Spin qubits in silicon are strong contenders for realizing a practical quantum computer. This technology has made remarkable progress with the demonstration of single and two-qubit gates above the fault-tolerant threshold and entanglement of up to three qubits. However, maintaining high fidelity operations while executing multi-qubit algorithms has remained elusive, only being achieved for two spin qubits to date due to the small qubit size, which makes it difficult to control qubits without creating crosstalk errors. Here, we use a four-qubit silicon processor with every operation above the fault tolerant limit and demonstrate Grover's algorithm with a ~95% probability of finding the marked state, one of the most successful implementations to date. Our four-qubit processor is made of three phosphorus atoms and one electron spin precision-patterned into 1.5 nm${}^2$ isotopically pure silicon. The strong resulting confinement potential, without additional confinement gates that can increase cross-talk, leverages the benefits of having both electron and phosphorus nuclear spins. Significantly, the all-to-all connectivity of the nuclear spins provided by the hyperfine interaction not only allows for efficient multi-qubit operations, but also provides individual qubit addressability. Together with the long coherence times of the nuclear and electron spins, this results in all four single qubit fidelities above 99.9% and controlled-Z gates between all pairs of nuclear spins above 99% fidelity. The high control fidelities, combined with >99% fidelity readout of all nuclear spins, allows for the creation of a three-qubit Greenberger-Horne-Zeilinger (GHZ) state with 96.2% fidelity, the highest reported for semiconductor spin qubits so far. Such nuclear spin registers can be coupled via electron exchange, establishing a path for larger scale fault-tolerant quantum processors.

Spin states in semiconductors provide exceptionally stable and noise-resistant environments for qubits, positioning them as optimal candidates for reliable quantum computing technologies. The proposal to use nuclear and electronic spins of donor atoms in silicon, introduced by Kane in 1998, sparked a new research field focused on the precise positioning of individual impurity atoms for quantum devices, utilising scanning tunnelling microscopy and ion implantation. This roadmap article reviews the advancements in the 25 years since Kane’s proposal, the current challenges, and the future directions in atomic-scale semiconductor device fabrication and measurement. It covers the quest to create a silicon-based quantum computer and expands to include diverse material systems and fabrication techniques, highlighting the potential for a broad range of semiconductor quantum technological applications. Key developments include phosphorus in silicon devices such as single-atom transistors, arrayed few-donor devices, one- and two-qubit gates, three-dimensional architectures, and the development of a toolbox for future quantum integrated circuits. The roadmap also explores new impurity species like arsenic and antimony for enhanced scalability and higher-dimensional spin systems, new chemistry for dopant precursors and lithographic resists, and the potential for germanium-based devices. Emerging methods, such as photon-based lithography and electron beam manipulation, are discussed for their disruptive potential. This roadmap charts the path toward scalable quantum computing and advanced semiconductor quantum technologies, emphasising the critical intersections of experiment, technological development, and theory.

The realisation of a large-scale error corrected quantum computer relies on our ability to reproducibly manufacture qubits that are fast, highly coherent, controllable and stable. The promise of achieving this in a highly manufacturable platform such as silicon requires a deep understanding of the materials issues that impact device operation. In this talk I will demonstrate how we engineer every aspect of the processor using atom qubits in silicon for fast, controllable exchange coupling [1], fast, high fidelity qubit initialisation and read-out [2]; low noise all epitaxial gates for highly stable qubits [3], [4]; and efficient, high fidelity qubit control [5], [6] leading to the demonstration of the highest fidelity Grover's algorithm to date [7].

Phosphorus atoms in silicon represent a promising platform for quantum computing, as their nuclear spins exhibit coherence times over seconds1,2 with high-fidelity readout and single-qubit control3. By placing several phosphorus atoms within a radius of a few nanometres, they couple by means of the hyperfine interaction to a single, shared electron. Such a nuclear spin register enables high-fidelity multi-qubit control4 and the execution of small-scale quantum algorithms5. An important requirement for scaling up is the ability to extend high-fidelity entanglement non-locally across several spin registers. Here we address this challenge with an 11-qubit atom processor composed of two multi-nuclear spin registers that are linked by means of electron exchange interaction. Through the advancement of calibration and control protocols, we achieve single-qubit and multi-qubit gates with all fidelities ranging from 99.10% to 99.99%. By entangling all combinations of local and non-local nuclear-spin pairs, we map out the performance of the processor and achieve state-of-the-art Bell-state fidelities of up to 99.5%. We then generate Greenberger-Horne-Zeilinger (GHZ) states with an increasing number of qubits and show entanglement of up to eight nuclear spins. By establishing high-fidelity operation across interconnected nuclear spin registers, we realize a key milestone towards fault-tolerant quantum computation with atom processors.

While traditionally considered a deleterious effect in quantum dot spin qubits, the spin-orbit interaction is recently being revisited as it allows for rapid coherent control by on-chip AC electric fields. For electrons in bulk silicon, spin-orbit coupling (SOC) is intrinsically weak, however, it can be enhanced at surfaces and interfaces, or through atomic placement. Here it is showed that the strength of the spin-orbit coupling can be locally enhanced by more than two orders of magnitude in the manybody wave functions of multi-donor quantum dots compared to a single donor, reaching strengths so far only reported for holes or two-donor system with certain symmetry. These findings may provide a pathway toward all-electrical control of donor-bound spins in silicon using electric dipole spin resonance (EDSR).

Correlated noise across multi-qubit architectures is known to be highly detrimental to the operation of error correcting codes and the long-term feasibility of quantum processors. The recent discovery of spatially dependent correlated noise in multi-qubit architectures of superconducting qubits arising from the impact of cosmic radiation and high-energy particles giving rise to quasiparticle poisoning within the substrate has led to intense investigations of mitigation strategies to address this. In contrast correlated noise in semiconductor spin qubits as a function of distance has not been reported to date. Here we report the magnitude, frequency and spatial dependence of noise correlations between four silicon quantum dot pairs as a function of inter-dot distance at frequencies from 0.3mHz to 1mHz. We find the magnitude of charge noise correlations, quantified by the magnitude square coherence C_xy, are significantly suppressed from >0.5 to <0.1 as the inter-dot distance increases from 75nm to 300nm. Using an analytical model we confirm that, in contrast to superconducting qubits, the dominant source of correlated noise arises from low frequency charge noise from the presence of two level fluctuators (TLFs) at the native silicon-silicon dioxide surface. Knowing this, we conclude with an important and timely discussion of charge noise mitigation strategies.

Spin-orbit interactions arise whenever the bulk inversion symmetry and/or structural inversion symmetry of a crystal is broken providing a bridge between a qubit's spin and orbital degree of freedom. While strong interactions can facilitate fast qubit operations by all-electrical control, they also provide a mechanism to couple charge noise thereby limiting qubit lifetimes. Previously believed to be negligible in bulk silicon, recent silicon nano-electronic devices have shown larger than bulk spin-orbit coupling strengths from Dresselhaus and Rashba couplings. Here, it is shown that with precision placement of phosphorus atoms in silicon along the [110] direction (without inversion symmetry) or [111] direction (with inversion symmetry), a wide range of Dresselhaus and Rashba coupling strength can be achieved from zero to 1113 x 10-13eV-cm. It is shown that with precision placement of phosphorus atoms, the local symmetry (C2v, D2d, and D3d) can be changed to engineer spin-orbit interactions. Since spin-orbit interactions affect both qubit operation and lifetimes, understanding their impact is essential for quantum processor design. Different Dresselhaus and Rashba spin-orbit strengths from 0 - 1113 x 10-13 eV cm for spin qubits can be engineered by placing phosphorus atoms in different lattice locations in the silicon crystal. The charge noise induced spin relaxation can therefore be minimized when there is no effective spin-orbit coupling. The results are verified by experimental measurements, atomistic simulations, and symmetry analysis. image

Atomic engineering in a solid-state material has the potential to functionalize the host with novel phenomena. STM-based lithographic techniques have enabled the placement of individual phosphorus atoms at selective lattice sites of silicon with atomic precision. Here, we show that by placing four phosphorus donors spaced 10-15 nm apart from their neighbours in a linear chain, it is possible to realize coherent spin coupling between the end dopants of the chain, analogous to the superexchange interaction in magnetic materials. Since phosphorus atoms are a promising building block of a silicon quantum computer, this enables spin coupling between their bound electrons beyond nearest neighbours, allowing the qubits to be spaced out by 30-45 nm. The added flexibility in architecture brought about by this long-range coupling not only reduces gate densities but can also reduce correlated noise between qubits from local noise sources that are detrimental to error correction codes. We base our calculations on a full configuration interaction technique in the atomistic tight-binding basis, solving the 4-electron problem exactly, over a domain of a million silicon atoms. Our calculations show that superexchange can be tuned electrically through gate voltages where it is less sensitive to charge noise and donor placement errors.

Precision-placed atom qubits in silicon offer a unique means to confine electrons and control their spins with extreme accuracy, which can be leveraged to construct powerful quantum computers. To date atom qubits in silicon have been successfully realized using electrons hosted either on a single phosphorus atom or on a multi-donor quantum dot. Here, a novel molecular regime is explored in which electrons are bound to two donor dots separated by approximate to 8 nm in a natural silicon substrate. The molecular state, provided by these spatially separated donors, is used to study with exquisite precision the impact of confinement potential on the electronic and spin properties of qubits. Unique spin filling measurements, performed on up to five electrons, confirm how electrons are shared between both sites of the molecule, forming hybridized molecular states. The precise atomic locations of the donor atoms in the silicon lattice are determined by combining the experimental electron spin resonance spectra and the state-of-the-art atomistic modeling of multi-electron wave-functions in presence of realistic electric fields. The donor molecule studied in this work exhibits excellent qubit properties and addresses the impact that the confinement potential has, at the atomic scale, on the desired properties of electron spin qubits. A formation of novel molecular spin states is shown using precision-placed atom qubits in silicon. This work explores this molecular regime to demonstrate that qubit confinement potential can be engineered at the atomic scale to control the shape and size of the electron wavefunction and consequently to optimize the properties of electron spin qubits.image

Phosphorus donor nuclear spins in silicon couple weakly to the environment making them promising candidates for high-fidelity qubits. The state of a donor nuclear spin qubit can be manipulated and read out using its hyperfine interaction with the electron confined by the donor potential. Here we use a master equation-based approach to investigate how the backaction from this electron-mediated measurement affects the lifetimes of single and multi-donor qubits. We analyze this process as a function of electric and magnetic fields, and hyperfine interaction strength. Apart from single nuclear spin flips, we identify an additional measurement-related mechanism, the nuclear spin flip-flop, which is specific to multi-donor qubits. Although this flip-flop mechanism reduces qubit lifetimes, we show that it can be effectively suppressed by the hyperfine Stark shift. We show that using atomic precision donor placement and engineered Stark shift, we can minimize the measurement backaction in multi-donor qubits, achieving larger nuclear spin lifetimes than single donor qubits.

Donor-based qubits in silicon, manufactured using scanning tunneling microscope (STM) lithography, provide a promising route to realizing full-scale quantum computing architectures. This is due to the precision of donor placement, long coherence times, and scalability of the silicon material platform. The properties of multiatom quantum dot qubits, however, depend on the exact number and location of the donor atoms within the quantum dots. In this work, we develop machine learning techniques that allow accurate and real-time prediction of the donor number at the qubit site during STM patterning. Machine learning image recognition is used to determine the probability distribution of donor numbers at the qubit site directly from STM images during device manufacturing. Models in excess of 90% accuracy are found to be consistently achieved by mitigating overfitting through reduced model complexity, image preprocessing, data augmentation, and examination of the intermediate layers of the convolutional neural networks. The results presented in this paper constitute an important milestone in automating the manufacture of atom-based qubits for computation and sensing applications.

Single electron spins bound to multi-phosphorus nuclear spin registers in silicon have demonstrated fast (0.8 ns) two-qubit √(SWAP) gates and long spin relaxation times ( 30 s). In these spin registers, when the donors are ionized, the nuclear spins remain weakly coupled to their environment, allowing exceptionally long coherence times. When the electron is present, the hyperfine interaction allows coupling of the spin and charge degrees of freedom for fast qubit operation and control. Here we demonstrate the use of the hyperfine interaction to enact electric dipole spin resonance to realize high-fidelity ( F=100_-6^+0

A robust initialization protocol has been demonstrated for a four-qubit nuclear spin register in silicon. The protocol, driven electrically through electric-dipole spin resonance, enables high-fidelity qubit control and hence a route to a register-based quantum computer that exploits the exceptional coherence properties of atom qubits in silicon.

Proposals for large-scale semiconductor spin-based quantum computers require high-fidelity single-shot qubit readout to perform error correction and read out qubit registers at the end of a computation. However, as devices scale to larger qubit numbers integrating readout sensors into densely packed qubit chips is a critical challenge. Two promising approaches are minimising the footprint of the sensors, and extending the range of each sensor to read more qubits. Here we show high-fidelity single-shot electron spin readout using a nanoscale single-lead quantum dot (SLQD) sensor that is both compact and capable of reading multiple qubits. Our gate-based SLQD sensor is deployed in an all-epitaxial silicon donor spin qubit device, and we demonstrate single-shot readout of three $^{31}$P donor quantum dot electron spins with a maximum fidelity of 95%. Importantly in our device the quantum dot confinement potentials are provided inherently by the donors, removing the need for additional metallic confinement gates and resulting in strong capacitive interactions between sensor and donor quantum dots. We observe a $1/d^{1.4}$ scaling of the capacitive coupling between sensor and $^{31}$P dots (where $d$ is the sensor-dot distance), compared to $1/d^{2.5-3.0}$ in gate-defined quantum dot devices. Due to the small qubit size and strong capacitive interactions in all-epitaxial donor devices, we estimate a single sensor can achieve single-shot readout of approximately 15 qubits in a linear array, compared to 3-4 qubits for a similar sensor in a gate-defined quantum dot device. Our results highlight the potential for spin qubit devices with significantly reduced sensor densities.

Universal quantum computing requires fast single- and two-qubit gates with individual qubit addressability to minimize decoherence errors during processor operation. Electron spin qubits using individual phosphorus donor atoms in silicon have demonstrated long coherence times with high fidelities, providing an attractive platform for scalable quantum computing. While individual qubit addressability has been demonstrated by controlling the hyperfine interaction between the electron and nuclear wave function in a global magnetic field, the small hyperfine Stark coefficient of 0.34 MHz/MV m-1 achieved to date has limited the speed of single quantum gates to ∼42 μs to avoid rotating neighboring qubits due to power broadening from the antenna. The use of molecular 2P qubits with more than one donor atom has not only demonstrated fast (0.8 ns) two-qubit SWAP gates and long spin relaxation times of ∼30 s but provides an alternate way to achieve high selectivity of the qubit resonance frequency. Here, we show in two different devices that by placing the donors with comparable interatomic spacings (∼0.8 nm) but along different crystallographic axes, either the [110] or [310] orientations using STM lithography, we can engineer the hyperfine Stark shift from 1 MHz/MV m-1 to 11.2 MHz/MV m-1, respectively, a factor of 10 difference. NEMO atomistic calculations show that larger hyperfine Stark coefficients of up to ∼70 MHz/MV m-1 can be achieved within 2P molecules by placing the donors ≥5 nm apart. When combined with Gaussian pulse shaping, we show that fast single qubit gates with 2π rotation times of 10 ns and ∼99% fidelity single qubit operations are feasible without affecting neighboring qubits. By increasing the single qubit gate time to ∼550 ns, two orders of magnitude faster than previously measured, our simulations confirm that >99.99% single qubit control fidelities are achievable.

Donor dots realized with phosphorus atoms in silicon have proven to be excellent hosts for electron spin qubits as they provide a strong confining potential that results in small wave functions and well-isolated ground states. As a promising candidate for large-scale quantum computers, such qubits have demonstrated fast, high-fidelity single-shot readout (99.8%) and extremely long coherence times (seconds) with single-qubit gates exceeding 99.94% fidelity. However, high-fidelity two-qubit gates in this platform have been elusive, with charge noise being one of the key limiting factors. Charge noise causes unwanted fluctuations in the exchange coupling between electron spins resulting in logic gate errors, a process that could be minimized if we could engineer a large enough magnetic field difference between the qubits. In this work, we show that using the donor nuclear spins as nanomagnets we can engineer a large magnetic field gradient (> 800 MHz) between the qubits thereby minimizing sensitivity to charge noise and reducing errors during two-qubit controlled-NOT (CNOT) gate operation. We develop a comprehensive theoretical framework with realistic noise sources for performing CNOT gates via controlled rotation (CROT) using multidonor dot qubits. We show that by engineering the number and location of donors within the dots we can control the hyperfine couplings to maximize the energy difference between electron spin qubits. As a result, we show that the CNOT gate error rates can be reduced by a factor of 4 when using multidonor dots as compared to single donors. Our results provide a theoretical roadmap to show how to achieve CNOT fidelities as high as 99.98% by optimizing both the local magnetic environment and the operating parameters of multidonor dot qubits.

Controlling electron tunneling is of fundamental importance in the design and operation of semiconductor nanostructures such as field effect transistors (FETs) and quantum computing device architectures. The exponential sensitivity of tunneling with distance requires precise fabrication techniques to engineer the desired device dimensions to achieve the appropriate tunneling resistances/tunnel rates. This is particularly important for high fidelity spin readout and qubit exchange in quantum computing architectures. Here, it is shown by combining precision fabrication techniques with accurate atomistic modeling, predictive device design criteria are achieved at atomic length scales. Such a tool is useful when devices become more complex or have arbitrary shapes/geometries. In particular, in this study, atomic precision patterning of monolayer degenerately phosphorus‐doped silicon tunnel junctions patterned by scanning tunnelling microscopy lithography and tight‐binding non‐equilibrium Green's function (TB‐NEGF) modeling is combined to describe the dependence of tunnel junction resistance R T on junction length. An agreement with experiment to within a factor of 2 over 4 orders of magnitude in R T is found, and this model allows to accurately determine the barrier height V 0 = 57.5 ± 1 meV and lateral seam s xy = 0.39 ± 0.01 nm in these nanoscale junctions. This study confirms the use of the TB‐NEGF formalism to accurately model highly doped atomically precise tunnel junctions in silicon. Further applications of this model will enable improved device performance at the nanoscale.

Future large-scale quantum computing devices based on semiconductor spin qubits require multiplexed microwave control signals for manipulation and readout of the qubits. However, interfacing these control signals between room temperature and cryogenic temperatures where the qubits operate is a complex technical challenge. Here, we show a microwave modulator based on a nanoengineered semiconductor quantum dot that is designed to operate at millikelvin temperatures alongside the qubits. We operate the modulator as a mixer and a frequency multiplier over a bandwidth of up to 25 GHz. We estimate the power dissipation when driving quantum gates using frequency-up-converted signals under realistic experimental conditions to be 4 pW, highly compatible with the cooling powers available in current commercial dilution refrigerators. The device is fabricated in silicon using atomic precision lithography, providing a pathway toward combining qubits and classical control functionality on the same integrated chip.

Donor electron spin qubits hosted within nanoscale devices have demonstrated seconds-long relaxation times at magnetic fields suitable for the operation of spin qubits in silicon of B = 1.5 T. The relaxation rates of these qubits have been shown at milliKelvin temperatures to be mediated by spin-orbit coupling with a B5 dependency on magnetic field for B > 3 T with a transition to a B3 dependency at magnetic fields below (B 3 T). This deviation has been observed in many spin qubit systems but is particularly notable in multidonor quantum dot qubits. The reason for this has remained a mystery. In this paper we show that for these multidonor low noise, crystalline qubits this deviation at low magnetic fields can be explained by a hyperfine mediated relaxation mechanism of the electron spin through a quantitative model of the relaxation rates. This model identifies the importance of donor nuclear spin flips which are more apparent in multidonor systems in which the larger numbers of donor nuclei creates stronger confinement potentials and enhanced hyperfine couplings. We show theoretically that with atomic precision engineering of the locations of the donor nuclei in these multidonor quantum dot qubits, and/or nuclear spin control, we can minimize the hyperfine mediated relaxation allowing T1 to extend to similar to 200 seconds (B = 1.5 T).

Quantum states of atomic systems can be directly addressed using quantum optical microscopes. However, solid-state microscopy techniques cannot typically achieve both local measurements and control of the state due to their measurement mechanism or the presence of a globally conductive substrate that impedes local gate control. Here we report a solid-state quantum microscope that can control and locally probe the wavefunctions of atomic quantum dots in silicon. Our microscope consists of a scanning tunnelling microscope tip, source and gate electrodes defined on an insulating silicon substrate by subsurface antimony implantation and phosphorus dopants incorporated with atomic precision. In contrast to conventional semiconductor qubit devices, the macroscopic electrodes are fabricated before patterning the nanoscale elements. A light-assisted method is designed to make the substrate conductive to stabilize the microscope tip close to the quantum dots, before reversing to an insulator for local gating and spectroscopy. We show that the microscope can be used to tune and map the charge states of single and double quantum dots, as well as control the relative electrochemical potential between two dots.