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Parity and Singlet-Triplet High-Fidelity Readout in a Silicon Double Quantum Dot at 0.5 K

David J. Niegemann, Victor El-Homsy, Baptiste Jadot, Martin Nurizzo, Bruna Cardoso Paz, Emmanuel Chanrion, Matthieu Dartiailh, Bernhard Klemt, Vivien Thiney, Christopher Bäuerle, Pierre-André Mortemousque, Benoît Bertrand, Heimanu Niebojewski, M. Vinet, Franck Balestro, Tristan Meunier, Matias Urdampilleta

Published Dec 26, 2022• 33 citations
Publisher

Abstract

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

DOI
10.1103/prxquantum.3.040335

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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
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.
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.
Abstract Fast and high-fidelity quantum state detection is essential for building robust spin-based quantum information processing platforms in semiconductors. The Pauli spin blockade (PSB)-based spin-to-charge conversion and its variants are widely used for the spin state discrimination of two-electron singlet–triplet (ST0) qubits; however, the single-shot measurement fidelity is limited by either the low signal contrast, or the short lifetime of the triplet state at the PSB energy detuning, especially due to strong mixing with singlet states at large magnetic field gradients. Ultimately, the limited single-shot measurement fidelity leads to low visibility of quantum operations. Here, we demonstrate an alternative method to achieve spin-to-charge conversion of ST0 qubit states using energy-selective tunneling between doubly occupied quantum dots (QDs) and electron reservoirs. We demonstrate a single-shot measurement fidelity of 90% and an S–T0 oscillation visibility of 81% at a field gradient of 100 mT (~500 MHz h (g*·μB)−1); this allows single-shot readout with full electron charge signal contrast and, at the same time, long and tunable measurement time with negligible effect of relaxation even at strong magnetic field gradients. Using an rf-sensor positioned opposite to the QD array, we apply this method to two ST0 qubits and show high-visibility readout of two individual single-qubit gate operations is possible with a single rf single-electron transistor sensor. We expect our measurement scheme for two-electron spin states can be applied to various hosting materials and provides a simplified and complementary route for multiple qubit state detection with high accuracy in QD-based quantum computing platforms.
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.
Three key metrics for readout systems in quantum processors are measurement speed, fidelity and footprint. Fast high-fidelity readout enables mid-circuit measurements, a necessary feature for many dynamic algorithms and quantum error correction, while a small footprint facilitates the design of scalable, highly-connected architectures with the associated increase in computing performance. Here, we present two complementary demonstrations of fast high-fidelity single-shot readout of spins in silicon quantum dots using a compact, dispersive charge sensor: a radio-frequency single-electron box. The sensor, despite requiring fewer electrodes than conventional detectors, performs at the state-of-the-art achieving spin read-out fidelity of 99.2% in less than 6 μμμs. We demonstrate that low-loss high-impedance resonators, highly coupled to the sensing dot, in conjunction with Josephson parametric amplification are instrumental in achieving optimal performance. We quantify the benefit of Pauli spin blockade over spin-dependent tunneling to a reservoir, as the spin-to-charge conversion mechanism in these readout schemes. Our results place dispersive charge sensing at the forefront of readout methodologies for scalable semiconductor spin-based quantum processors.
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.