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The encoding of qubits in semiconductor spin carriers has been recognized as a promising approach to a commercial quantum computer that can be lithographically produced and integrated at scale1–10. However, the operation of the large number of qubits required for advantageous quantum applications11–13will produce a thermal load exceeding the available cooling power of cryostats at millikelvin temperatures. As the scale-up accelerates, it becomes imperative to establish fault-tolerant operation above 1 K, at which the cooling power is orders of magnitude higher14–18. Here we tune up and operate spin qubits in silicon above 1 K, with fidelities in the range required for fault-tolerant operations at these temperatures19–21. We design an algorithmic initialization protocol to prepare a pure two-qubit state even when the thermal energy is substantially above the qubit energies and incorporate radiofrequency readout to achieve fidelities up to 99.34% for both readout and initialization. We also demonstrate single-qubit Clifford gate fidelities up to 99.85% and a two-qubit gate fidelity of 98.92%. These advances overcome the fundamental limitation that the thermal energy must be well below the qubit energies for the high-fidelity operation to be possible, surmounting a main obstacle in the pathway to scalable and fault-tolerant quantum computation.

Achieving high-fidelity entangling operations between qubits consistently is essential for the performance of multi-qubit systems. Solid-state platforms are particularly exposed to errors arising from materials-induced variability between qubits, which leads to performance inconsistencies. Here we study the errors in a spin qubit processor, tying them to their physical origins. We use this knowledge to demonstrate consistent and repeatable operation with above 99% fidelity of two-qubit gates in the technologically important silicon metal-oxide-semiconductor quantum dot platform. Analysis of the physical errors and fidelities in multiple devices over extended periods allows us to ensure that we capture the variation and the most common error types. Physical error sources include the slow nuclear and electrical noise on single qubits and contextual noise that depends on the applied control sequence. Furthermore, we investigate the impact of qubit design, feedback systems and robust gate design to inform the design of future scalable, high-fidelity control strategies. Our results highlight both the capabilities and challenges for the scaling-up of silicon spin-based qubits into full-scale quantum processors.

Purpose: This article presents a process of building a practice-driven research agenda for Quebrada de Humahuaca, a World Heritage cultural landscape in northern Argentina, developed under the framework of the Heritage Place Lab (2021–2022) led by the World Heritage Leadership Programme. The research agenda aims to improve the property's management and governance structures through an inclusive approach that considers the participation of all stakeholders and rights holders. Design/methodology/approach: Through collaborative work, a step-by-step methodology was employed that included identifying the property's values and attributes, the involvement of different actors in its management and their specific roles, and the factors that might cause real or potential impacts. The systematisation and analysis of this information served to define research priorities and a practice-driven research agenda. Findings: A range of conflicts and threats were identified, and the values and attributes that define the property were recognised. The collaborative process helped define research priorities and allowed the development of a preliminary research agenda, which, in the long term, can meet the needs of the property's World Heritage Management Unit. Originality/value: The originality of this work lies in the collaborative work undertaken by the research and practice teams to define a new research agenda based on practical needs to improve the management and governance structures of the World Heritage property.

Once called a ‘classically non-describable two-valuedness’ by Pauli, the electron spin forms a qubit that is naturally robust to electric fluctuations. Paradoxically, a common control strategy is the integration of micromagnets to enhance the coupling between spins and electric fields, which, in turn, hampers noise immunity and adds architectural complexity. Here we exploit a switchable interaction between spins and orbital motion of electrons in silicon quantum dots, without a micromagnet. The weak effects of relativistic spin–orbit interaction in silicon are enhanced, leading to a speed up in Rabi frequency by a factor of up to 650 by controlling the energy quantization of electrons in the nanostructure. Fast electrical control is demonstrated in multiple devices and electronic configurations. Using the electrical drive, we achieve a coherence time T2,Hahn≈ 50 μs, fast single-qubit gates with Tπ/2= 3 ns and gate fidelities of 99.93%, probed by randomized benchmarking. High-performance all-electrical control improves the prospects for scalable silicon quantum computing.

Nuclear spins were among the first physical platforms to be considered for quantum information processing1,2, because of their exceptional quantum coherence3and atomic-scale footprint. However, their full potential for quantum computing has not yet been realized, owing to the lack of methods with which to link nuclear qubits within a scalable device combined with multi-qubit operations with sufficient fidelity to sustain fault-tolerant quantum computation. Here we demonstrate universal quantum logic operations using a pair of ion-implanted 31P donor nuclei in a silicon nanoelectronic device. A nuclear two-qubit controlled-Zgate is obtained by imparting a geometric phase to a shared electron spin4, and used to prepare entangled Bell states with fidelities up to 94.2(2.7)%. The quantum operations are precisely characterized using gate set tomography (GST)5, yielding one-qubit average gate fidelities up to 99.95(2)%, two-qubit average gate fidelity of 99.37(11)% and two-qubit preparation/measurement fidelities of 98.95(4)%. These three metrics indicate that nuclear spins in silicon are approaching the performance demanded in fault-tolerant quantum processors6. We then demonstrate entanglement between the two nuclei and the shared electron by producing a Greenberger–Horne–Zeilinger three-qubit state with 92.5(1.0)% fidelity. Because electron spin qubits in semiconductors can be further coupled to other electrons7–9or physically shuttled across different locations10,11, these results establish a viable route for scalable quantum information processing using donor nuclear and electron spins.

For the past three decades nanoscience has widely affected many areas in physics, chemistry and engineering, and has led to numerous fundamental discoveries, as well as applications and products. Concurrently, quantum science and technology has developed into a cross-disciplinary research endeavour connecting these same areas and holds burgeoning commercial promise. Although quantum physics dictates the behaviour of nanoscale objects, quantum coherence, which is central to quantum information, communication and sensing, has not played an explicit role in much of nanoscience. This Review describes fundamental principles and practical applications of quantum coherence in nanoscale systems, a research area we call quantum-coherent nanoscience. We structure this Review according to specific degrees of freedom that can be quantum-coherently controlled in a given nanoscale system, such as charge, spin, mechanical motion and photons. We review the current state of the art and focus on outstanding challenges and opportunities unlocked by the merging of nanoscience and coherent quantum operations.

Quantum gates between spin qubits can be implemented leveraging the natural Heisenberg exchange interaction between two electrons in contact with each other. This interaction is controllable by electrically tailoring the overlap between electronic wave functions in quantum dot systems, as long as they occupy neighboring dots. An alternative route is the exploration of superexchange—the coupling between remote spins mediated by a third idle electron that bridges the distance between quantum dots. We experimentally demonstrate direct exchange coupling and provide evidence for second neighbor mediated superexchange in a linear array of three single-electron spin qubits in silicon, inferred from the electron spin resonance frequency spectra. We confirm theoretically, through atomistic modeling, that the device geometry only allows for sizable direct exchange coupling for neighboring dots, while next-nearest neighbor coupling cannot stem from the vanishingly small tail of the electronic wave function of the remote dots, and is only possible if mediated.

Nuclear spins are highly coherent quantum objects. In large ensembles, their control and detection via magnetic resonance is widely exploited, for example, in chemistry, medicine, materials science and mining. Nuclear spins also featured in early proposals for solid-state quantum computers1and demonstrations of quantum search2and factoring3algorithms. Scaling up such concepts requires controlling individual nuclei, which can be detected when coupled to an electron4–6. However, the need to address the nuclei via oscillating magnetic fields complicates their integration in multi-spin nanoscale devices, because the field cannot be localized or screened. Control via electric fields would resolve this problem, but previous methods7–9relied on transducing electric signals into magnetic fields via the electron–nuclear hyperfine interaction, which severely affects nuclear coherence. Here we demonstrate the coherent quantum control of a single 123Sb (spin-7/2) nucleus using localized electric fields produced within a silicon nanoelectronic device. The method exploits an idea proposed in 196110but not previously realized experimentally with a single nucleus. Our results are quantitatively supported by a microscopic theoretical model that reveals how the purely electrical modulation of the nuclear electric quadrupole interaction results in coherent nuclear spin transitions that are uniquely addressable owing to lattice strain. The spin dephasing time, 0.1 seconds, is orders of magnitude longer than those obtained by methods that require a coupled electron spin to achieve electrical driving. These results show that high-spin quadrupolar nuclei could be deployed as chaotic models, strain sensors and hybrid spin-mechanical quantum systems using all-electrical controls. Integrating electrically controllable nuclei with quantum dots11,12could pave the way to scalable, nuclear- and electron-spin-based quantum computers in silicon that operate without the need for oscillating magnetic fields.

Single nuclear spins in the solid state are a potential future platform for quantum computing1–3, because they possess long coherence times4–6and offer excellent controllability7. Measurements can be performed via localized electrons, such as those in single atom dopants8,9or crystal defects10–12. However, establishing long-range interactions between multiple dopants or defects is challenging13,14. Conversely, in lithographically defined quantum dots, tunable interdot electron tunnelling allows direct coupling of electron spin-based qubits in neighbouring dots15–20. Moreover, the compatibility with semiconductor fabrication techniques21may allow for scaling to large numbers of qubits in the future. Unfortunately, hyperfine interactions are typically too weak to address single nuclei. Here we show that for electrons in silicon metal–oxide–semiconductor quantum dots the hyperfine interaction is sufficient to initialize, read out and control single 29Si nuclear spins. This approach combines the long coherence times of nuclear spins with the flexibility and scalability of quantum dot systems. We demonstrate high-fidelity projective readout and control of the nuclear spin qubit, as well as entanglement between the nuclear and electron spins. Crucially, we find that both the nuclear spin and electron spin retain their coherence while moving the electron between quantum dots. Hence we envision long-range nuclear–nuclear entanglement via electron shuttling3. Our results establish nuclear spins in quantum dots as a powerful new resource for quantum processing.

Electron spins in silicon quantum dots provide a promising route towards realizing the large number of coupled qubits required for a useful quantum processor1–7. For the implementation of quantum algorithms and error detection8–10, qubit measurements are ideally performed in a single shot, which is presently achieved using on-chip charge sensors, capacitively coupled to the quantum dots11. However, as the number of qubits is increased, this approach becomes impractical due to the footprint and complexity of the charge sensors, combined with the required proximity to the quantum dots12. Alternatively, the spin state can be measured directly by detecting the complex impedance of spin-dependent electron tunnelling between quantum dots13–15. This can be achieved using radiofrequency reflectometry on a single gate electrode defining the quantum dot itself15–19, significantly reducing the gate count and architectural complexity, but thus far it has not been possible to achieve single-shot spin readout using this technique. Here, we detect single electron tunnelling in a double quantum dot and demonstrate that gate-based sensing can be used to read out the electron spin state in a single shot, with an average readout fidelity of 73%. The result demonstrates a key step towards the readout of many spin qubits in parallel, using a compact gate design that will be needed for a large-scale semiconductor quantum processor.

Bell's theorem proves the existence of entangled quantum states with no classical counterpart. An experimental violation of Bell's inequality demands simultaneously high fidelities in the preparation, manipulation and measurement of multipartite quantum entangled states, and provides a single-number benchmark for the performance of devices that use such states for quantum computing. We demonstrate a Bell/ Clauser–Horne–Shimony–Holt inequality violation with Bell signals up to 2.70(9), using the electron and the nuclear spins of a single phosphorus atom embedded in a silicon nanoelectronic device. Two-qubit state tomography reveals that our prepared states match the target maximally entangled Bell states with >96% fidelity. These experiments demonstrate complete control of the two-qubit Hilbert space of a phosphorus atom and highlight the important function of the nuclear qubit to expand the computational basis and maximize the readout fidelity.

This paper aims to analyse the characteristics of a formerly quite important town, product of the (English) railway system established in the rural area of the province of Buenos Aires, which has been deeply affected by the changes of the last decades of the twentieth century, as well as to describe its current situation and the actions conceived and carried out in order to revitalise it. Since the authors have been involved in the surveys and evaluation procedures, it is a first-hand reflection on successes and failures.

A terbium-based molecular magnet, containing four nuclear quantum states, or a qudit, experimentally validates the Grover algorithm for database searches.

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This review describes recent groundbreaking results in Si, Si/SiGe, and dopant-based quantum dots, and it highlights the remarkable advances in Si-based quantum physics that have occurred in the past few years. This progress has been possible thanks to materials development of Si quantum devices, and the physical understanding of quantum effects in silicon. Recent critical steps include the isolation of single electrons, the observation of spin blockade, and single-shot readout of individual electron spins in both dopants and gated quantum dots in Si. Each of these results has come with physics that was not anticipated from previous work in other material systems. These advances underline the significant progress toward the realization of spin quantum bits in a material with a long spin coherence time, crucial for quantum computation and spintronics. [ABSTRACT FROM AUTHOR]