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High-dimensional quantum systems are a valuable resource for quantum information processing. They can be used to encode error-correctable logical qubits, for instance in continuous-variable states of oscillators such as microwave cavities or the motional modes of trapped ions. Powerful encodings include 'Schr\"odinger cat' states, superpositions of widely displaced coherent states, which also embody the challenge of quantum effects at the large scale. Alternatively, recent proposals suggest encoding logical qubits in high-spin atomic nuclei, which can host hardware-efficient versions of continuous-variable codes on a finite-dimensional system. Here we demonstrate the creation and manipulation of Schr\"odinger cat states using the spin-7/2 nucleus of a single antimony ($^{123}$Sb) atom, embedded and operated within a silicon nanoelectronic device. We use a coherent multi-frequency control scheme to produce spin rotations that preserve the SU(2) symmetry of the qudit, and constitute logical Pauli operations for logical qubits encoded in the Schr\"odinger cat states. The Wigner function of the cat states exhibits parity oscillations with a contrast up to 0.982(5), and state fidelities up to 0.913(2). These results demonstrate high-fidelity preparation of nonclassical resource states and logical control in a single atomic-scale object, opening up applications in quantum information processing and quantum error correction within a scalable, manufacturable semiconductor platform., Comment: 40 pages including main and supplementary information

Scalable quantum processors require high-fidelity universal quantum logic operations in a manufacturable physical platform. Donors in silicon provide atomic size, excellent quantum coherence and compatibility with standard semiconductor processing, but no entanglement between donor-bound electron spins has been demonstrated to date. Here we present the experimental demonstration and tomography of universal 1- and 2-qubit gates in a system of two weakly exchange-coupled electrons, bound to single phosphorus donors introduced in silicon by ion implantation. We surprisingly observe that the exchange interaction has no effect on the qubit coherence. We quantify the fidelity of the quantum operations using gate set tomography (GST), and we use the universal gate set to create entangled Bell states of the electrons spins, with fidelity ~ 93%, and concurrence 0.91 +/- 0.08. These results form the necessary basis for scaling up donor-based quantum computers.

Semiconductor spin qubits combine excellent quantum performance with the prospect of manufacturing quantum devices using industry-standard metal-oxide-semiconductor (MOS) processes. This applies also to ion-implanted donor spins, which further afford exceptional coherence times and large Hilbert space dimension in their nuclear spin. Here we demonstrate and integrate multiple strategies to manufacture scale-up donor-based quantum computers. We use $^{31}$PF$_{2}$ molecule implants to triple the placement certainty compared to $^{31}$P ions, while attaining 99.99$\,$% confidence in detecting the implant. Similar confidence is retained by implanting heavier atoms such as $^{123}$Sb and $^{209}$Bi, which represent high-dimensional qudits for quantum information processing, while Sb$_2$ molecules enable deterministic formation of closely-spaced qudits. We demonstrate the deterministic formation of regular arrays of donor atoms with 300$\,$nm spacing, using step-and-repeat implantation through a nano aperture. These methods cover the full gamut of technological requirements for the construction of donor-based quantum computers in silicon., Comment: 11 pages, 6 figures, 2 tables

Solid-state spin qubits within silicon crystals at mK temperatures show great promise in the realisation of a fully scalable quantum computation platform. Qubit coherence times are limited in natural silicon owing to coupling to the isotope ${ }^{29} \mathrm{Si}$ which has a non-zero nuclear spin. This work presents a method for the depletion of ${ }^{29} \mathrm{Si}$ in localised volumes of natural silicon wafers by irradiation using a 45 keV ${ }^{28} \mathrm{Si}$ focused ion beam with fluences above $1 \times 10^{19} \, \mathrm{ions} \, \mathrm{cm}^{-2}$. Nanoscale secondary ion mass spectrometry analysis of the irradiated volumes shows unprecedented quality enriched silicon that reaches a minimal residual ${ }^{29} \mathrm{Si}$ value of 2.3 $\pm$ 0.7 ppm and with residual C and O comparable to the background concentration in the unimplanted wafer. Transmission electron microscopy lattice images confirm the solid phase epitaxial re-crystallization of the as-implanted amorphous enriched volume extending over 200 nm in depth upon annealing. The ease of fabrication, requiring only commercially available natural silicon wafers and ion sources, opens the possibility for co-integration of qubits in localised highly enriched volumes with control circuitry in the surrounding natural silicon for large-scale devices., Comment: 8 pages, 4 figures, 2 tables

Donor spins in silicon-28 ($^{28}$Si) are among the most performant qubits in the solid state, offering record coherence times and gate fidelities above 99%. Donor spin qubits can be fabricated using the semiconductor-industry compatible method of deterministic ion implantation. Here we show that the precision of this fabrication method can be boosted by implanting molecule ions instead of single atoms. The bystander ions, co-implanted with the dopant of interest, carry additional kinetic energy and thus increase the detection confidence of deterministic donor implantation employing single ion detectors to signal the induced electron-hole pairs. This allows the placement uncertainty of donor qubits to be minimised without compromising on detection confidence. We investigate the suitability of phosphorus difluoride (PF$_2^+$) molecule ions to produce high quality P donor qubits. Since $^{19}$F nuclei have a spin of $I = 1/2$, it is imperative to ensure that they do not hyperfine couple to P donor electrons as they would cause decoherence by adding magnetic noise. Using secondary ion mass spectrometry, we confirm that F diffuses away from the active region of qubit devices while the P donors remain close to their original location during a donor activation anneal. PF$_2$-implanted qubit devices were then fabricated and electron spin resonance (ESR) measurements were performed on the P donor electron. A pure dephasing time of $T_2^* = 20.5 \pm 0.5$ $\mu$s and a coherence time of $T_2^{Hahn} = 424 \pm 5$ $\mu$s were extracted for the P donor electron-values comparable to those found in previous P-implanted qubit devices. Closer investigation of the P donor ESR spectrum revealed that no $^{19}$F nuclear spins were found in the vicinity of the P donor. Molecule ions therefore show great promise for producing high-precision deterministically-implanted arrays of long-lived donor spin qubits., Comment: 8 pages, 5 figures, 1 table

Colour centre ensembles in diamond have been the subject of intensive investigation for many applications including single photon sources for quantum communication, quantum computation with optical inputs and outputs, and magnetic field sensing down to the nanoscale. Some of these applications are realised with a single centre or randomly distributed ensembles in chips, but the most demanding application for a large-scale quantum computer will require ordered arrays. By configuring an electronic-grade diamond substrate with a biased surface graphene electrode connected to charge-sensitive electronics, it is possible to demonstrate deterministic single ion implantation for ions stopping between 30 and 130~nm deep from a typical stochastic ion source. An implantation event is signalled by a charge pulse induced by the drift of electron-hole pairs from the ion implantation. The ion implantation site is localised with an AFM nanostencil or a focused ion beam. This allows the construction of ordered arrays of single atoms with associated colour centres that paves the way for the fabrication of deterministic colour center networks in a monolithic device., Comment: 11 pages, 5 figures

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., Comment: 31 pages and 19 figures including Supplementary Materials

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. 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., Comment: 26 pages, 17 figures. v3 includes Supplementary Materials

The demonstration of universal quantum logic operations near the fault-tolerance threshold establishes ion-implanted near-surface donor atoms as a plausible platform for scalable quantum computing in silicon. The next technological step forward requires a deterministic fabrication method to create large-scale arrays of donors, featuring few hundred nanometre inter-donor spacing. Here, we explore the feasibility of this approach by implanting low-energy ions into silicon devices featuring an enlarged 60x60 $\mu$m sensitive area and an ultra-thin 3.2 nm gate oxide - capable of hosting large-scale donor arrays. By combining a focused ion beam system incorporating an electron-beam-ion-source with in-vacuum ultra-low noise ion detection electronics, we first demonstrate a versatile method to spatially map the device response characteristics to shallowly implanted 12 keV $^1$H$_2^+$ ions. Despite the weak internal electric field, near-unity charge collection efficiency is obtained from the entire sensitive area. This can be explained by the critical role that the high-quality thermal gate oxide plays in the ion detection response, allowing an initial rapid diffusion of ion induced charge away from the implant site. Next, we adapt our approach to perform deterministic implantation of a few thousand 24 keV $^{40}$Ar$^{2+}$ ions into a predefined micro-volume, without any additional collimation. Despite the reduced ionisation from the heavier ion species, a fluence-independent detection confidence of $\geq$99.99% was obtained. Our system thus represents not only a new method for mapping the near-surface electrical landscape of electronic devices, but also an attractive framework towards mask-free prototyping of large-scale donor arrays in silicon., Comment: 10 pages, 5 figures

Fault-tolerant quantum computing requires initializing the quantum register in a well-defined fiducial state. In solid-state systems, this is typically achieved through thermalization to a cold reservoir, such that the initialization fidelity is fundamentally limited by temperature. Here, we present a method of preparing a fiducial quantum state with a confidence beyond the thermal limit. It is based on real time monitoring of the qubit through a negative-result measurement -- the equivalent of a `Maxwell's demon' that triggers the experiment only upon the appearance of a qubit in the lowest-energy state. We experimentally apply it to initialize an electron spin qubit in silicon, achieving a ground-state initialization fidelity of 98.9(4)%, corresponding to a 20$\times$ reduction in initialization error compared to the unmonitored system. A fidelity approaching 99.9% could be achieved with realistic improvements in the bandwidth of the amplifier chain or by slowing down the rate of electron tunneling from the reservoir. We use a nuclear spin ancilla, measured in quantum nondemolition mode, to prove the value of the electron initialization fidelity far beyond the intrinsic fidelity of the electron readout. However, the method itself does not require an ancilla for its execution, saving the need for additional resources. The quantitative analysis of the initialization fidelity reveals that a simple picture of spin-dependent electron tunneling does not correctly describe the data. Our digital `Maxwell's demon' can be applied to a wide range of quantum systems, with minimal demands on control and detection hardware., Comment: 15 pages, 7 figures

Nuclear spins were among the first physical platforms to be considered for quantum information processing, because of their exceptional quantum coherence and atomic-scale footprint. However, their full potential for quantum computing has not yet been realized, due to the lack of methods 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 spin, and used to prepare entangled Bell states with fidelities up to 94.2(2.7)%. The quantum operations are precisely characterised using gate set tomography (GST), 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 processors. 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. Since electron spin qubits in semiconductors can be further coupled to other electrons or physically shuttled across different locations, these results establish a viable route for scalable quantum information processing using donor nuclear and electron spins., Comment: 51 pages, including supplementary information. v3 reflects the final published version

Dopant atoms are ubiquitous in semiconductor technologies, providing the tailored electronic properties that underpin the modern digital information era. Harnessing the quantum nature of these atomic-scale objects represents a new and exciting technological revolution. In this article we describe the use of ion-implanted donor spins in silicon for quantum technologies. We review how to fabricate and operate single-atom spin qubits in silicon, obtaining some of the most coherent solid-state qubits, and we discuss pathways to scale up these qubits to build large quantum processors. Heavier group-V donors with large nuclear spins display electric quadrupole couplings that enable nuclear electric resonance, quantum chaos and strain sensing. Donor ensembles can be coupled to microwave cavities to develop hybrid quantum Turing machines. Counted, deterministic implantation of single donors, combined with novel methods for precision placement, will allow the integration of individual donors spins with industry-standard silicon fabrication processes, making implanted donors a prime physical platform for the second quantum revolution., Comment: 18 pages, 11 figures, 134 references. Published in the special issue of Advanced Quantum Technologies "Advancing Quantum Technologies - Chances and Challenges" edited by Rainer Blatt

The attributes of group-V-donor spins implanted in an isotopically purified $^{28}$Si crystal make them attractive qubits for large-scale quantum computer devices. Important features include long nuclear and electron spin lifetimes of $^{31}$P, hyperfine clock transitions in $^{209}$Bi and electrically controllable $^{123}$Sb nuclear spins. However, architectures for scalable quantum devices require the ability to fabricate deterministic arrays of individual donor atoms, placed with sufficient precision to enable high-fidelity quantum operations. Here we employ on-chip electrodes with charge-sensitive electronics to demonstrate the implantation of single low-energy (14 keV) P$^+$ ions with an unprecedented $99.87\pm0.02$% confidence, while operating close to room-temperature. This permits integration with an atomic force microscope equipped with a scanning-probe ion aperture to address the critical issue of directing the implanted ions to precise locations. These results show that deterministic single-ion implantation can be a viable pathway for manufacturing large-scale donor arrays for quantum computation and other applications., Comment: 12 pages, 4 figures

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 $^{31}$P donors implanted in silicon. The coupling strength, $J = 32.06 \pm 0.06$ MHz, is measured spectroscopically with unprecedented precision. Since the coupling is weaker than the electron-nuclear hyperfine coupling $A \approx 90$ 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., Comment: 10 pages, 5 figures, plus Supplementary Information. v2 contains additional references, and a simpler explanation of two-qubit CROT gates for donors in silicon

The quantum coherence and gate fidelity of electron spin qubits in semiconductors is often limited by noise arising from coupling to a bath of nuclear spins. Isotopic enrichment of spin-zero nuclei such as $^{28}$Si has led to spectacular improvements of the dephasing time $T_2^*$ which, surprisingly, can extend two orders of magnitude beyond theoretical expectations. Using a single-atom $^{31}$P qubit in enriched $^{28}$Si, we show that the abnormally long $T_2^*$ is due to the controllable freezing of the dynamics of the residual $^{29}$Si nuclei close to the donor. Our conclusions are supported by a nearly parameter-free modeling of the $^{29}$Si nuclear spin dynamics, which reveals the degree of back-action provided by the electron spin as it interacts with the nuclear bath. This study clarifies the limits of ergodic assumptions in analyzing many-body spin-problems under conditions of strong, frequent measurement, and provides novel strategies for maximizing coherence and gate fidelity of spin qubits in semiconductors., Comment: 11 pages, 5 figures

We analyze the electron spin relaxation rate $1/T_1$ of individual ion-implanted $^{31}$P donors, in a large set of metal-oxide-semiconductor (MOS) silicon nanoscale devices, with the aim of identifying spin relaxation mechanisms peculiar to the environment of the spins. The measurements are conducted at low temperatures ($T\approx 100$~mK), as a function of external magnetic field $B_0$ and donor electrochemical potential $\mu_{\rm D}$. We observe a magnetic field dependence of the form $1/T_1\propto B_0^5$ for $B_0\gtrsim 3\,$ T, corresponding to the phonon-induced relaxation typical of donors in the bulk. However, the relaxation rate varies by up to two orders of magnitude between different devices. We attribute these differences to variations in lattice strain at the location of the donor. For $B_0\lesssim 3\,$T, the relaxation rate changes to $1/T_1\propto B_0$ for two devices. This is consistent with relaxation induced by evanescent-wave Johnson noise created by the metal structures fabricated above the donors. At such low fields, where $T_1>1\,$s, we also observe and quantify the spurious increase of $1/T_1$ when the electrochemical potential of the spin excited state $|\uparrow\rangle$ comes in proximity to empty states in the charge reservoir, leading to spin-dependent tunneling that resets the spin to $|\downarrow\rangle$. These results give precious insights into the microscopic phenomena that affect spin relaxation in MOS nanoscale devices, and provide strategies for engineering spin qubits with improved spin lifetimes., Comment: 14 pages, 8 figures. Version 2 has extensive text revisions, typo corrections, and two extra authors

Whispering Gallery (WG) mode resonators have been machined from a boule of single-crystal isotopically pure silicon-28. Before machining, the as-grown rod was measured in a cavity, with the best Bragg confined modes exhibiting microwave $Q$-factors on the order of a million for frequencies between 10 and 15 GHz. After machining the rod into smaller cylindrical WG mode resonators, the frequencies of the fundamental mode families were used to determine the relative permittivity of the material to be $11.488\pm0.024$ near 4 K, with the precision limited only by the dimensional accuracy of the resonator. However, the Q-factors were degraded by the machining to below $4\times10^4$. Raman spectroscopy was used to optimize post-machining surface treatments to restore high $Q$-factors. This is an enabling step for the use of such resonators for hybrid quantum systems and frequency conversion applications, as silicon-28 also has very low phonon losses, can host very narrow linewidth spin ensembles and is a material commonly used in optical applications., Comment: 7 pages, 6 figures

We investigate the dynamics of a strongly-driven, microwave-dressed, donor-bound electron spin qubit in silicon. A resonant oscillating magnetic field $B_1$ is used to dress the electron spin and create a new quantum system with a level splitting proportional to $B_1$. The dressed two-level system can then be driven by modulating the detuning $\Delta\nu$ between the microwave source frequency $\nu_{\rm MW}$ and the electron spin transition frequency $\nu_e$ at the frequency of the level splitting. The resulting dressed qubit Rabi frequency $\Omega_{R\rho}$ is defined by the modulation amplitude, which can be made comparable to the level splitting using frequency modulation on the microwave source. This allows us to investigate the regime where the rotating wave approximation breaks down, without requiring microwave power levels that would be incompatible with a cryogenic environment. We observe clear deviations from normal Rabi oscillations and can numerically simulate the time evolution of the states in excellent agreement with the experimental data.

Coherent dressing of a quantum two-level system provides access to a new quantum system with improved properties - a different and easily tuneable level splitting, faster control, and longer coherence times. In our work we investigate the properties of the dressed, donor-bound electron spin in silicon, and probe its potential for the use as quantum bit in scalable architectures. The two dressed spin-polariton levels constitute a quantum bit that can be coherently driven with an oscillating magnetic field, an oscillating electric field, by frequency modulating the driving field, or by a simple detuning pulse. We measure coherence times of $T_{2\rho}^*=2.4$ ms and $T_{2\rho}^{\rm Hahn}=9$ ms, one order of magnitude longer than those of the undressed qubit. Furthermore, the use of the dressed states enables coherent coupling of the solid-state spins to electric fields and mechanical oscillations.

Bell's theorem sets a boundary between the classical and quantum realms, by providing a strict proof of 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. For this reason the Bell signal has been tagged as a single-number benchmark for the performance of quantum computing devices. Here we demonstrate deterministic, on-demand generation of two-qubit entangled states of the electron and the nuclear spin of a single phosphorus atom embedded in a silicon nanoelectronic device. By sequentially reading the electron and the nucleus, we show that these entangled states violate the Bell/CHSH inequality with a Bell signal of 2.50(10). An even higher value of 2.70(9) is obtained by mapping the parity of the two-qubit state onto the nuclear spin, which allows for high-fidelity quantum non-demolition measurement (QND) of the parity. Furthermore, we complement the Bell inequality entanglement witness with full two-qubit state tomography exploiting QND measurement, which 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 show that this system is able to maintain its simultaneously high initialization, manipulation and measurement fidelities past the single-qubit regime., Comment: 10 pages, 3 figures, 1 table, 4 extended data figures

Large-scale quantum computers must be built upon quantum bits that are both highly coherent and locally controllable. We demonstrate the quantum control of the electron and the nuclear spin of a single 31P atom in silicon, using a continuous microwave magnetic field together with nanoscale electrostatic gates. The qubits are tuned into resonance with the microwave field by a local change in electric field, which induces a Stark shift of the qubit energies. This method, known as A-gate control, preserves the excellent coherence times and gate fidelities of isolated spins, and can be extended to arbitrarily many qubits without requiring multiple microwave sources., Comment: Main paper: 13 pages, 4 figures. Supplementary information: 25 pages, 13 figures

Magnetic fluctuations caused by the nuclear spins of a host crystal are often the leading source of decoherence for many types of solid-state spin qubit. In group-IV materials, the spin-bearing nuclei are sufficiently rare that it is possible to identify and control individual host nuclear spins. This work presents the first experimental detection and manipulation of a single $^{29}$Si nuclear spin. The quantum non-demolition (QND) single-shot readout of the spin is demonstrated, and a Hahn echo measurement reveals a coherence time of $T_2 = 6.3(7)$ ms - in excellent agreement with bulk experiments. Atomistic modeling combined with extracted experimental parameters provides possible lattice sites for the $^{29}$Si atom under investigation. These results demonstrate that single $^{29}$Si nuclear spins could serve as a valuable resource in a silicon spin-based quantum computer.

The spin of an electron or a nucleus in a semiconductor [1] naturally implements the unit of quantum information -- the qubit -- while providing a technological link to the established electronics industry [2]. The solid-state environment, however, may provide deleterious interactions between the qubit and the nuclear spins of surrounding atoms [3], or charge and spin fluctuators in defects, oxides and interfaces [4]. For group IV materials such as silicon, enrichment of the spin-zero 28-Si isotope drastically reduces spin-bath decoherence [5]. Experiments on bulk spin ensembles in 28-Si crystals have indeed demonstrated extraordinary coherence times [6-8]. However, it remained unclear whether these would persist at the single-spin level, in gated nanostructures near amorphous interfaces. Here we present the coherent operation of individual 31-P electron and nuclear spin qubits in a top-gated nanostructure, fabricated on an isotopically engineered 28-Si substrate. We report new benchmarks for coherence time (> 30 seconds) and control fidelity (> 99.99%) of any single qubit in solid state, and perform a detailed noise spectroscopy [9] to demonstrate that -- contrary to widespread belief -- the coherence is not limited by the proximity to an interface. Our results represent a fundamental advance in control and understanding of spin qubits in nanostructures.

We present the experimental observation of a large exchange coupling $J \approx 300$ $\mu$eV between two $^{31}$P electron spin qubits in silicon. The singlet and triplet states of the coupled spins are monitored in real time by a Single-Electron Transistor, which detects ionization from tunnel-rate-dependent processes in the coupled spin system, yielding single-shot readout fidelities above 95%. The triplet to singlet relaxation time $T_1 \approx 4$ ms at zero magnetic field agrees with the theoretical prediction for $J$-coupled $^{31}$P dimers in silicon. The time evolution of the 2-electron state populations gives further insight into the valley-orbit eigenstates of the donor dimer, valley selection rules and relaxation rates, and the role of hyperfine interactions. These results pave the way to the realization of 2-qubit quantum logic gates with spins in silicon, and highlight the necessity to adopt gating schemes compatible with weak $J$-coupling strengths., Comment: Main: 5 pages, 4 figures. Supp.Mat: 1 page, 1 figure. Final version with journal reference

The main limitation to the high-fidelity quantum control of spins in semiconductors is the presence of strongly fluctuating fields arising from the nuclear spin bath of the host material. We demonstrate here a substantial improvement in single-qubit gate fidelities for an electron spin qubit bound to a $^{31}$P atom in natural silicon, by applying adiabatic inversion instead of narrow-band pulses. We achieve an inversion fidelity of 97%, and we observe signatures in the spin resonance spectra and the spin coherence time that are consistent with the presence of an additional exchange-coupled donor. This work highlights the effectiveness of adiabatic inversion techniques for spin control in fluctuating environments., Comment: 4 pages, 2 figures

A single atom is the prototypical quantum system, and a natural candidate for a quantum bit - the elementary unit of a quantum computer. Atoms have been successfully used to store and process quantum information in electromagnetic traps, as well as in diamond through the use of the NV-center point defect. Solid state electrical devices possess great potential to scale up such demonstrations from few-qubit control to larger scale quantum processors. In this direction, coherent control of spin qubits has been achieved in lithographically-defined double quantum dots in both GaAs and Si. However, it is a formidable challenge to combine the electrical measurement capabilities of engineered nanostructures with the benefits inherent to atomic spin qubits. Here we demonstrate the coherent manipulation of an individual electron spin qubit bound to a phosphorus donor atom in natural silicon, measured electrically via single-shot readout. We use electron spin resonance to drive Rabi oscillations, while a Hahn echo pulse sequence reveals a spin coherence time (T2) exceeding 200 \mu s. This figure is expected to become even longer in isotopically enriched 28Si samples. Together with the use of a device architecture that is compatible with modern integrated circuit technology, these results indicate that the electron spin of a single phosphorus atom in silicon is an excellent platform on which to build a scalable quantum computer., Comment: 13 pages, 4 figures

A single nuclear spin holds the promise of being a long-lived quantum bit or quantum memory, with the high fidelities required for fault-tolerant quantum computing. We show here that such promise could be fulfilled by a single phosphorus (31P) nuclear spin in a silicon nanostructure. By integrating single-shot readout of the electron spin with on-chip electron spin resonance, we demonstrate the quantum non-demolition, electrical single-shot readout of the nuclear spin, with readout fidelity better than 99.8% - the highest for any solid-state qubit. The single nuclear spin is then operated as a qubit by applying coherent radiofrequency (RF) pulses. For an ionized 31P donor we find a nuclear spin coherence time of 60 ms and a 1-qubit gate control fidelity exceeding 98%. These results demonstrate that the dominant technology of modern electronics can be adapted to host a complete electrical measurement and control platform for nuclear spin-based quantum information processing., Comment: 18 pages, 5 figures

The size of silicon transistors used in microelectronic devices is shrinking to the level where quantum effects become important. While this presents a significant challenge for the further scaling of microprocessors, it provides the potential for radical innovations in the form of spin-based quantum computers and spintronic devices. An electron spin in Si can represent a well-isolated quantum bit with long coherence times because of the weak spin-orbit coupling and the possibility to eliminate nuclear spins from the bulk crystal. However, the control of single electrons in Si has proved challenging, and has so far hindered the observation and manipulation of a single spin. Here we report the first demonstration of single-shot, time-resolved readout of an electron spin in Si. This has been performed in a device consisting of implanted phosphorus donors coupled to a metal-oxide-semiconductor single-electron transistor - compatible with current microelectronic technology. We observed a spin lifetime approaching 1 second at magnetic fields below 2 T, and achieved spin readout fidelity better than 90%. High-fidelity single-shot spin readout in Si opens the path to the development of a new generation of quantum computing and spintronic devices, built using the most important material in the semiconductor industry., Comment: 5 pages, 4 figures

We investigate a hybrid structure consisting of $20\pm4$ implanted $^{31}$P atoms close to a gate-induced silicon single electron transistor (SiSET). In this configuration, the SiSET is extremely sensitive to the charge state of the nearby centers, turning from the off state to the conducting state when the charge configuration is changed. We present a method to measure fast electron tunnel rates between donors and the SiSET island, using a pulsed voltage scheme and low-bandwidth current detection. The experimental findings are quantitatively discussed using a rate equation model, enabling the extraction of the capture and emission rates., Comment: 10 pages, 3 figures

We have developed nano-scale double-gated field-effect-transistors for the study of electron states and transport properties of single deliberately-implanted phosphorus donors. The devices provide a high-level of control of key parameters required for potential applications in nanoelectronics. For the donors, we resolve transitions corresponding to two charge states successively occupied by spin down and spin up electrons. The charging energies and the Lande g-factors are consistent with expectations for donors in gated nanostructures., Comment: 6 pages, 3 figures, journal

The use of adiabatic passage techniques to mediate particle transport through real space, rather than phase space is becoming an interesting possibility. We have investigated the properties of Coherent Tunneling Adiabatic Passage (CTAP) with alternating tunneling matrix elements. This geometry, not previously considered in the donor in silicon paradigm, provides an interesting route to long-range quantum transport. We introduce simplified coupling protocols, and transient eigenspectra as well as a realistic gate design for this transport protocol. Using a pairwise treatment of the tunnel couplings for a 5 donor device with 30nm donor spacings, 120nm total chain length, we estimate the time scale required for adiabatic operation to be ~70ns, a time well within measured electron spin and estimated charge relaxation and times for phosphorus donors in silicon., Comment: 13 pages, 5 figures, minor revisions

Triple donor devices have the potential to exhibit adiabatic tunneling via the CTAP (Coherent Tunneling Adiabatic Passage) protocol which is a candidate transport mechanism for scalable quantum computing. We examine theoretically the statistics of dopant placement using counted ion implantation by employing an analytical treatment of CTAP transport properties under hydrogenic assumptions. We determine theoretical device yields for proof of concept devices for different implant energies. In particular, we determine a significant theoretical device yield (~80%) for 14keV phosphorus in silicon with nominal 20nm spacing., Comment: 10 pages, 3 figures

Coherent population trapping at zero magnetic field was observed for nitrogen-vacancy centers in diamond under optical excitation. This was measured as a reduction in photoluminescence when the detuning between two excitation lasers matched the 2.88 GHz crystal-field splitting of the color center ground states. This behavior is highly sensitive to strain, which modifies the excited states, and was unexpected following recent experiments demonstrating optical readout of single nitrogen-vacancy electron spins based on cycling transitions. These results demonstrate for the first time that three-level Lambda configurations suitable for proposed quantum information applications can be realized simultaneously for all four orientations of nitrogen-vacancy centers at zero magnetic field., Comment: 8 pages, 5 figures, new figure added

The single electron transistor (SET) offers unparalled opportunities as a nano-scale electrometer, capable of measuring sub-electron charge variations. SETs have been proposed for read-out schema in solid-state quantum computing where quantum information processing outcomes depend on the location of a single electron on nearby quantum dots. In this paper we investigate various geometries of a SET in order to maximize the device's sensitivity to charge transfer between quantum dots. Through the use of finite element modeling we model the materials and geometries of an Al/Al2O3 SET measuring the state of quantum dots in the Si substrate beneath. The investigation is motivated by the quest to build a scalable quantum computer, though the methodology used is primarily that of circuit theory. As such we provide useful techniques for any electronic device operating at the classical/quantum interface., Comment: 13 pages, 17 figures