Bounds to electron spin qubit variability for scalable CMOS architectures.

Spins of electrons in silicon MOS quantum dots combine exquisite quantum properties and scalable fabrication. In the age of quantum technology, however, the metrics that crowned Si/SiO2 as the microelectronics standard need to be reassessed with respect to their impact upon qubit performance. We chart spin qubit variability due to the unavoidable atomic-scale roughness of the Si/SiO2 interface, compiling experiments across 12 devices, and develop theoretical tools to analyse these results. Atomistic tight binding and path integral Monte Carlo methods are adapted to describe fluctuations in devices with millions of atoms by directly analysing their wavefunctions and electron paths instead of their energy spectra. We correlate the effect of roughness with the variability in qubit position, deformation, valley splitting, valley phase, spin-orbit coupling and exchange coupling. These variabilities are found to be bounded, and they lie within the tolerances for scalable architectures for quantum computing as long as robust control methods are incorporated.

High-fidelity spin qubit operation and algorithmic initialization above 1 K.

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 applications11-13 will 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.

Navigating the 16-dimensional Hilbert space of a high-spin donor qudit with electric and magnetic fields.

Efficient scaling and flexible control are key aspects of useful quantum computing hardware. Spins in semiconductors combine quantum information processing with electrons, holes or nuclei, control with electric or magnetic fields, and scalable coupling via exchange or dipole interaction. However, accessing large Hilbert space dimensions has remained challenging, due to the short-distance nature of the interactions. Here, we present an atom-based semiconductor platform where a 16-dimensional Hilbert space is built by the combined electron-nuclear states of a single antimony donor in silicon. We demonstrate the ability to navigate this large Hilbert space using both electric and magnetic fields, with gate fidelity exceeding 99.8% on the nuclear spin, and unveil fine details of the system Hamiltonian and its susceptibility to control and noise fields. These results establish high-spin donors as a rich platform for practical quantum information and to explore quantum foundations.

Jellybean Quantum Dots in Silicon for Qubit Coupling and On-Chip Quantum Chemistry.

The small size and excellent integrability of silicon metal-oxide-semiconductor (SiMOS) quantum dot spin qubits make them an attractive system for mass-manufacturable, scaled-up quantum processors. Furthermore, classical control electronics can be integrated on-chip, in-between the qubits, if an architecture with sparse arrays of qubits is chosen. In such an architecture qubits are either transported across the chip via shuttling or coupled via mediating quantum systems over short-to-intermediate distances. This paper investigates the charge and spin characteristics of an elongated quantum dot-a so-called jellybean quantum dot-for the prospects of acting as a qubit-qubit coupler. Charge transport, charge sensing, and magneto-spectroscopy measurements are performed on a SiMOS quantum dot device at mK temperature and compared to Hartree-Fock multi-electron simulations. At low electron occupancies where disorder effects and strong electron-electron interaction dominate over the electrostatic confinement potential, the data reveals the formation of three coupled dots, akin to a tunable, artificial molecule. One dot is formed centrally under the gate and two are formed at the edges. At high electron occupancies, these dots merge into one large dot with well-defined spin states, verifying that jellybean dots have the potential to be used as qubit couplers in future quantum computing architectures.

An electrically driven single-atom "flip-flop" qubit.

The spins of atoms and atom-like systems are among the most coherent objects in which to store quantum information. However, the need to address them using oscillating magnetic fields hinders their integration with quantum electronic devices. Here, we circumvent this hurdle by operating a single-atom "flip-flop" qubit in silicon, where quantum information is encoded in the electron-nuclear states of a phosphorus donor. The qubit is controlled using local electric fields at microwave frequencies, produced within a metal-oxide-semiconductor device. The electrical drive is mediated by the modulation of the electron-nuclear hyperfine coupling, a method that can be extended to many other atomic and molecular systems and to the hyperpolarization of nuclear spin ensembles. These results pave the way to the construction of solid-state quantum processors where dense arrays of atoms can be controlled using only local electric fields.

Combining n-MOS Charge Sensing with p-MOS Silicon Hole Double Quantum Dots in a CMOS platform.

Holes in silicon quantum dots are receiving attention due to their potential as fast, tunable, and scalable qubits in semiconductor quantum circuits. Despite this, challenges remain in this material system including difficulties using charge sensing to determine the number of holes in a quantum dot, and in controlling the coupling between adjacent quantum dots. We address these problems by fabricating an ambipolar complementary metal-oxide-semiconductor (CMOS) device using multilayer palladium gates. The device consists of an electron charge sensor adjacent to a hole double quantum dot. We demonstrate control of the spin state via electric dipole spin resonance. We achieve smooth control of the interdot coupling rate over 1 order of magnitude and use the charge sensor to perform spin-to-charge conversion to measure the hole singlet-triplet relaxation time of 11 µs for a known hole occupation. These results provide a path toward improving the quality and controllability of hole spin-qubits.

On-demand electrical control of spin qubits.

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.

Precision tomography of a three-qubit donor quantum processor in silicon.

Nuclear spins were among the first physical platforms to be considered for quantum information processing1,2, because of their exceptional quantum coherence3 and 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-Z gate 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 electrons7-9 or physically shuttled across different locations10,11, these results establish a viable route for scalable quantum information processing using donor nuclear and electron spins.

Single-electron spin resonance in a nanoelectronic device using a global field.

Spin-based silicon quantum electronic circuits offer a scalable platform for quantum computation, combining the manufacturability of semiconductor devices with the long coherence times afforded by spins in silicon. Advancing from current few-qubit devices to silicon quantum processors with upward of a million qubits, as required for fault-tolerant operation, presents several unique challenges, one of the most demanding being the ability to deliver microwave signals for large-scale qubit control. Here, we demonstrate a potential solution to this problem by using a three-dimensional dielectric resonator to broadcast a global microwave signal across a quantum nanoelectronic circuit. Critically, this technique uses only a single microwave source and is capable of delivering control signals to millions of qubits simultaneously. We show that the global field can be used to perform spin resonance of single electrons confined in a silicon double quantum dot device, establishing the feasibility of this approach for scalable spin qubit control.

Bell-state tomography in a silicon many-electron artificial molecule.

An error-corrected quantum processor will require millions of qubits, accentuating the advantage of nanoscale devices with small footprints, such as silicon quantum dots. However, as for every device with nanoscale dimensions, disorder at the atomic level is detrimental to quantum dot uniformity. Here we investigate two spin qubits confined in a silicon double quantum dot artificial molecule. Each quantum dot has a robust shell structure and, when operated at an occupancy of 5 or 13 electrons, has single spin-[Formula: see text] valence electron in its p- or d-orbital, respectively. These higher electron occupancies screen static electric fields arising from atomic-level disorder. The larger multielectron wavefunctions also enable significant overlap between neighbouring qubit electrons, while making space for an interstitial exchange-gate electrode. We implement a universal gate set using the magnetic field gradient of a micromagnet for electrically driven single qubit gates, and a gate-voltage-controlled inter-dot barrier to perform two-qubit gates by pulsed exchange coupling. We use this gate set to demonstrate a Bell state preparation between multielectron qubits with fidelity 90.3%, confirmed by two-qubit state tomography using spin parity measurements.

A High-Sensitivity Charge Sensor for Silicon Qubits above 1 K.

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.

Roadmap on quantum nanotechnologies.

Quantum phenomena are typically observable at length and time scales smaller than those of our everyday experience, often involving individual particles or excitations. The past few decades have seen a revolution in the ability to structure matter at the nanoscale, and experiments at the single particle level have become commonplace. This has opened wide new avenues for exploring and harnessing quantum mechanical effects in condensed matter. These quantum phenomena, in turn, have the potential to revolutionize the way we communicate, compute and probe the nanoscale world. Here, we review developments in key areas of quantum research in light of the nanotechnologies that enable them, with a view to what the future holds. Materials and devices with nanoscale features are used for quantum metrology and sensing, as building blocks for quantum computing, and as sources and detectors for quantum communication. They enable explorations of quantum behaviour and unconventional states in nano- and opto-mechanical systems, low-dimensional systems, molecular devices, nano-plasmonics, quantum electrodynamics, scanning tunnelling microscopy, and more. This rapidly expanding intersection of nanotechnology and quantum science/technology is mutually beneficial to both fields, laying claim to some of the most exciting scientific leaps of the last decade, with more on the horizon.

Exchange Coupling in a Linear Chain of Three Quantum-Dot Spin Qubits in Silicon.

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.

Conditional quantum operation of two exchange-coupled single-donor spin qubits in a MOS-compatible silicon device.

Silicon nanoelectronic devices can host single-qubit quantum logic operations with fidelity better than 99.9%. For the spins of an electron bound to a single-donor atom, introduced in the silicon by ion implantation, the quantum information can be stored for nearly 1 second. However, manufacturing a scalable quantum processor with this method is considered challenging, because of the exponential sensitivity of the exchange interaction that mediates the coupling between the qubits. Here we demonstrate the conditional, coherent control of an electron spin qubit in an exchange-coupled pair of 31P donors implanted in silicon. The coupling strength, J = 32.06 ± 0.06 MHz, is measured spectroscopically with high precision. Since the coupling is weaker than the electron-nuclear hyperfine coupling A ≈ 90 MHz which detunes the two electrons, a native two-qubit controlled-rotation gate can be obtained via a simple electron spin resonance pulse. This scheme is insensitive to the precise value of J, which makes it suitable for the scale-up of donor-based quantum computers in silicon that exploit the metal-oxide-semiconductor fabrication protocols commonly used in the classical electronics industry.

Single-Electron Operation of a Silicon-CMOS 2 × 2 Quantum Dot Array with Integrated Charge Sensing.

The advanced nanoscale integration available in CMOS technology provides a key motivation for its use in spin-based quantum computing applications. Initial demonstrations of quantum dot formation and spin blockade in CMOS foundry-compatible devices are encouraging, but results are yet to match the control of individual electrons demonstrated in university-fabricated multigate designs. We show that quantum dots formed in a CMOS nanowire device can be measured with a remote single electron transistor (SET) formed in an adjacent nanowire, via floating coupling gates. By biasing the SET nanowire with respect to the nanowire hosting the quantum dots, we controllably form ancillary quantum dots under the floating gates, thus enabling control of all quantum dots in a 2 × 2 array, and charge sensing down to the last electron in each dot. We use effective mass theory to investigate the ideal geometrical parameters in order to achieve interdot tunnel rates required for spin-based quantum computation.

Controllable freezing of the nuclear spin bath in a single-atom spin qubit.

The quantum coherence and gate fidelity of electron spin qubits in semiconductors are often limited by nuclear spin fluctuations. Enrichment of spin-zero isotopes in silicon markedly improves the dephasing time [Formula: see text], which, unexpectedly, can extend two orders of magnitude beyond theoretical expectations. Using a single-atom 31P qubit in enriched 28Si, we show that the abnormally long [Formula: see text] is due to the freezing of the dynamics of the residual 29Si nuclei, caused by the electron-nuclear hyperfine interaction. Inserting a waiting period when the electron is controllably removed unfreezes the nuclear dynamics and restores the ergodic [Formula: see text] value. Our conclusions are supported by a nearly parameter-free modeling of the 29Si nuclear spin dynamics, which reveals the degree of backaction provided by the electron spin. This study clarifies the limits of ergodic assumptions in nuclear bath dynamics and provides previously unidentified strategies for maximizing coherence and gate fidelity of spin qubits in semiconductors.

Coherent electrical control of a single high-spin nucleus in silicon.

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 computers1 and demonstrations of quantum search2 and factoring3 algorithms. 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 methods7-9 relied 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 196110 but 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 dots11,12 could pave the way to scalable, nuclear- and electron-spin-based quantum computers in silicon that operate without the need for oscillating magnetic fields.

A silicon quantum-dot-coupled nuclear spin qubit.

Single nuclear spins in the solid state are a potential future platform for quantum computing1-3, because they possess long coherence times4-6 and offer excellent controllability7. Measurements can be performed via localized electrons, such as those in single atom dopants8,9 or 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 techniques21 may 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.

Gate-based single-shot readout of spins in silicon.

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.

Gigahertz Single-Electron Pumping Mediated by Parasitic States.

In quantum metrology, semiconductor single-electron pumps are used to generate accurate electric currents with the ultimate goal of implementing the emerging quantum standard of the ampere. Pumps based on electrostatically defined tunable quantum dots (QDs) have thus far shown the most promising performance in combining fast and accurate charge transfer. However, at frequencies exceeding approximately 1 GHz the accuracy typically decreases. Recently, hybrid pumps based on QDs coupled to trap states have led to increased transfer rates due to tighter electrostatic confinement. Here, we operate a hybrid electron pump in silicon obtained by coupling a QD to multiple parasitic states and achieve robust current quantization up to a few gigahertz. We show that the fidelity of the electron capture depends on the sequence in which the parasitic states become available for loading, resulting in distinctive frequency-dependent features in the pumped current.