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arXiv:2601.11245 · Physical review. B./Physical review. B

Concatenated continuous driving of silicon qubit by amplitude and phase modulation

Takuma Kuno, Takeru Utsugi, Andrew J. Ramsay, Normann Mertig, Noriyuki Lee, Itaru Yanagi, Toshiyuki Mine, Nobuhiro Kusuno, Hideo Arimoto, Sofie Beyne, Julien Jussot, Stefan Kubicek, Yann Canvel, Clement Godfrin, Bart Raes, Yosuke Shimura, Roger Loo, Sylvain Baudot, Danny Wan, Kristiaan De Greve, Shinichi Saito, Digh Hisamoto, Ryuta Tsuchiya, Tetsuo Kodera, Hiroyuki Mizuno

quant-phSubmitted Jan 16, 2026• Announced Jan 19, 2026• 1 citation
v1 · Jan 16, 2026v2 · Apr 21, 2026v3 · May 17, 2026
arXivHTMLPDF

Abstract

The rate of coherence loss is lower for a qubit under Rabi drive compared to a freely evolving qubit, $T_{2}^{\rm{Rabi}}>T_{2}^*$. 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 new 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 (CM)-CCD cancels the counter-rotating 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 $^{28}$Si-MOS quantum dot and evaluate its robustness by applying static detuning and Rabi frequency errors. The robustness is significantly improved compared to standard Rabi-drive, showing the effectiveness of this scheme for qubit arrays with variation in qubit frequency, coupling to 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.

Journal reference
Phys. Rev. B 113, 195303 (2026)
DOI
10.1103/f2kd-x628
Comments
12 pages, 10 figures

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The rate of coherence loss is lower for a qubit under Rabi drive compared to a freely evolving qubit, T2Rabi>T2∗T_{2}^{\rm{Rabi}}>T_{2}^*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 new 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 (CM)-CCD cancels the counter-rotating 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 28^{28}28Si-MOS quantum dot and evaluate its robustness by applying static detuning and Rabi frequency errors.
The robustness is significantly improved compared to standard Rabi-drive, showing the effectiveness of this scheme for qubit arrays with variation in qubit frequency, coupling to 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.
Hole spins in silicon quantum dots are a promising platform for quantum computing due to their strong intrinsic spin-orbit coupling (SOC), which enables fast, all-electrical control. However, this coupling also increases their susceptibility to charge noise, thereby limiting coherence times. Moreover, holes in silicon are also affected by hyperfine interactions with residual nuclear spins in the silicon substrate, introducing a non-negligible source of low-frequency noise. Here, we implement a phase-modulated concatenated continuous driving (CCD) technique for hole spin qubits to suppress low-frequency noise through microwave phase modulation. This approach stabilizes Rabi oscillations and extends the oscillation decay time compared to the conventional method. Furthermore, by defining a qubit in the CCD frame, we achieve coherent control while simultaneously protecting the qubit from noise, confirming coherence protection during gate operations. These results demonstrate a viable route toward noise-robust hole spin qubits.
Exchange-based two-qubit gates in semiconductor spin qubits are sensitive to low-frequency detuning noise and control errors. Here, we extend concatenated continuous driving (CCD), implemented by phase modulation of a global microwave drive, to exchange-based SWAP and SWAP\sqrt{\mathrm{SWAP}}SWAP​ operations between double-dressed spin qubits and investigate its effectiveness for protecting two-qubit gates. We find that CCD retains strong protection against quasistatic common-mode detuning errors while substantially improving robustness against Rabi-frequency errors and qubit-to-qubit Rabi-frequency mismatch compared with conventional continuous dressing. By contrast, the gate fidelity is impacted by differential detuning errors. By modeling partially correlated quasistatic detuning noise, we further show that the noise-averaged gate fidelity depends strongly on the spatial correlation of the qubit-frequency fluctuations, with positive correlations enhancing CCD protection by suppressing the differential-noise component. These results identify the symmetry and spatial correlation of qubit-frequency noise as key factors governing continuous-drive protection in coupled spin-qubit systems.
Performing qubit gate operations as quickly as possible can be important to minimize the effects of decoherence. For resonant gates, this requires applying a strong ac drive. However, strong driving can present control challenges by causing leakage to levels that lie outside the qubit subspace. Strong driving can also present theoretical challenges because preferred tools such as the rotating wave approximation can break down, resulting in complex dynamics that are difficult to control. Here we analyze resonant XXX rotations of a silicon-quantum-double-dot hybrid qubit within a dressed-state formalism, obtaining results beyond the rotating wave approximation. We obtain analytic formulas for the optimum driving frequency and the Rabi frequency, which are both affected by strong driving. While the qubit states exhibit fast oscillations due to counter-rotating terms and leakage, we show that they can be suppressed to the point that gate fidelities above 99.9999.99%99.99 are possible, in the absence of decoherence. Hence decoherence mechanisms, rather than strong-driving effects, should represent the limiting factor for resonant-gate fidelities in quantum dot hybrid qubits.
Abstract Dense ensembles of spin qubits are valuable for quantum applications, even though their coherence protection remains challenging. Continuous dynamical decoupling can protect ensemble qubits from noise while allowing gate operations, but it is hindered by the additional noise introduced by the driving. Concatenated continuous driving (CCD) techniques can, in principle, mitigate this problem. Here we provide deeper insights into the dynamics under CCD, based on Floquet theory, that lead to optimized state protection by adjusting driving parameters in the CCD scheme to induce mode evolution control. We experimentally demonstrate the improved control by simultaneously addressing a dense nitrogen-vacancy (NV) ensemble with 1010 spins. We achieve an experimental 15-fold improvement in coherence time for an arbitrary, unknown state, and a 500-fold improvement for an arbitrary, known state, corresponding to driving the sidebands and the center band of the resulting Mollow triplet, respectively. We can achieve such coherence time gains by optimizing the driving parameters to take into account the noise affecting our system. By extending the generalized Bloch equation approach to the CCD scenario, we identify the noise sources that dominate the decay mechanisms in NV ensembles, confirm our model by experimental results, and identify the driving strengths yielding optimal coherence. Our results can be directly used to optimize qubit coherence protection under continuous driving and bath driving, and enable applications in robust pulse design and quantum sensing.
Global control strategies for arrays of qubits are a promising pathway to scalable quantum computing. A continuous-wave global field provides decoupling of the qubits from background noise. However, this approach is limited by variability in the parameters of individual qubits in the array. Here we show that by modulating a global field simultaneously applied to the entire array, we are able to encode qubits that are less sensitive to the statistical scatter in qubit resonance frequency and microwave amplitude fluctuations, which are problems expected in a large-scale system. We name this approach the SMART (sinusoidally modulated, always rotating, and tailored) qubit protocol. We show that there exist optimal modulation conditions for qubits in a global field that robustly provide improved coherence times. We discuss in further detail the example of spins in silicon quantum dots, in which universal one- and two-qubit control is achieved electrically by controlling the spin-orbit coupling of individual qubits and the exchange coupling between spins in neighboring dots. This paper provides a high-fidelity qubit operation scheme in a global field, significantly improving the prospects for scalability of spin-based quantum computer architectures.
Qubit decoherence unavoidably degrades the fidelity of quantum logic gates. Accordingly, realizing gates that are as fast as possible is a guiding principle for qubit control, necessitating protocols for mitigating error channels that become significant as gate time is decreased. One such error channel arises from the counter-rotating component of strong, linearly polarized drives. This error channel is particularly important when gate times approach the qubit Larmor period and represents the dominant source of infidelity for sufficiently fast single-qubit gates with low-frequency qubits such as fluxonium. In this work, we develop and demonstrate two complementary protocols for mitigating this error channel. The first protocol realizes circularly polarized driving in circuit QED through simultaneous charge and flux control. The second protocol—commensurate pulses—leverages the coherent and periodic nature of counter-rotating fields to regularize their contributions to gates, enabling single-qubit gate fidelities reliably exceeding 99.997%. This protocol is platform independent and requires no additional calibration overhead. This work establishes straightforward strategies for mitigating counter-rotating effects from strong drives in circuit QED and other platforms, which we expect to be helpful in the effort to realize high-fidelity control for fault-tolerant quantum computing. Published by the American Physical Society 2024