates, including X, Hadamard, phase, and cz gates, with control errors well below 0.1%. These results suggest that frequency-modulated microwave control can provide a flexible route to fast, high-fidelity gates in superconducting quantum processors.

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PRX Quantum 7, 033066– Published 24 September, 2026
  • Received 4 November 2025
  • Accepted 18 August 2026
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