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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., Comment: 94 pages

The realization of a quantum computer represents a tremendous scientific and technological challenge due to the extreme fragility of quantum information. The physical support of information, namely the quantum bit or qubit, must at the same time be strongly coupled to other qubits by gates to compute information, and well decoupled from its environment to keep its quantum behavior. An interesting physical system for realizing such qubits are magnetic impurities in semiconductors, such as bismuth donors in silicon. Indeed, spins associated to bismuth donors can reach an extremely long coherence time -- of the order of seconds. Yet it is extremely difficult to establish and control efficient gates between these spins. Here we demonstrate a protocol where single bismuth donors can coherently transfer their quantum information to a superconducting flux qubit, which acts as a mediator or quantum bus. This superconducting device allows to connect distant spins on-demand with little impact on their coherent behavior., Comment: 22 pages, 4 figures and 5 extended data figures

Superconducting flux qubits are promising candidates for the physical realization of a scalable quantum processor. Indeed, these circuits may have both a small decoherence rate and a large anharmonicity. These properties enable the application of fast quantum gates with high fidelity and reduce scaling limitations due to frequency crowding. The major difficulty of flux qubits' design consists of controlling precisely their transition energy - the so-called qubit gap - while keeping long and reproducible relaxation times. Solving this problem is challenging and requires extremely good control of e-beam lithography, oxidation parameters of the junctions and sample surface. Here we present measurements of a large batch of flux qubits and demonstrate a high level of reproducibility and control of qubit gaps, relaxation times and pure echo dephasing times. These results open the way for potential applications in the fields of quantum hybrid circuits and quantum computation., Comment: Supplementary Materials at the end of the file

Spins in the `semiconductor vacuum' of silicon-28 ($^{28}$Si) are suitable qubit candidates due to their long coherence times. An isotopically purified substrate of $^{28}$Si is required to limit the decoherence pathway caused by magnetic perturbations from surrounding $^{29}$Si nuclear spins (I=1/2), present in natural Si (nat Si) at an abundance of 4.67%. We isotopically enrich surface layers of nat Si by sputtering using high fluence $^{28}$Si$^-$ implantation. Phosphorus (P) donors implanted into one such $^{28}$Si layer with ~3000 ppm $^{29}$Si, produced by implanting 30 keV $^{28}$Si$^-$ ions at a fluence of 4x10^18 cm^-2, were measured with pulsed electron spin resonance, confirming successful donor activation upon annealing. The mono-exponential decay of the Hahn echo signal indicates a depletion of $^{29}$Si. A coherence time of T2 = 285 +/- 14 us is extracted, which is longer than that obtained in nat Si for similar doping concentrations and can be increased by reducing the P concentration in future. The isotopic enrichment was improved by employing one-for-one ion sputtering using 45 keV $^{28}$Si$^-$ implantation. A fluence of 2.63x10^18 cm^-2 $^{28}$Si$^-$ ions were implanted at this energy into nat Si, resulting in an isotopically enriched surface layer ~100 nm thick; suitable for providing a sufficient volume of $^{28}$Si for donor qubits implanted into the near-surface region. We observe a depletion of $^{29}$Si to 250 ppm as measured by secondary ion mass spectrometry. The impurity content and the crystallization kinetics via solid phase epitaxy are discussed. The $^{28}$Si layer is confirmed to be a single crystal using transmission electron microscopy. This method of Si isotopic enrichment shows promise for incorporating into the fabrication process flow of Si spin qubit devices.

The understanding of weak measurements and interaction-free measurements has greatly expanded the conceptual and experimental toolbox to explore the quantum world. Here we demonstrate single-shot variable-strength weak measurements of the electron and the nuclear spin states of a single $^{31}$P donor in silicon. We first show how the partial collapse of the nuclear spin due to measurement can be used to coherently rotate the spin to a desired pure state. We explicitly demonstrate that phase coherence is preserved throughout multiple sequential single-shot weak measurements, and that the partial state collapse can be reversed. Second, we use the relation between measurement strength and perturbation of the nuclear state as a physical meter to extract the tunneling rates between the $^{31}$P donor and a nearby electron reservoir from data, conditioned on observing no tunneling events. Our experiments open avenues to measurement-based state preparation, steering and feedback protocols for spin systems in the solid state, and highlight the fundamental connection between information gain and state modification in quantum mechanics., Comment: 6 pages main text + 3 pages supplementary

We report on the Raman and photoluminescence characterization of three-dimensional microstructures created in single crystal diamond with a Focused Ion Beam (FIB) assisted lift-off technique. The method is based on MeV ion implantation to create a buried etchable layer, followed by FIB patterning and selective etching. In the applications of such microstructures where the properties of high quality single crystal diamond are most relevant, residual damage after the fabrication process represents a critical technological issue. The results of Raman and photoluminescence characterization indicate that the partial distortion of the sp3-bonded lattice and the formation of isolated point defects are effectively removed after thermal annealing, leaving low amounts of residual damage in the final structures. Three-dimensional microstructures in single-crystal diamond offer a large range of applications, such as quantum optics devices and fully integrated opto mechanical assemblies., Comment: 30 pages, 7 figures

We demonstrate the fabrication of sub-micron layers of single-crystal diamond suitable for subsequent processing as demonstrated by this test ring structure. This method is a significant enabling technology for nanomechanical and photonic structures incorporating colour-centres. The process uses a novel double implant process, annealing and chemical etching to produce membranes of diamond from single-crystal starting material, the thinnest layers achieved to date are 210 nm thick., Comment: 21 pages, 4 figures

Long coherence times and fast gate operations are desirable but often conflicting requirements for physical qubits. This conflict can be resolved by resorting to fast qubits for operations, and by storing their state in a `quantum memory' while idle. The $^{31}$P donor in silicon comes naturally equipped with a fast qubit (the electron spin) and a long-lived qubit (the $^{31}$P nuclear spin), coexisting in a bound state at cryogenic temperatures. Here, we demonstrate storage and retrieval of quantum information from a single donor electron spin to its host phosphorus nucleus in isotopically-enriched $^{28}$Si. The fidelity of the memory process is characterised via both state and process tomography. We report an overall process fidelity of $F_p =$81${\pm}$7%, a memory fidelity ($F_m$) of over 90%, and memory storage times up to 80 ms. These values are limited by a transient shift of the electron spin resonance frequency following high-power radiofrequency pulses., Comment: 14 pages, 6 figures. v2 has minor cosmetic improvements, and 11 additional references

Building upon the demonstration of coherent control and single-shot readout of the electron and nuclear spins of individual 31-P atoms in silicon, we present here a systematic experimental estimate of quantum gate fidelities using randomized benchmarking of 1-qubit gates in the Clifford group. We apply this analysis to the electron and the ionized 31-P nucleus of a single P donor in isotopically purified 28-Si. We find average gate fidelities of 99.95 % for the electron, and 99.99 % for the nuclear spin. These values are above certain error correction thresholds, and demonstrate the potential of donor-based quantum computing in silicon. By studying the influence of the shape and power of the control pulses, we find evidence that the present limitation to the gate fidelity is mostly related to the external hardware, and not the intrinsic behaviour of the qubit.

We demonstrate single dopant implantation into the channel of a silicon nanoscale metal-oxide-semiconductor field-effect-transistor. This is achieved by monitoring the drain current modulation during ion irradiation. Deterministic doping is crucial for overcoming dopant number variability in present nanoscale devices and for exploiting single atom degrees of freedom. The two main ion stopping processes that induce drain current modulation are examined. We employ 500~keV He ions, in which electronic stopping is dominant, leading to discrete increases in drain current and 14~keV P dopants for which nuclear stopping is dominant leading to discrete decreases in drain current., Comment: 13 pages, 3 figures, 1 table, accepted for Applied Physics Letters

We present a systematic study of quasi-one-dimensional density of states (DOS) in electron accumulation layers near a Si-SiO2 interface. In the experiments we have employed two conceptually different objects to probe DOS, namely, a phosphorus donor and a quantum dot, both operating in the single-electron tunneling regime. We demonstrate how the peaks in DOS can be moved in the transport window independently of the other device properties, and in agreement with the theoretical analysis. This method introduces a fast and convenient way of identifying excited states in these emerging nanostructures., Comment: 4 pages, 4 figures

We describe a method to control and detect in single-shot the electron spin state of an individual donor in silicon with greatly enhanced sensitivity. A silicon-based Single-Electron Transistor (SET) allows for spin-dependent tunneling of the donor electron directly into the SET island during the read-out phase. Simulations show that the charge transfer signals are typically \Delta q > 0.2 e - over an order of magnitude larger than achievable with metallic SETs on the SiO2 surface. A complete spin-based qubit structure is obtained by adding a local Electron Spin Resonance line for coherent spin control. This architecture is ideally suited to demonstrate and study the coherent properties of donor electron spins, but can be expanded and integrated with classical control electronics in the context of scale-up., Comment: 5 pages, 4 figures

We report a detailed study of low-temperature (mK) transport properties of a silicon double-dot system fabricated by phosphorous ion implantation. The device under study consists of two phosphorous nanoscale islands doped to above the metal-insulator transition, separated from each other and the source and drain reservoirs by nominally undoped (intrinsic) silicon tunnel barriers. Metallic control gates, together with an Al-AlOx single-electron transistor, were positioned on the substrate surface, capacitively coupled to the buried dots. The individual double-dot charge states were probed using source-drain bias spectroscopy combined with non-invasive SET charge sensing. The system was measured in linear (VSD = 0) and non-linear (VSD <> 0) regimes allowing calculations of the relevant capacitances. Simultaneous detection using both SET sensing and source-drain current measurements was demonstrated, providing a valuable combination for the analysis of the system. Evolution of the triple points with applied bias was observed using both charge and current sensing. Coulomb diamonds, showing the interplay between the Coulomb charging effects of the two dots, were measured using simultaneous detection and compared with numerical simulations., Comment: 7 pages, 6 figures

Nitrogen vacancy (NV) centers in diamond have distinct promise as solid-state qubits. This is because of their large dipole moment, convenient level structure and very long room-temperature coherence times. In general, a combination of ion irradiation and subsequent annealing is used to create the centers, however for the rigorous demands of quantum computing all processes need to be optimized, and decoherence due to the residual damage caused by the implantation process itself must be mitigated. To that end we have studied photoluminescence (PL) from NV$^-$, NV$^0$ and GR1 centers formed by ion implantation of 2MeV He ions over a wide range of fluences. The sample was annealed at $600^{\circ}$C to minimize residual vacancy diffusion, allowing for the concurrent analysis of PL from NV centers and irradiation induced vacancies (GR1). We find non-monotic PL intensities with increasing ion fluence, monotonic increasing PL in NV$^0$/NV$^-$ and GR1/(NV$^0$ + NV$^1$) ratios, and increasing inhomogeneous broadening of the zero-phonon lines with increasing ion fluence. All these results shed important light on the optimal formation conditions for NV qubits. We apply our findings to an off-resonant photonic quantum memory scheme using vibronic sidebands.

We present low temperature charge sensing measurements of nanoscale phosphorus-implanted double-dots in silicon. The implanted phosphorus forms two 50 nm diameter islands with source and drain leads, which are separated from each other by undoped silicon tunnel barriers. Occupancy of the dots is controlled by surface gates and monitored using an aluminium single electron transistor which is capacitively coupled to the dots. We observe a charge stability diagram consistent with the designed many-electron double-dot system and this agrees well with capacitance modelling of the structure. We discuss the significance of these results to the realisation of smaller devices which may be used as charge or spin qubits., Comment: accepted for publication in Nanotechnology

We report on millikelvin charge sensing measurements of a silicon double-dot system fabricated by phosphorus ion implantation. An aluminum single-electron transistor (SET) is capacitively coupled to each of the implanted dots enabling the charging behavior of the double-dot system to be studied independently of current transport. Using an electrostatic gate, the interdot coupling can be tuned from weak to strong coupling. In the weak interdot coupling regime, the system exhibits well-defined double-dot charging behavior. By contrast, in the strong interdot coupling regime, the system behaves as a single-dot., Comment: 11 pages, 5 figures

Recently, magnetic order in highly oriented pyrolytic graphite (HOPG) induced by proton broad- and microbeam irradiation was discovered. Theoretical models propose that hydrogen could play a major role in the magnetism mechanism. We analysed the hydrogen distribution of pristine as well as irradiated HOPG samples, which were implanted to micrometer-sized spots as well as extended areas with various doses of 2.25 MeV protons at the Leipzig microprobe LIPSION. For this we used the sensitive 3D hydrogen microscopy system at the Munich microprobe SNAKE. The background hydrogen level in pristine HOPG is determined to be less than 0.3 at-ppm. About 4.8e15 H-atoms/cm^2 are observed in the near-surface region (4 um depth resolution). The depth profiles of the implants show hydrogen located within a confined peak at the end of range, in agreement with SRIM Monte Carlo simulations, and no evidence of diffusion broadening along the c-axis. At sample with microspots, up to 40 at-% of the implanted hydrogen is not detected, providing support for lateral hydrogen diffusion., Comment: accepted for publication in Nucl. Instr. and Meth

Nitrogen-vacancy (NV-) color centers in diamond were created by implantation of 7 keV 15N (I = 1/2) ions into type IIa diamond. Optically detected magnetic resonance was employed to measure the hyperfine coupling of the NV- centers. The hyperfine spectrum from 15NV- arising from implanted 15N can be distinguished from 14NV- centers created by native 14N (I = 1) sites. Analysis indicates 1 in 40 implanted 15N atoms give rise to an optically observable 15NV- center. This report ultimately demonstrates a mechanism by which the yield of NV- center formation by nitrogen implantation can be measured., Comment: 14 pages, 3 figures, to appear in Applied Physics Letters

We study the low temperature electrical transport behaviour of a silicon single electron transistor. The island and leads are defined by patterned phosphorus doped regions achieved by ion implantation through a polymer resist mask. In the device a 50 nm diameter island, containing ~600 donors and having a metallic density of states, is separated from source and drain leads by undoped silicon tunnel barriers. The central island and tunnel barriers are covered by a surface gate in a field effect transistor geometry allowing the coupling between the leads and island to be controlled. Coulomb blockade due to charging of the doped island is measured, the oscillation period is observed to be constant while the charging energy is dependent on the surface gate voltage. We discuss the possibilities of approaching the few electron regime in these structures, with the aim of observing and manipulating discrete quantum mechanical states., Comment: accepted into the proceedings of MNE 2005 in Microelectronic Engineering

We report on the fabrication and electrical characterization at millikelvin temperatures of a novel silicon single-electron transistor (Si-SET). The island and source-drain leads of the Si-SET are formed by the implantation of phosphorus ions to a density above the metal-insulator-transition, with the tunnel junctions created by undoped regions. Surface gates above each of the tunnel junctions independently control the tunnel coupling between the Si-SET island and leads. The device shows periodic Coulomb blockade with a charging energy e$^2$/2C$_\Sigma$ $\sim$ 250 $\mu$eV, and demonstrates a reproducible and controllable pathway to a silicon-based SET using CMOS processing techniques., Comment: 3 pages, 3 figures

We demonstrate electrical control of Si:P double dots in which the potential is defined by nanoscale phosphorus doped regions. Each dot contains approximately 600 phosphorus atoms and has a diameter close to 30 nm. On application of a differential bias across the dots, electron transfer is observed, using single electron transistors in both dc- and rf-mode as charge detectors. With the possibility to scale the dots down to few and even single atoms these results open the way to a new class of precision-doped quantum dots in silicon., Comment: 3 figures, 3 pages

Inter-valley interference between degenerate conduction band minima has been shown to lead to oscillations in the exchange energy between neighbouring phosphorus donor electron states in silicon \cite{Koiller02,Koiller02A}. These same effects lead to an extreme sensitivity of the exchange energy on the relative orientation of the donor atoms, an issue of crucial importance in the construction silicon-based spin quantum computers. In this article we calculate the donor electron exchange coupling as a function of donor position incorporating the full Bloch structure of the Kohn-Luttinger electron wavefunctions. It is found that due to the rapidly oscillating nature of the terms they produce, the periodic part of the Bloch functions can be safely ignored in the Heitler-London integrals as was done by Koiller et. al. [Phys. Rev. Lett. 88,027903(2002),Phys. Rev. B. 66,115201(2002)], significantly reducing the complexity of calculations. We address issues of fabrication and calculate the expected exchange coupling between neighbouring donors that have been implanted into the silicon substrate using an 15keV ion beam in the so-called 'top down' fabrication scheme for a Kane solid-state quantum computer. In addition we calculate the exchange coupling as a function of the voltage bias on control gates used to manipulate the electron wavefunctions and implement quantum logic operations in the Kane proposal, and find that these gate biases can be used to both increase and decrease the magnitude of the exchange coupling between neighbouring donor electrons. The zero-bias results reconfirm those previously obtained by Koiller., Comment: 10 Pages, 8 Figures. To appear in Physical Review B

We report a nanofabrication, control and measurement scheme for charge-based silicon quantum computing which utilises a new technique of controlled single ion implantation. Each qubit consists of two phosphorus dopant atoms ~50 nm apart, one of which is singly ionized. The lowest two energy states of the remaining electron form the logical states. Surface electrodes control the qubit using voltage pulses and dual single electron transistors operating near the quantum limit provide fast readout with spurious signal rejection. A low energy (keV) ion beam is used to implant the phosphorus atoms in high-purity Si. Single atom control during the implantation is achieved by monitoring on-chip detector electrodes, integrated within the device structure, while positional accuracy is provided by a nanomachined resist mask. We describe a construction process for implanted single atom and atom cluster devices with all components registered to better than 20 nm, together with electrical characterisation of the readout circuitry. We also discuss universal one- and two-qubit gate operations for this architecture, providing a possible path towards quantum computing in silicon., Comment: 9 pages, 5 figures