Charge-Based Single-Shot Readout Systems in Quantum Computing [Feature

Quantum computers have been attractive because they could realize large-scale and highly complicated calculations that conventional computers cannot solve within a finite time. The large-scale integration of qubits, which are the building block of quantum computers, is required to realize their practical application. Indeed, fault-tolerant quantum computers require the integration of one million qubits. Therefore, silicon qubits is a high-profile candidate because they have advanced process and miniaturization technologies developed with VLSI. In addition, silicon qubits are advantageous in operation temperature. Superconductor qubits operate at the cryogenic temperature at around a few tens mK; in contrast, the operation principle of silicon qubits can operate at a much higher temperature over 1 K. The high-temperature operation can realize quantum computers with small and high-power refrigerators; therefore, we can expect desktop quantum computers instead of ongoing supercomputer-size ones. We must promote integration technology development for silicon qubits; however, the silicon qubit research was mainly in the physics field. Then, nowadays, the integration technology development is accelerated in the world.The challenges are in all conventional research fields: devices, integration, and circuits. We must re-develop the silicon technologies for quantum. For example, on the device design, now we do not have a good tool to design the qubits like TCAD; therefore, we must re-develop the TCAD technologies for quantum [1]. Actually, this is the starting point of our recent research activities; we are going to develop a quantum device simulator, clarify the requirements on the fabrication process of silicon qubits, and propose new technologies to reduce the variability to realize large-scale integration [2]. As for the integration, the quantum calculation circuits require several integrated items: qubits, qubit couplers, micro-magnets, and readout systems. The situation is quite different from the conventional VLSI case for which only the transistors should be integrated. Therefore, we must go re-developing new technologies to integrate all these items. Regarding the circuits, we must use CMOS circuits to generate input signals for qubits and readout the results of quantum calculation, which should be operated at cryogenic temperature. This is so-called “cryo-CMOS.” We must explore a new side of the transistor technologies, which is not investigated so far, because the physics of the MOSFET operation is quite different from the conventional room-temperature operation, hampering the circuit design due to the lack of the device operation model. In this situation, despite the long history of MOSFETs, new phenomena of transistor operation are discovered. For example, the low-frequency current noise increases at a low temperature. The origin of the noise is on the interface traps, instead of the fixed charges in the gate oxides as is the case for room temperature operation [3]. Therefore, we must re-developing CMOS circuit technologies from the bottom of the technologies, device physics.In this presentation, I’m going to overview the status of silicon technology developments for quantum from the viewpoints of devices, integration, and circuits. Also, we introduce some of our recent results to contribute to the developments.Acknowledgment: Our work is supported by MEXT Quantum Leap Flagship Program (Q-LEAP) JPMXS0118069228.[1] H. Asai et al., IEEE Electron Devices Technology and Manufacturing Conference 2021.[2] S. Iizuka et al., Tech. Dig. Symp. VLSI Technology 2021.[3] H. Oka et al., Tech. Dig. Symp. VLSI Technology 2020.

The recent decade has witnessed substantial advancements in silicon quantum computing. Important milestones include demonstrations of quantum gates exceeding the fault-tolerance threshold, high-fidelity single-shot spin readout, hot quantum bits (hot qubits), and compact scalable spin arrays. Silicon qubits hold promise to leverage semiconductor industry technologies into scalable qubit manufacturing. Both the academic and industry communities are striving to push this advantage into reality. However, formidable challenges persist in the quest to develop a fully operational universal quantum computer. This review focuses on single-spin qubits in silicon. First, we start with foundational spin qubit theory. Then, we discuss gate-defined quantum dots and donor dot systems, with a particular emphasis on two-qubit gate operations and the scalability of qubit arrays. Lastly, we address long-distance coupling, highlighting key areas for future research and potential scale-up strategies for this rapidly evolving field.

Quantum computation is a revolutionary new paradigm that has experienced tremendous growth since the mid 1990s and has inspired a number of ingenious schemes whose long-term goal is to realize a large-scale, fast, parallel, and easily fabricated quantum computer (QC). Silicon-based solid-state proposals using spins of dopants, such as phosphorus, as qubits are attractive because of the long spin relaxation times and the potential for scaling the device to a large number of qubits and integrating the QC with existing silicon technology. We propose a modified Kane1 architecture in which we address the difficult fabrication and addressing problems by simplifying the device structure and utilizing an existing, reliable optical detection method. The device consists of linear arrays of P atoms, which will be entangled through their exchange interactions. Scanning tunneling microscopy is used to fabricate the device and an external magnetic field and a large field gradient enable individual spin addressability. The lone P electron spin is used to control the nuclear spin qubit orientation. Excitons, generated in the substrate via a laser, are used to probe the spin states. A He-3 cryostat-based spin manipulation and readout system has been developed but many challenges exist in making a nano-scale quantum device in a real materials system.

A single atom is the prototypical quantum system, and a natural candidate for a quantum bit, or qubit--the elementary unit of a quantum computer. Atoms have been successfully used to store and process quantum information in electromagnetic traps, as well as in diamond through the use of the nitrogen-vacancy-centre point defect. Solid-state electrical devices possess great potential to scale up such demonstrations from few-qubit control to larger-scale quantum processors. Coherent control of spin qubits has been achieved in lithographically defined double quantum dots in both GaAs (refs 3-5) and Si (ref. 6). However, it is a formidable challenge to combine the electrical measurement capabilities of engineered nanostructures with the benefits inherent in atomic spin qubits. Here we demonstrate the coherent manipulation of an individual electron spin qubit bound to a phosphorus donor atom in natural silicon, measured electrically via single-shot read-out. We use electron spin resonance to drive Rabi oscillations, and a Hahn echo pulse sequence reveals a spin coherence time exceeding 200 µs. This time should be even longer in isotopically enriched (28)Si samples. Combined with a device architecture that is compatible with modern integrated circuit technology, the electron spin of a single phosphorus atom in silicon should be an excellent platform on which to build a scalable quantum computer.

The radio-frequency single-electron transistor (rf-SET) possesses key requirements necessary for reading out a solid state quantum computer. This work explores the use of the rf-SET as a single-shot readout device in the presence of 1∕f and telegraph charge noise. For a typical spectrum of 1∕f noise we find that high fidelity, single-shot measurements are possible for signals Δq>0.01e. For the case of telegraph noise, we present a cross-correlation measurement technique that uses two rf-SETs to suppress the effect of random switching events on readout. We demonstrate this technique by monitoring the charge state of a metal double dot system on microsecond time scales. Such a scheme will be advantageous in achieving high readout fidelity in a solid-state quantum computer.

Without resorting to spin-spin coupling, we propose a scalable spin quantum computing scheme assisted with a semiconductor multiple-quantum-dot structure. The techniques of single electron transitions and the nanostructure of quantum-dot cellular automata (QCA) are used to generate charge entangled states of two electrons, which are then converted into spin entanglement states using single-spin rotations only. Deterministic two-qubit quantum gates are also manipulated using only single-spin rotations with the help of QCA. A single-shot readout of spin states can be carried out by coupling the multiple dot structure to a quantum point contact. As a result, deterministic spin-interaction-free quantum computing can be implemented in semiconductor nanostructure.

Error correction is important in classical and quantum computation. Decoherence caused by the inevitable interaction of quantum bits with their environment leads to dephasing or even relaxation. Correction of the concomitant errors is therefore a fundamental requirement for scalable quantum computation. Although algorithms for error correction have been known for some time, experimental realizations are scarce. Here we show quantum error correction in a heterogeneous, solid-state spin system. We demonstrate that joint initialization, projective readout and fast local and non-local gate operations can all be achieved in diamond spin systems, even under ambient conditions. High-fidelity initialization of a whole spin register (99 per cent) and single-shot readout of multiple individual nuclear spins are achieved by using the ancillary electron spin of a nitrogen-vacancy defect. Implementation of a novel non-local gate generic to our electron-nuclear quantum register allows the preparation of entangled states of three nuclear spins, with fidelities exceeding 85 per cent. With these techniques, we demonstrate three-qubit phase-flip error correction. Using optimal control, all of the above operations achieve fidelities approaching those needed for fault-tolerant quantum operation, thus paving the way to large-scale quantum computation. Besides their use with diamond spin systems, our techniques can be used to improve scaling of quantum networks relying on phosphorus in silicon, quantum dots, silicon carbide or rare-earth ions in solids.

<sec>Spin qubits in silicon-based semiconductor quantum dots have become one of the prominent candidates for realizing fault-tolerant quantum computing due to their long coherence time, good controllability, and compatibility with modern advanced integrated circuit manufacturing processes. In recent years, due to the remarkable advances in silicon-based materials, the structure of quantum dot and its fabrication process, and qubit manipulation technology, the great progress of high-fidelity state preparation and readout, single- and two-qubit gates of spin qubits for silicon based semiconductor quantum computation has been achieved. The control fidelities for single- and two-qubit gates all exceed 99%—fault tolerance threshold required by the surface code known for its exceptionally high tolerance to errors. In this paper, we briefly introduce the basic concepts of silicon-based semiconductor quantum dots, discuss the state-of-art technologies used to improve the fidelities of single- and two-qubit gates, and finally highlight the research directions that should be focused on.</sec><sec>This paper is organized as follows. Firstly, we introduce three major types of quantum dot (QD) devices fabricated on different silicon-based substrates, including Si/SiGe heterojunction and Si/SiO<sub>2</sub>. The spin degree of electron or nucleus hosted in QD can be encoded into spin qubits. Electron spin qubits can be thermally initialized to ground state by using an electron reservoirs, and can be read out by spin-charge conversion mechanism: energy-selective readout (Elzerman readout) with reservoirs or Pauli spin blockade (PSB) without reservoirs. Additionally, high fidelity single-shot readout has been demonstrated by using radio-frequency gate reflectometry combined with the PSB, which has unique advantages in large-scale qubit array. To coherently control the spin qubits, electron dipole resonance (ESR) or electron dipole spin resonance (EDSR) for electron and nuclear magnetic resonance (NMR) for nucleus are introduced. With the help of isotope purification greatly improving the dephasing time of qubit and fast single-qubit manipulation based on EDSR, fidelity above 99.9% can be reached. For the two-qubit gates based on exchange interaction between electron spins, the strength of interaction <inline-formula><tex-math id="M1">\begin{document}$ J $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M1.png"/></alternatives></inline-formula> combined with Zeeman energy difference <inline-formula><tex-math id="M2">\begin{document}$ \Delta {E}_{z} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M2.png"/></alternatives></inline-formula> determines the energy levels of system, which lead to the different two-qubit gates, such as controlled-Z (CZ), controlled-Rotation (CROT), and the square root of the SWAP gate (<inline-formula><tex-math id="M3">\begin{document}$ \sqrt{\rm{S}\rm{W}\rm{A}\rm{P}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M3.png"/></alternatives></inline-formula>) gates. In order to improve the fidelity of two-qubit gates, a series of key technologies is used experimentally, they being isotope purification, symmetry operation, careful Hamiltonian engineering, and gate set tomography. Fidelity of two-qubit gates exceeding 99% has been demonstrated for electron spin qubits in Si/SiGe quantum dots and nuclear spin qubits in donors. These advances have pushed the silicon-based spin qubit platform to become a major stepping stone towards fault-tolerant quantum computation. Finally, we discuss the future study of spin qubits, that is, how to effectively expand the number of qubits, and many other problems to be explored and solved.</sec>

Silicon-based spin qubits offer a potential pathway toward realizing a scalable quantum computer owing to their compatibility with semiconductor manufacturing technologies. Recent experiments in this system have demonstrated crucial technologies, including high-fidelity quantum gates and multiqubit operation. However, the realization of a fault-tolerant quantum computer requires a high-fidelity spin measurement faster than decoherence. To address this challenge, we characterize and optimize the initialization and measurement procedures using the parity-mode Pauli spin blockade technique. Here, we demonstrate a rapid (with a duration of a few μs) and accurate (with >99% fidelity) parity spin measurement in a silicon double quantum dot. These results represent a significant step forward toward implementing measurement-based quantum error correction in silicon.

Single-shot readout of charge and spin states by charge sensors such as quantum point contacts and quantum dots are essential technologies for the operation of semiconductor spin qubits. The fidelity of the single-shot readout depends both on experimental conditions such as signal-to-noise ratio, system temperature, and numerical parameters such as threshold values. Accurate charge sensing schemes that are robust under noisy environments are indispensable for developing a scalable fault-tolerant quantum computation architecture. In this study, we present a novel single-shot readout classification method that is robust to noises using a deep neural network (DNN). Importantly, the DNN classifier is automatically configured for spin-up and spin-down traces in any noise environment by tuning the trainable parameters using the datasets of charge transition signals experimentally obtained at a charging line. Moreover, we verify that our DNN classification is robust under noisy environment in comparison to the two conventional classification methods used for charge and spin state measurements in various quantum dot experiments.

Quantum networks based on solid-state spin defects present a transformative approach to secure communication and distributed quantum computing, utilizing quantum entanglement and coherent spin–photon interfaces. Silicon carbide (SiC) stands out as a compelling material platform due to its unique combination of a wide bandgap, high optical nonlinearity, CMOS-compatible fabrication, and controllable spin-active defects. These intrinsic properties facilitate efficient photon emission, robust spin coherence at both room and cryogenic temperatures, and integration with photonic nanostructures. Recent advancements in defect engineering and micro-nanophotonics have unlocked the potential of SiC quantum nodes, which feature electron-nuclear spin systems for high-fidelity quantum operations and long-lived quantum memories. Key steps such as single-shot readout and spin-photon entanglement have been successfully demonstrated, bringing SiC closer to a real quantum network platform. This review offers a comprehensive overview of the advancements in SiC-based quantum networks, encompassing key aspects such as defect fabrication methodologies, optimization of spin-photon interfaces, and strategies for photonic integration. Additionally, it examines the existing challenges and outlines promising future directions in this rapidly evolving field.

An rf-SQUID under appropriate temperature and bias conditions can be used to perform tests on macroscopic quantum coherence, or as a qubit element for quantum computing. For both these purposes it is necessary a readout system allowing to discriminate stroboscopically the rfSQUID state with high fidelity. This task can be performed by means of a hysteretic dc-SQUID inductively coupled to the rf-SQUID and turned on by a fast bias current pulse. We have proposed and realized an integrated system where all the devices, the rf-SQUID, the hysteretic dc-SQUID, and a SQUID magnetometer are on the same chip. This system can perform single-shot detection of the rf-SQUID state with a fidelity better than 98%. The rf-SQUID has been coupled to a high-frequency line working in the microwave region (2–26 GHz), and has been tested and characterized from 4.2 K to the mK region of temperatures.

Recent studies of silicon spin qubits at temperatures above 1 K are encouraging demonstrations that the cooling requirements for solid-state quantum computing can be considerably relaxed. However, qubit readout mechanisms that rely on charge sensing with a single-island single-electron transistor (SISET) quickly lose sensitivity due to thermal broadening of the electron distribution in the reservoirs. Here we exploit the tunneling between two quantized states in a double-island single-electron transistor (SET) to demonstrate a charge sensor with an improvement in the signal-to-noise ratio by an order of magnitude compared to a standard SISET, and a single-shot charge readout fidelity above 99% up to 8 K at a bandwidth greater than 100 kHz. These improvements are consistent with our theoretical modeling of the temperature-dependent current transport for both types of SETs. With minor additional hardware overhead, these sensors can be integrated into existing qubit architectures for a high-fidelity charge readout at few-kelvin temperatures.

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 622MHz with a Josephson parametric amplifier, that operates in the 500-800MHz 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 200mK with a contribution from the Josephson parametric amplifier (25%), cryogenic amplifier (25%) and the resonator (50%), showing routes to further increase the readout speed.

Josephson traveling wave parametric amplifiers can have high gain and wide frequency range, high sensitivity, and low noise, which makes them promising for quantum computing, array receiver readout systems, spectroscopy, single-photon detectors, etc. In this paper, the authors investigate samples of traveling wave parametric amplifiers based on a three-layer Nb/AlOx/Nb superconductor–insulator–superconductor (SIS) structure with a SNAIL (Superconducting Nonlinear Asymmetric Inductive Elements) series array. Each SNAIL cell consists of the kinetic inductance of four SIS junctions and the nonlinear inductance of a smaller SIS junction. The cells are alternately connected in antiphase with respect to the magnetic flux, which ensures a change in the sign of the Kerr nonlinearity and a reduction in the phase mismatch for the pump frequency, signal frequency, and idler frequency. The transmission spectra of the samples were measured at temperatures of 4.2 and 2.8 K in the frequency range of 0.1–6 GHz.