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Concatenated continuous driving of silicon qubit by amplitude and phase modulation

Takuma Kuno1,2,*, Takeru Utsugi1, Andrew J. Ramsay3, Normann Mertig3, Noriyuki Lee1, Itaru Yanagi1, Toshiyuki Mine1, Nobuhiro Kusuno1, Hideo Arimoto1 et al.

Sofie Beyne4, Julien Jussot4, Stefan Kubicek4, Yann Canvel4, Clement Godfrin4, Bart Raes4, Yosuke Shimura4, Roger Loo4,5, Sylvain Baudot4, Danny Wan4, Kristiaan De Greve4,6, Shinichi Saito1, Digh Hisamoto1, Ryuta Tsuchiya1, Tetsuo Kodera2, and Hiroyuki Mizuno1

  • *Contact author: takuma.kuno.pg@hitachi.com

Phys. Rev. B 113, 195303 – Published 13 May, 2026

DOI: https://doi.org/10.1103/f2kd-x628

Abstract

The rate of coherence loss is lower for a qubit under the Rabi drive than a freely evolving qubit T2Rabi>T2*. Building on this principle, concatenated continuous driving (CCD) keeps the qubit under continuous drive to suppress noise and manipulate dressed states by either phase or amplitude modulation. In this work, we propose a variant of CCD which simultaneously modulates both the amplitude and phase of the driving field to generate a circularly polarized field in the rotating frame of the carrier frequency. This circular-modulated CCD (CMCCD) cancels the counterrotating term in the second rotating frame, eliminating a systematic pulse-area error that arises from an imperfect rotating wave approximation for fast gates. Numerical simulations demonstrate that the proposed CMCCD achieves higher gate fidelity than conventional CCD schemes. We further implement and compare different CCD protocols using an electron spin-qubit in an isotopically purified Si-MOS28 quantum dot and evaluate its robustness by applying static detuning and Rabi frequency errors. The robustness is significantly improved compared with the standard Rabi drive, showing the effectiveness of this scheme for qubit arrays with variation in qubit frequency, coupling to the Rabi drive, and low-frequency noise. The proposed scheme can be applied to various physical systems, including trapped atoms, cold atoms, superconducting qubits, and NV centers.

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