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arXiv:2309.09723 · Physical Review Applied

Singlet-triplet-state readout in silicon metal-oxide-semiconductor double quantum dots

Rong-Long Ma, Sheng-Kai Zhu, Zhenzhen Kong, Tai‐Ping Sun, Ming Ni, Yu-Chen Zhou, Yuan Lin Zhou, Gang Luo, Gang Cao, Guilei Wang, Hai-Ou Li, Guo‐Ping Guo

Published Mar 13, 2024• 7 citations
arXivHTMLPDF

Abstract

High-fidelity singlet-triplet state readout is essential for large-scale quantum computing. However, the widely used threshold method of comparing a mean value with the fixed threshold will limit the judgment accuracy, especially for the relaxed triplet state, under the restriction of relaxation time and signal-to-noise ratio. Here, we achieve an enhanced latching readout based on Pauli spin blockade in a Si-MOS double quantum dot device and demonstrate an average singlet-triplet-state readout fidelity of 97.59% by the threshold method. We reveal the inherent deficiency of the threshold method for the relaxed triplet-state classification and introduce machine learning as a noise-resilient and relaxation-independent readout method to reduce the misjudgment. The readout fidelity for classifying the simulated single-shot traces can be improved to 99.67% by the machine-learning method, better than the threshold method of 97.54%, which is consistent with the experimental result. This work indicates that the machine-learning method can be a strong potential candidate for alleviating the restrictions of stably achieving high-fidelity and high-accuracy singlet-triplet-state readout in large-scale quantum computing.

DOI
10.1103/physrevapplied.21.034022

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High-fidelity singlet-triplet state readout is essential for large-scale quantum computing. However, the widely used threshold method of comparing a mean value with the fixed threshold will limit the judgment accuracy, especially for the relaxed triplet state, under the restriction of relaxation time and signal-to-noise ratio. Here, we achieve an enhanced latching readout based on Pauli spin blockade in a Si-MOS double quantum dot device and demonstrate an average singlet-triplet-state readout fidelity of 97.59% by the threshold method. We reveal the inherent deficiency of the threshold method for the relaxed triplet-state classification and introduce machine learning as a noise-resilient and relaxation-independent readout method to reduce the misjudgment. The readout fidelity for classifying the simulated single-shot traces can be improved to 99.67% by the machine-learning method, better than the threshold method of 97.54%, which is consistent with the experimental result. This work indicates that the machine-learning method can be a strong potential candidate for alleviating the restrictions of stably achieving high-fidelity and high-accuracy singlet-triplet-state readout in large-scale quantum computing.
Pauli-spin-blockade (PSB) measurements have so far achieved the highest fidelity of spin readout in semiconductor quantum dots, overcoming the 99% threshold. Moreover, in contrast to energy-selective readout, PSB is less error prone to thermal energy, an important feature for large-scale architectures that could be operated at temperatures above a few hundreds of millikelvins. In this work, we use rf reflectometry on a single-lead quantum dot to perform charge sensing and to probe the spin state of a double quantum dot at 0.5 K. At this relatively elevated temperature, we characterize both singlet-triplet and parity readout, which are complementary measurements to perform a complete readout of a two-spin system. We demonstrate high-fidelity spin readout with an average fidelity above 99.9 % for a readout time of 20 μs and 99 % for 4 μs. Finally, we succeed in initializing a singlet state in a single dot with a fidelity higher than 99 % and separate the two electrons while retaining the same spin state with a 95.6 % fidelity
Spins in silicon quantum devices are promising candidates for large-scale quantum computing. Gate-based sensing of spin qubits offers a compact and scalable readout with high fidelity, however, further improvements in sensitivity are required to meet the fidelity thresholds and measurement timescales needed for the implementation of fast feedback in error correction protocols. Here, we combine radio-frequency gate-based sensing at 622 MHz with a Josephson parametric amplifier, that operates in the 500-800 MHz band, to reduce the integration time required to read the state of a silicon double quantum dot formed in a nanowire transistor. Based on our achieved signal-to-noise ratio, we estimate that singlet-triplet single-shot readout with an average fidelity of 99.7% could be performed in 1 μs, well below the requirements for fault-tolerant readout and 30 times faster than without the Josephson parametric amplifier. Additionally, the Josephson parametric amplifier allows operation at a lower radio-frequency power while maintaining identical signal-to-noise ratio. We determine a noise temperature of 200 mK with a contribution from the Josephson parametric amplifier (25%), cryogenic amplifier (25%) and the resonator (50%), showing routes to further increase the readout speed.
We demonstrate singlet-triplet readout and parity readout allowing to distinguish T0 and the polarized triplet states. We achieve high fidelity spin readout with an average fidelity above 99.9%99.9\%99.9% for a readout time of 20 μ20~μ20 μs and 99%99\%99% for 4 μ4~μ4 μs at a temperature of 0.5 K0.5~K0.5 K. We initialize a singlet state in a single dot with a fidelity higher than 99%99\%99% and separate the two electrons while keeping the same spin state with a≈95.6%a \approx 95.6\%a≈95.6% fidelity.
Singlet-triplet qubits typically require large magnetic field gradients on the order of militeslas to achieve high-fidelity electrically-controlled qubit operations. However, such large magnetic field gradients in quantum dot systems also increase charge noise and provide a relaxation pathway from the triplet to singlet qubit state, making high-fidelity readout challenging. Recently, shelving and latched readout have been employed in gate-defined quantum dots and donor-dot systems to achieve readout fidelities of 80% and 99.86%, respectively. In this paper, we theoretically examine shelving and latched singlet-triplet readout techniques for multidonor-based qubits in silicon where the large phosphorus hyperfine interaction of the order of 100 MHz gives rise to large effective magnetic field gradients (equivalent to tens of mT) but where it can change in time due to the presence of nuclear spin flips. Using numerical simulations, we show that shelving readout does not work giving a zero average visibility for mutidonor quantum dots, due to the time-varying nuclear spin polarization. To remedy this we propose adding a calibration step, in which we derive the nuclear spin polarization from a single shelving readout of a singlet state, before every qubit operation. The derived information can then be used via a feed-forward protocol to apply correct readout mapping, greatly improving the overall readout fidelity to >99>99%>99. We also simulate the latched readout mechanism, which is resistant to nuclear polarization changes and is thus promising for achieving high visibility readout. Here we observe a nonzero readout visibility irrespective of the nuclear spin flipping. Finally, we discuss how to optimize the readout visibility in the presence of strong hyperfine interactions and show that for both readout methods we can obtain readout fidelity >99>99%>99. These results demonstrate that singlet-triplet qubits based on multidonor quantum dots are a promising route for future electrically controlled qubits in silicon.
Single-electron spin qubits defined in quantum dots are used as building blocks of a semiconductor-based quantum computer. Readout in a scaled-up version of such a quantum computer is expected to rely on the Pauli Spin Blockade (PSB) mechanism. A desired functionality of PSB readout is that it reveals two bits of information on the two spin qubits that are involved in the process, such that the four computational basis states can be discriminated. In this work, we propose and quantitatively analyze an experimental procedure, based on gate reflectometry, which enables this four-state discrimination in a single measurement. We provide an intuitive recipe to maximize the contrast between the quantum capacitances of the four basis states. Focusing on silicon double quantum dots equipped with a micromagnet, we quantify how amplifier noise and phonon-mediated relaxation influence readout fidelity. Our results highlight a realistic opportunity to mitigate the overhead of readout ancilla qubits in a spin-based quantum computer.
High-fidelity qubit readout is critical in order to obtain the thresholds needed to implement quantum error-correction protocols and achieve fault-tolerant quantum computing. Large-scale silicon qubit devices will have densely packed arrays of quantum dots with multiple charge sensors that are, on average, farther away from the quantum dots, entailing a reduction in readout fidelities. Here, we present a readout technique that enhances the readout fidelity in a linear SiMOS four-dot array by amplifying correlations between a pair of single-electron transistors, known as a twin SET. By recording and subsequently correlating the twin SET traces as we modulate the dot detuning across a charge transition, we demonstrate a reduction in the charge readout infidelity by over one order of magnitude compared to traditional readout methods. We also study the spin-to-charge conversion errors introduced by the modulation technique and conclude that faster modulation frequencies avoid relaxation-induced errors without introducing significant spin-flip errors, favoring the use of the technique at short integration times. This method not only allows for faster and higher-fidelity qubit measurements but it also enhances the signal corresponding to charge transitions that take place farther away from the sensors, enabling a way to circumvent the reduction in readout fidelities in large arrays of qubits. Published by the American Physical Society 2024