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Applied Physics Express

Stabilization of a silicon double quantum dot based on a multi-dimensional gradient descent technique

Chutian Wen, Hiroki Takahashi, Sayyid Irsyadul Ibad, Shimpei Nishiyama, Kimihiko Kato, Yongxun Liu, Shigenori Murakami, Takahiro Mori, Raisei Mizokuchi, Jun Yoneda, Tetsuo Kodera

Published Dec 5, 2024• 3 citations
Publisher

Abstract

Abstract With a view to long-term qubit device operation, we report on a method to stabilize a silicon double quantum dot against slow drift in a two-dimensional gate-voltage space based on a current gradient-based feedback technique. We demonstrate that, unlike conventional single-axis feedback schemes, our method can maintain the double-dot potential configuration. We measure a feedback bandwidth of up to 300 mHz, consistent with the sampling rate and the digital filter cutoff frequency used in the experiment.

DOI
10.35848/1882-0786/ad9af8

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Abstract With a view to long-term qubit device operation, we report on a method to stabilize a silicon double quantum dot against slow drift in a two-dimensional gate-voltage space based on a current gradient-based feedback technique. We demonstrate that, unlike conventional single-axis feedback schemes, our method can maintain the double-dot potential configuration. We measure a feedback bandwidth of up to 300 mHz, consistent with the sampling rate and the digital filter cutoff frequency used in the experiment.
Long term operation of semiconductor spin qubits requires active stabilization of quantum dot potentials against low-frequency charge noise. To address this, we demonstrate a gradient-descent feedback approach in a silicon double quantum dot device using high-bandwidth radio-frequency (rf) reflectometry readout and a field-programmable gate array (FPGA) for digital signal processing. This architecture enables continuous multi-parameter gradient calculation and quick gate voltage updates, significantly increasing the effective feedback bandwidth compared to previous methods relying on slow direct-current transport measurements. By operating with 8 steps per feedback cycle and an integration time of 25.6 μμμs, this high-speed stabilization scheme maintains better than -6 dB of noise suppression up to 5 kHz, achieving an attenuation of −7.4±0.2-7.4 \pm 0.2−7.4±0.2 dB at the maximum measured frequency. This effectively suppresses low-frequency 1/f noise, maintaining device stability over longer time periods, and potentially enables real-time control in large-scale quantum dot arrays.
The performance and scalability of semiconductor quantum-dot (QD) qubits are limited by electrostatic drift and charge noise that shift operating points and destabilize qubit parameters. As systems expand to large one- and two-dimensional arrays, manual recalibration becomes impractical, creating a need for autonomous stabilization frameworks. Here, we introduce a method that uses the full network of charge-transition lines in repeatedly acquired double-quantum-dot charge stability diagrams (CSDs) as a multidimensional probe of the local electrostatic environment. By accurately tracking the motion of selected transitions in time, we detect voltage drifts, identify abrupt charge reconfigurations, and apply compensating updates to maintain stable operating conditions. We demonstrate our approach on a 10-QD device, showing robust stabilization and real-time diagnostic access to dot-specific noise processes. The high acquisition rate of radio-frequency reflectometry CSD measurements also enables time-domain noise spectroscopy, allowing the extraction of noise power spectral densities, the identification of two-level fluctuators, and the analysis of spatial noise correlations across the array. From our analysis, we find that the background noise at 100~μμμ\si{\hertz} is dominated by drift with a power law of 1/f21/f^21/f2, accompanied by a few dominant two-level fluctuators and an average linear correlation length of (188±38)(188 \pm 38)(188±38)~\si{\nano\meter} in the device. These capabilities form the basis of a scalable, autonomous calibration and characterization module for QD-based quantum processors, providing essential feedback for long-duration, high-fidelity qubit operations.
Gate-defined semiconductor quantum dots utilize fast electrical control to manipulate spin and charge states of individual electrons. Electrical pulse distortions can limit control fidelities but are difficult to measure at the device level. Here, we use detuning-axis pulsed spectroscopy to characterize baseband pulse distortions in a silicon double quantum-dot. We extract the gate-voltage impulse response and apply a digital pre-distortion filter to eliminate pulse distortions on timescales longer than 1~ns. With the pre-distortion, we reduce the frequency chirp of coherent exchange oscillations in a singlet-triplet qubit. Our results suggest a scalable and tuning-efficient method for characterizing pulse distortions in quantum-dot spin qubits.
Abstract Quantum dots in silicon are a promising architecture for semiconductor quantum computing due to a high degree of electric control and compatibility with existing silicon fabrication processes. Although electron charge and spin are prominent methods for encoding the qubit state, valley states in silicon can also store quantum information via valley-orbit coupling with protection against charge noise. By observing coherent oscillations between valley states in a Si/SiGe double quantum dot device tuned to the two-electron charge configuration, we measure the valley energy splitting in both quantum dots individually. We further demonstrate two-axis quantum control of the valley qubit using gated pulse sequences with X and Z rotations occurring within a fast operation time of 300 ps. This control is used to completely map out the surface of the Bloch sphere in a single phase-space plot that is subsequently used for state and process tomography.
Fast measurement, signal processing, and accurate estimation of Hamiltonian parameters are essential for feedback control in quantum-classical interface circuitry. However, existing frequentist and Bayesian inference methods typically require a large number of measurements to achieve the accuracy needed to mitigate qubit decoherence. Consequently, feedback control of semiconductor qubits has largely been limited to single-qubit frequency stabilization, whereas two-qubit parameter stabilization remains experimentally unexplored. Here, we demonstrate a real-time feedback framework based on sequential Monte Carlo estimation using one bit of data from a single-shot measurement. Using a four-qubit semiconductor quantum dot device, we rapidly estimate individual qubit frequencies, yielding an approximately twofold increase in coherence time compared with a conventional Bayesian strategy. Moreover, sequential two-qubit parameter estimation using two bits of data enables stabilization of qubit-qubit coupling, allowing both quasi-static frequency drift and exchange-interaction noise to be estimated and suppressed. By shortening the time required for precise parameter estimation, these results demonstrate the importance of the synergistic development of classical and quantum electronics for building robust and scalable quantum technologies in fluctuating environments.
Abstract Electron spins in semiconductors are promising qubits because their long coherence times enable nearly 10 9 coherent quantum gate operations. However, developing a scalable high-fidelity two-qubit gate remains challenging. Here, we demonstrate an entangling gate between two double-quantum-dot spin qubits in GaAs by using a magnetic field gradient between the two dots in each qubit to suppress decoherence due to charge noise. When the magnetic gradient dominates the voltage-controlled exchange interaction between electrons, qubit coherence times increase by an order of magnitude. Using randomized benchmarking, we measure single-qubit gate fidelities of ~ 99%, and through self-consistent quantum measurement, state, and process tomography, we measure an entangling gate fidelity of 90%. In the future, operating double quantum dot spin qubits with large gradients in nuclear-spin-free materials, such as Si, should enable a two-qubit gate fidelity surpassing the threshold for fault-tolerant quantum information processing.