Quantum coherence is of crucial importance for the applicability of donor based quantum computing. In this Letter we describe the observation of the interference of conduction paths induced by two donors in a nano-MOSFET resulting in a Fano resonance. This demonstrates the coherent exchange of electrons between two donors. In addition, the phase difference between the two conduction paths can be tuned by means of a magnetic field, in full analogy to the Aharonov-Bohm effect.
Spins of donor electrons and nuclei in silicon are promising quantum bit (qubit) candidates which combine long coherence times with the fabrication finesse of the silicon nanotechnology industry. We outline a potentially scalable spin qubit architecture where donor nuclear and electron spins are coupled to spins of electrons in quantum dots and discuss requirements for donor placement aligned to quantum dots by single ion implantation.
An atomistic method of calculating the spin-lattice relaxation times ($T_1$) is presented for donors in silicon nanostructures comprising of millions of atoms. The method takes into account the full band structure of silicon including the spin-orbit interaction. The electron-phonon Hamiltonian, and hence the deformation potential, is directly evaluated from the strain-dependent tight-binding Hamiltonian. The technique is applied to single donors and donor clusters in silicon, and explains the variation of $T_1$ with the number of donors and electrons, as well as donor locations. Without any ad…
We study the charge transfer dynamics between a silicon quantum dot and an individual phosphorous donor using the conduction through the quantum dot as a probe for the donor ionization state. We use a silicon n-MOSFET (metal oxide field effect transistor) biased near threshold in the SET regime with two side gates to control both the device conductance and the donor charge. Temperature and magnetic field independent tunneling time is measured. We measure the statistics of the transfer of electrons observed when the ground state D0 of the donor is aligned with the SET states.
We propose a method to electrically control electron spins in donor-based qubits in silicon. By taking advantage of the hyperfine coupling difference between a single-donor and a two-donor quantum dot, spin rotation can be driven by inducing an electric dipole between them and applying an alternating electric field generated by in-plane gates. These qubits can be coupled with exchange interaction controlled by top detuning gates. The qubit device can be fabricated deep in the silicon lattice with atomic precision by scanning tunneling probe technique. We have combined a large-scale full band a…
Single donors in semiconductor nanostructures represent a key element to develop spin related quantum functionalities in atomic scale devices. Quantum transport through a single Arsenic donor in the channel of a Silicon nano-field effect transistor under microwave irradiation is investigated. The device is characterized at mK temperatures in the regime of Coulomb-blockade. Photon assisted tunneling and microwave induced electron pumping regimes are revealed respectively at low and high microwave power. At sufficiently high power, the microwave irradiation induces tunneling through the first ex…
We measure a large valley-orbit splitting for shallow isolated phosphorus donors in a silicon gated nanowire. This splitting is close to the bulk value and well above previous reports in silicon nanostructures. It was determined using a double dopant transport spectroscopy which eliminates artifacts induced by the environment. Quantitative simulations taking into account the position of the donors with respect to the Si/SiO$_2$ interface and electric field in the wire show that the values found are consistent with the device geometry.
Single electron transistor (SET) is an advanced tool to exploit in quantum devices. Working of such devices at room-temperature is essential for practical utilization. Dopant based single-electron devices are well studied at low-temperature although a few devices are developed for high-temperature operation with certain limitations. Here, we propose and theoretically exhibit that nitrogen (N) donor in silicon is an important candidate for effective designing of such devices. Theoretical calculation of density-of-states using semi-empirical DFT method indicates that N-donor in silicon has deep …
Donors in silicon can now be positioned with an accuracy of about one lattice constant, making it possible in principle to form donor arrays for quantum computation or quantum simulation applications. However the multi-valley character of the silicon conduction band combines with central cell corrections to the donor state Hamiltonian to translate atomic scale imperfections in donor placement into strongly disordered inter-donor hybridization. We present a simple model that is able to account accurately for central-cell corrections, and use it to assess the impact of donor-placement disorder o…
Deterministic control over the location and number of donors is crucial to donor spin quantum bits (qubits) in semiconductor based quantum computing. In this work, a focused ion beam is used to implant antimony donors close to quantum dots. Ion detectors are integrated next to the quantum dots to sense the implants. The numbers of donors implanted can be counted to a precision of a single ion. In low-temperature transport measurements, regular coulomb blockade is observed from the quantum dots. Charge offsets indicative of donor ionization are also observed in devices with counted donor implan…
We unravel theoretically a key intrinsic relaxation mechanism among the low-lying singlet and triplet donor-pair states in silicon, an important element in the fast-developing field of spintronics and quantum computation. Despite the perceived weak spin-orbit coupling (SOC) in Si, we find that our discovered relaxation mechanism, combined with the electron-phonon and inter-donor interactions, dominantly drives the transitions in the two-electron states over a large range of donor coupling regime. The scaling of the relaxation rate with inter-donor exchange interaction $J$ goes from $J^5$ to $J…
We report low frequency charge noise measurement on silicon substrates with different phosphorus doping densities. The measurements are performed with aluminum single electron transistors (SETs) at millikelvin temperatures where the substrates are in the insulating regime. By measuring the SET Coulomb oscillations, we find a gate voltage dependent charge noise on the more heavily doped substrate. This charge noise, which is seen to have a 1/f spectrum, is attributed to the electric field induced tunneling of electrons from their phosphorus donor potentials.
Selenium impurities in silicon are deep double donors and their optical and electronic properties have been recently investigated due to their application for infrared detection. However, a singly-ionised selenium donor (Se$^{+}$) possesses an electron spin which makes it a potential candidate as a silicon-based spin qubit, with significant potential advantages compared to the more commonly studied group V donors. Here we study the electron spin relaxation ($T_1$) and coherence ($T_2$) times of Se$^{+}$ in isotopically purified 28-silicon, and find them to be up to two orders of magnitude long…
A scaled quantum computer with donor spins in silicon would benefit from a viable semiconductor framework and a strong inherent decoupling of the qubits from the noisy environment. Coupling neighbouring spins via the natural exchange interaction according to current designs requires gate control structures with extremely small length scales. We present a silicon architecture where bismuth donors with long coherence times are coupled to electrons that can shuttle between adjacent quantum dots, thus relaxing the pitch requirements and allowing space between donors for classical control devices. …
Recent experimental efforts have led to considerable interest in donor-based localized electron spins in Si as viable qubits for a scalable silicon quantum computer. With the use of isotopically purified $^{28}$Si and the realization of extremely long spin coherence time in single-donor electrons, the recent experimental focus is on two-coupled donors with the eventual goal of a scaled-up quantum circuit. Motivated by this development, we simulate the statistical distribution of the exchange coupling $J$ between a pair of donors under realistic donor placement straggles, and quantify the error…
By varying the gate and substrate voltage in a short silicon-on-insulator trigate field effect transistor we control the ionization state of three arsenic donors. We obtain a good quantitative agreement between 3D electrostatic simulation and experiment for the control voltage at which the ionization takes place. It allows us observing the three doubly occupied states As- at strong electric field in the presence of nearby source-drain electrodes.
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.
Phosphorus donor impurities in silicon are a promising candidate for solid-state quantum computing due to their exceptionally long coherence times and high fidelities. However, individual addressability of exchange coupled donor qubits with separations ~15nm is challenging. Here we show that by using atomic-precision lithography we can place a single P donor next to a 2P molecule 16(+/-1)nm apart and use their distinctive hyperfine coupling strengths to address qubits at vastly different resonance frequencies. In particular the single donor yields two hyperfine peaks separated by 97(+/-2.5)MHz…
Spectral diffusion arising from $^{29}$Si nuclear spin flip-flops, known to be a primary source of electron spin decoherence in silicon, is also predicted to limit the coherence times of neutral donor nuclear spins in silicon. Here, the impact of this mechanism on $^{31}$P nuclear spin coherence is measured as a function of $^{29}$Si concentration using X-band pulsed electron nuclear double resonance (ENDOR). The $^{31}$P nuclear spin echo decays show that decoherence is controlled by $^{29}$Si flip-flops resulting in both fast (exponential) and slow (non-exponential) spectral diffusion proces…
Nuclear spin registers in the vicinity of electron spins in solid state systems offer a powerful resource to address the challenge of scalability in quantum architectures. We investigate here the properties of $^{29}$Si nuclear spins surrounding donor atoms in silicon, and consider the use of such spins, combined with the donor nuclear spin, as a quantum register coupled to the donor electron spin. We find the coherence of the nearby $^{29}$Si nuclear spins is effectively protected by the presence of the donor electron spin, leading to coherence times in the second timescale - over two orders …
The s manifold energy levels for phosphorus donors in silicon are important input parameters for the design and modelling of electronic devices on the nanoscale. In this paper we calculate these energy levels from first principles using density functional theory. The wavefunction of the donor electron's ground state is found to have a form that is similar to an atomic s orbital, with an effective Bohr radius of 1.8 nm. The corresponding binding energy of this state is found to be 41 meV, which is in good agreement with the currently accepted value of 45.59 meV. We also calculate the energies o…
We investigate the electrical control of the exchange coupling (J) between donor bound electrons in silicon with a detuning gate bias, crucial for the implementation of the two-qubit gate in a silicon quantum computer. We find the asymmetric 2P-1P system provides a highly tunable exchange-curve with mitigated J-oscillation, in which 5 orders of magnitude change in the exchange energy can be achieved using a modest range of electric field for 15 nm qubit separation. Compared to the barrier gate control of exchange in the Kane qubit, the detuning gate design reduces the demanding constraints of …
Two-electron states bound to donors in silicon are important for both two qubit gates and spin readout. We present a full configuration interaction technique in the atomistic tight-binding basis to capture multi-electron exchange and correlation effects taking into account the full bandstructure of silicon and the atomic scale granularity of a nanoscale device. Excited $s$-like states of $A_1$-symmetry are found to strongly influence the charging energy of a negative donor centre. We apply the technique on sub-surface dopants subjected to gate electric fields, and show that bound triplet state…
Electron and nuclear spins of donor ensembles in isotopically pure silicon experience a vacuum-like environment, giving them extraordinary coherence. However, in contrast to a real vacuum, electrons in silicon occupy quantum superpositions of valleys in momentum space. Addressable single-qubit and two-qubit operations in silicon require that qubits are placed near interfaces, modifying the valley degrees of freedom associated with these quantum superpositions and strongly influencing qubit relaxation and exchange processes. Yet to date, spectroscopic measurements only indirectly probe wavefunc…
We report fabrication of transistors in a FinFET geometry using isotopically purified silicon-28 -on-insulator (28-SOI) substrates. Donor electron spin coherence in natural silicon is limited by spectral diffusion due to the residual $^{29}$Si nuclear spin bath, making isotopically enriched nuclear spin-free $^{28}$Si substrates a promising candidate for forming spin quantum bit devices. The FinFET architecture is fully compatible with single-ion implant detection for donor-based qubits, and the donor spin-state readout through electrical detection of spin resonance. We describe device process…
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 Δq > 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 cont…
Electrical detection of spins is an essential tool in understanding the dynamics of spins in semiconductor devices, providing valuable insights for applications ranging from optoelectronics and spintronics to quantum information processing. For electron spins bound to shallow donors in silicon, bulk electrically-detected magnetic resonance has relied on coupling to spin readout partners such as paramagnetic defects or conduction electrons which fundamentally limits spin coherence times. Here we demonstrate electrical detection of phosphorus donor electron spin resonance by transport through a …
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…
Donor impurity spins in silicon-28 are highly competitive qubits for upcoming solid-state quantum technologies, yet a proven scalable strategy for multi-qubit devices remains conspicuously absent. These CMOS-compatible, atomically identical qubits offer significant advantages including 3-hour coherence ($T_2$) lifetimes, as well as simultaneous qubit initialization, manipulation and readout fidelities near $\sim\!99.9\%$. These properties meet the requirements for many modern quantum error correction protocols, which are essential for constructing large-scale universal quantum technologies. Ho…
We demonstrate the possibility of engineering a single donor transistor directly from a phosphorous doped quantum dot by making use of the intrinsic glassy behaviour of the structure as well as the complex electron dynamics during cooldown. Characterisation of the device at low temperatures and in magnetic field shows single donors can be electrostatically isolated near one of the tunnel barrier with either a single or a doubly occupancy. Such a model is well supported by capacitance-based simulations. Ability of using the D0 of such isolated donor as a charge detector is demonstrated by obser…
Shifts from the expected nuclear magnetic resonance frequencies of antimony and bismuth donors in silicon of greater than a megahertz are observed in electrically detected magnetic resonance spectra. Defects created by ion implantation of the donors are discussed as the source of effective electric field gradients generating these shifts via quadrupole interaction with the nuclear spins. The experimental results are modeled quantitatively by molecular orbital theory for a coupled pair consisting of a donor and a spin-dependent recombination readout center.
We construct a model to study the localization properties of nanowires of dopants in silicon (Si) fabricated by precise ionic implantation or STM lithography. Experiments have shown that Ohm's law holds in some cases, in apparent defiance to the Anderson localization theory in one dimension. We investigate how valley interference affects the traditional theory of electronic structure of disordered systems. Each isolated donor orbital is realistically described by multi-valley effective mass theory (MV-EMT). We extend this model to describe chains of donors as a linear combination of dopant orb…
Electric fields can be used to tune donor spins in silicon using the Stark shift, whereby the donor electron wave function is displaced by an electric field, modifying the hyperfine coupling between the electron spin and the donor nuclear spin. We present a technique based on dynamic decoupling of the electron spin to accurately determine the Stark shift, and illustrate this using antimony donors in isotopically purified silicon-28. We then demonstrate two different methods to use a DC electric field combined with an applied resonant radio-frequency (RF) field to conditionally control donor nu…
We provide here a roadmap for modeling silicon nano-devices with one or two group V donors (D). We discuss systems containing one or two electrons, that is, D^0, D^-, D_2^+ and D_2^0 centers. The impact of different levels of approximation is discussed. The most accurate instances -- for which we provide quantitative results -- are within multivalley effective mass including the central cell correction and a configuration interaction account of the electron-electron correlations. We also derive insightful, yet less accurate, analytical approximations and discuss their validity and limitations …
The influence of the electric field created by a gate potential of the silicon quantum computer on the hyperfine interaction constant (HIC) is obtained. The errors due to technological inaccuracy of location of donor atoms under a gate are evaluated. The energy spectra of electron-nuclear spin system of two interacting donor atoms with various values of HIC are calculated. The presence of two pairs of anticrossing levels in the ground electronic state is shown. Parameters of the structure at which errors rate can be greatly minimized are found.
Using the effective mass theory and the multi-valley envelope function representation, we have developed a theoretical framework for computing the single-electron electronic structure of several phosphorus donors interacting in an arbitrary geometrical configuration in silicon taking into account the valley-orbit coupling. The methodology is applied to three coupled phosphorus donors, arranged in a linear chain and in a triangle, and to six donors arranged in a regular hexagon. The results of the simulations evidence that the valley composition of the single-electron states strongly depends on…
We present atomistic simulations of the D0 to D- charging energies of a gated donor in silicon as a function of applied fields and donor depths and find good agreement with experimental measure- ments. A self-consistent field large-scale tight-binding method is used to compute the D- binding energies with a domain of over 1.4 million atoms, taking into account the full bandstructure of the host, applied fields, and interfaces. An applied field pulls the loosely bound D- electron towards the interface and reduces the charging energy significantly below the bulk values. This enables formation of…
We experimentally study the coupling of Group V donor spins in silicon to mechanical strain, and measure strain-induced frequency shifts which are linear in strain, in contrast to the quadratic dependence predicted by the valley repopulation model (VRM), and therefore orders of magnitude greater than that predicted by the VRM for small strains $|\varepsilon| < 10^{-5}$. Through both tight-binding and first principles calculations we find that these shifts arise from a linear tuning of the donor hyperfine interaction term by the hydrostatic component of strain and achieve semi-quantitative agre…
Donor spin in silicon have achieved record values of coherence times and single-qubit gate fidelities. The next stage of development involves demonstrating high-fidelity two-qubit logic gates, where the most natural coupling is the exchange interaction. To aid the efficient design of scalable donor-based quantum processors, we model the two-electron wave function using a full configuration interaction method within a multi-valley effective mass theory. We exploit the high computational efficiency of our code to investigate the exchange interaction, valley population, and electron densities for…
For donor nuclear spins in silicon, we show how to deterministically prepare various symmetric and asymmetric Dicke states which span a complete basis of the many-body Hilbert space. The state preparation is realized by cooperative pumping of nuclear spins by coupled donor electrons, and the required controls are in situ to the prototype Kane proposal for quantum computation. This scheme only requires a sub-gigahertz donor exchange coupling which can be readily achieved without atomically precise donor placement, hence it offers a practical way to prepare multipartite entanglement of spins in …
The electronic structure of the three-particle donor bound exciton (D$^0$X) in silicon is computed using a large-scale atomic orbital tight-binding method within the Hartree approximation. The calculations yield a transition energy close to the experimentally measured value of 1150 meV in bulk, and show how the transition energy and transition probability can change with applied fields and proximity to surfaces, mimicking the conditions of realistic devices. The spin-resolved transition energy from a neutral donor state (D$^0$) to D$^0$X depends on the three-particle Coulomb energy, and the in…
Gate control of donor electrons near interfaces is a generic ingredient of donor-based quantum computing. Here, we address the question: how is the phonon-assisted qubit relaxation time $T_1$ affected as the electron is shuttled between the donor and the interface? We focus on the example of the `flip-flop qubit' [Tosi et al., arXiv:1509.08538v1], defined as a combination of the nuclear and electronic states of a phosphorous donor in silicon, promising fast electrical control and long dephasing times when the electron is halfway between the donor and the interface. We theoretically describe or…
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…
We propose a novel optical and electrical hybrid scheme for the measurement of nuclear spin qubits in silicon. By combining the environmental insensitivity of the integer quantum Hall effect with the optically distinguishable hyperfine states of phosphorus impurities in silicon, our system can simultaneously offer nuclear spin measurement and robustness against environmental defects. 31P donor spins in isotopically purified 28Si are often discussed as very promising quantum memory qubits due to their extremely long decoherence times, and our proposed device offers an effective implementation f…
Donors in silicon, conceptually described as hydrogen atom analogues in a semiconductor environment, have become a key ingredient of many "More-than-Moore" proposals such as quantum information processing [1-5] and single-dopant electronics [6, 7]. The level of maturity this field has reached has enabled the fabrication and demonstration of transistors that base their functionality on a single impurity atom [8, 9] allowing the predicted single-donor energy spectrum to be checked by an electrical transport measurement. Generalizing the concept, a donor pair may behave as a hydrogen molecule ana…
Strain is extensively used to controllably tailor the electronic properties of materials. In the context of indirect band-gap semiconductors such as silicon, strain lifts the valley degeneracy of the six conduction band minima, and by extension the valley states of electrons bound to phosphorus donors. Here, single phosphorus atoms are embedded in an engineered thin layer of silicon strained to 0.8% and their wave function imaged using spatially resolved spectroscopy. A prevalence of the out-of-plane valleys is confirmed from the real-space images, and a combination of theoretical modelling to…
We compare charge transitions on a deterministic single P donor in silicon using radio frequency reflectometry measurements with a tunnel coupled reservoir and DC charge sensing using a capacitively coupled single electron transistor (SET). By measuring the conductance through the SET and comparing this with the phase shift of the reflected RF excitation from the reservoir, we can discriminate between charge transfer within the SET channel and tunneling between the donor and reservoir. The RF measurement allows observation of donor electron transitions at every charge degeneracy point in contr…
Gate control of phosphorus donor based charge qubits in Si is investigated using a tight-binding approach. Excited molecular states of P2+ are found to impose limits on the allowed donor separations and operating gate voltages. The effects of surface (S) and barrier (B) gates are analyzed in various voltage regimes with respect to the quantum confined states of the whole device. Effects such as interface ionization, saturation of the tunnel coupling, sensitivity to donor and gate placement are also studied. It is found that realistic gate control is smooth for any donor separation, although at…
Donors in silicon are now demonstrated as one of the leading candidates for implementing qubits and quantum information processing. Single qubit operations, measurements and long coherence times are firmly established, but progress on controlling two qubit interactions has been slower. One reason for this is that the inter donor exchange coupling has been predicted to oscillate with separation, making it hard to estimate in device designs. We present a multivalley effective mass theory of a donor pair in silicon, including both a central cell potential and the effective mass anisotropy intrins…
Excited states of a single donor in bulk silicon have previously been studied extensively based on effective mass theory. However, a proper theoretical description of the excited states of a donor cluster is still scarce. Here we study the excitations of lines of defects within a single-valley spherical band approximation, thus mapping the problem to a scaled hydrogen atom array. A series of detailed full configuration-interaction and time-dependent hybrid density-functional theory calculations have been performed to understand linear clusters of up to 10 donors. Our studies illustrate the gen…
Arrays of dopants in silicon are promising platforms for the quantum simulation of the Fermi-Hubbard model. We show that the simplest model with only on-site interaction is insufficient to describe the physics of an array of phosphorous donors in silicon due to the strong intersite interaction in the system. We also study the resonant tunneling transport in the array at low temperature as a mean of probing the features of the Hubbard physics, such as the Hubbard bands and the Mott gap. Two mechanisms of localization which suppresses transport in the array are investigated: The first arises fro…
Opto-Electrical Detection of Donor Bound Excitons in Silicon-on-Insulator Substrate
University of Jyväskylä（于韦斯屈莱大学）；QuTech（奎泰克）；Netherlands Organisation for Applied Scientific Research (TNO)（荷兰应用科学研究组织）；Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学卡弗里纳米科学研究所）
We present Auger-electron-detected magnetic resonance (AEDMR) experiments on phosphorus donors in silicon, where the selective optical generation of donor-bound excitons is used for the electrical detection of the electron spin state. Because of the long dephasing times of the electron spins in isotopically purified $^{28}$Si, weak microwave fields are sufficient, which allow to realize broadband AEDMR in a commercial ESR resonator. Implementing Auger-electron-detected ENDOR, we further demonstrate the optically-assisted control of the nuclear spin under conditions where the hyperfine splittin…
Substitutional donor atoms in silicon are promising qubits for quantum computation with extremely long relaxation and dephasing times demonstrated. One of the critical challenges of scaling these systems is determining inter-donor distances to achieve controllable wavefunction overlap while at the same time performing high fidelity spin readout on each qubit. Here we achieve such a device by means of scanning tunnelling microscopy lithography. We measure anti-correlated spin states between two donor-based spin qubits in silicon separated by 16${\pm}1$ nm. By utilizing an asymmetric system with…
We report electrically detected magnetic resonance of phosphorus donors in a silicon field-effect transistor. An on-chip transmission line is used to generate the oscillating magnetic field allowing broadband operation. At milli-kelvin temperatures, continuous wave spectra were obtained up to 40 GHz, using both magnetic field and microwave frequency modulation. The spectra reveal the hyperfine-split electron spin resonances characteristic for Si:P and a central feature which displays the fingerprint of spin-spin scattering in the two-dimensional electron gas.
We present two strategies for performing two-qubit operations on the electron spins of an exchange-coupled pair of phosphorus donors in silicon, using the ability to set the donor nuclear spins in arbitrary states. The effective magnetic detuning of the two electron qubits is provided by the hyperfine interaction when the $^{31}$P nuclei are prepared in opposite spin states. This can be exploited to switch on and off SWAP operations with modest tuning of the electron exchange interaction. Furthermore, the hyperfine detuning enables high-fidelity conditional rotation gates based on selective re…
