Concatenated continuous driving of silicon qubit by amplitude and phase modulation

Concatenated continuous driving (CCD) is a control technique that maintains a qubit under continuous drive to enhance coherence by cancelling noise via phase or amplitude modulation [1]. Recently, we demonstrated that the coherence of an electron spin in natural silicon can be extended and controlled using a phase-modulated CCD scheme [2]. In this work, we propose a new variant, circularly-modulated CCD (CMCCD), which simultaneously modulates both amplitude and phase to generate a circularly polarized field in the rotating frame. This cancels the counter-rotating term in the second rotating frame, mitigating gate infidelities due to the breakdown of the rotating wave approximation during fast gates. Numerical simulations show that CMCCD achieves higher gate fidelities than conventional CCD. Furthermore, we implement and compare CCD protocols using an electron spin qubit in an isotopically enriched ²⁸Si-MOS quantum dot. Robustness is experimentally evaluated under static detuning and Rabi frequency errors. The scheme is applicable to various platforms including trapped ions, cold atoms, superconducting qubits, and NV centers.

[1] A. J. Ramsay et al., Nat. Commun. 14, 461 (2023). [2] T.Kuno et al., arXiv:2503.19410 (2025).