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Chinese Physics B

Enhancing idle gate coherence through concatenated continuous driving in SiMOS quantum dot

Wei-Zhu Liao, Ao-Ran Li, Zhen-Zhen Kong, Gang Luo, Di Liu, G Z Wang, Gang Cao, Hai-Ou Li, Guo G

Published Jun 16, 2026• 0 citations
Publisher

Abstract

Abstract Spin qubits based on semiconductor quantum dots have recently emerged as strong candidates for scalable quantum computation. However, due to substantial charge noise in the system, the coherence time remains insufficient to support large-scale quantum computations. Moreover, the fidelity of idle gates is severely degraded by the short dephasing time, which may compromise the overall quality of full quantum algorithms. Here, we demonstrate a circular-modulated concatenated continuous driving (CM-CCD) qubit realized in $^{28}$Si metal-oxide-semiconductor (SiMOS) devices to overcome this challenge. This scheme significantly enhances the qubit's resilience to noise and substantially improves its coherence: the dephasing time $T_{2}^{*}$ is extended from $717.7\ \text{ns}$ to $101.5\ \mu\text{s}$, and the Rabi coherence time $T_{2}^{\text{Rabi}}$ is improved from $7.8\ \mu\text{s}$ to $77.6\ \mu\text{s}$. We further propose a scheme to resolve the timing misalignment of CCD-based idle gates, improving the idle gate fidelity from 95.95% to 99.01%. Collectively, these results demonstrate that the CCD scheme offers a promising pathway to overcome the idle-gate challenge in large-scale quantum computations.

DOI
10.1088/1674-1056/ae7dbb

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Abstract Spin qubits based on semiconductor quantum dots have recently emerged as strong candidates for scalable quantum computation. However, due to substantial charge noise in the system, the coherence time remains insufficient to support large-scale quantum computations. Moreover, the fidelity of idle gates is severely degraded by the short dephasing time, which may compromise the overall quality of full quantum algorithms. Here, we demonstrate a circular-modulated concatenated continuous driving (CM-CCD) qubit realized in 28^{28}28Si metal-oxide-semiconductor (SiMOS) devices to overcome this challenge. This scheme significantly enhances the qubit's resilience to noise and substantially improves its coherence: the dephasing time T2∗T_{2}^{*}T2∗​ is extended from 717.7 ns717.7\ \text{ns}717.7 ns to 101.5 μs101.5\ \mu\text{s}101.5 μs, and the Rabi coherence time T2RabiT_{2}^{\text{Rabi}}T2Rabi​ is improved from 7.8 μs7.8\ \mu\text{s}7.8 μs to 77.6 μs77.6\ \mu\text{s}77.6 μs. We further propose a scheme to resolve the timing misalignment of CCD-based idle gates, improving the idle gate fidelity from 95.95% to 99.01%. Collectively, these results demonstrate that the CCD scheme offers a promising pathway to overcome the idle-gate challenge in large-scale quantum computations.
The rate of coherence loss is lower for a qubit under the Rabi drive than 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 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 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 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.
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.
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.
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.
In semiconductor single-spin qubits, high-fidelity quantum gates have been demonstrated; however, achieving consistent performance remains challenging due to variations in driven qubit coherence, which is less explored than free-evolution coherence such as T2∗T_2^*T2∗​. Here, we report single-qubit gate fidelities above 99.999%, achieved by dramatically extending the driven-spin coherence time and suppressing off-resonant driving effects that are detrimental to accurate fidelity benchmarking. We demonstrate that removing proximal reservoirs significantly enhances the spin-locking coherence time (T1ρT_{1ρ}T1ρ​), a critical metric for qubits under microwave driving. Furthermore, we reveal that in typical spin qubit setups using parity readout and rectangular pulses, off-resonant excitation of neighboring qubits causes substantial benchmarking artifacts. By optimizing device conditions to mitigate microwave-induced degradation and implementing spectrally tailored pulse shaping, we achieve a π/2π/2π/2 gate fidelity of 99.99920(2)%, with remaining errors primarily limited by incoherent noise. These results showcase the mechanisms that bound fidelity benchmarking in state-of-the-art silicon spin qubits and provide practical guidelines for achieving and verifying high fidelities in these systems.
The coherence of electron spin qubits in semiconductor quantum dots suffers mostly from low-frequency noise.During the past decade, efforts have been devoted to mitigate such noise by material engineering, leading to substantial enhancement of the spin dephasing time for an idling qubit.However, the role of the environmental noise during spin manipulation, which determines the control fidelity, is less understood.We demonstrate an electron spin qubit whose coherence in the driven evolution is limited by highfrequency charge noise rather than the quasistatic noise inherent to any semiconductor device.We employ a feedback-control technique to actively suppress the latter, demonstrating a π-flip gate fidelity as high as 99.04 Æ 0.23% in a gallium arsenide quantum dot.We show that the driven-evolution coherence is limited by the longitudinal noise at the Rabi frequency, whose spectrum resembles the 1=f noise observed in isotopically purified silicon qubits.