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

Nuclear spins were among the first physical platforms to be considered for quantum information processing1,2, because of their exceptional quantum coherence3 and atomic-scale footprint. However, their full potential for quantum computing has not yet been realized, owing to the lack of methods with which to link nuclear qubits within a scalable device combined with multi-qubit operations with sufficient fidelity to sustain fault-tolerant quantum computation. Here we demonstrate universal quantum logic operations using a pair of ion-implanted 31P donor nuclei in a silicon nanoelectronic device. A nuclear two-qubit controlled-Z gate is obtained by imparting a geometric phase to a shared electron spin4, and used to prepare entangled Bell states with fidelities up to 94.2(2.7)%. The quantum operations are precisely characterized using gate set tomography (GST)5, yielding one-qubit average gate fidelities up to 99.95(2)%, two-qubit average gate fidelity of 99.37(11)% and two-qubit preparation/measurement fidelities of 98.95(4)%. These three metrics indicate that nuclear spins in silicon are approaching the performance demanded in fault-tolerant quantum processors6. We then demonstrate entanglement between the two nuclei and the shared electron by producing a Greenberger-Horne-Zeilinger three-qubit state with 92.5(1.0)% fidelity. Because electron spin qubits in semiconductors can be further coupled to other electrons7-9 or physically shuttled across different locations10,11, these results establish a viable route for scalable quantum information processing using donor nuclear and electron spins.

High-fidelity readout and control of a nuclear spin qubit in silicon.

Detection of nuclear spin precession is critical for a wide range of scientific techniques that have applications in diverse fields including analytical chemistry, materials science, medicine and biology. Fundamentally, it is possible because of the extreme isolation of nuclear spins from their environment. This isolation also makes single nuclear spins desirable for quantum-information processing, as shown by pioneering studies on nitrogen-vacancy centres in diamond. The nuclear spin of a (31)P donor in silicon is very promising as a quantum bit: bulk measurements indicate that it has excellent coherence times and silicon is the dominant material in the microelectronics industry. Here we demonstrate electrical detection and coherent manipulation of a single (31)P nuclear spin qubit with sufficiently high fidelities for fault-tolerant quantum computing. By integrating single-shot readout of the electron spin with on-chip electron spin resonance, we demonstrate quantum non-demolition and electrical single-shot readout of the nuclear spin with a readout fidelity higher than 99.8 percent-the highest so far reported for any solid-state qubit. The single nuclear spin is then operated as a qubit by applying coherent radio-frequency pulses. For an ionized (31)P donor, we find a nuclear spin coherence time of 60 milliseconds and a one-qubit gate control fidelity exceeding 98 percent. 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.

A single-atom electron spin qubit in silicon.

A single atom is the prototypical quantum system, and a natural candidate for a quantum bit, or qubit--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 nitrogen-vacancy-centre point defect. Solid-state electrical devices possess great potential to scale up such demonstrations from few-qubit control to larger-scale quantum processors. Coherent control of spin qubits has been achieved in lithographically defined double quantum dots in both GaAs (refs 3-5) and Si (ref. 6). However, it is a formidable challenge to combine the electrical measurement capabilities of engineered nanostructures with the benefits inherent in 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 read-out. We use electron spin resonance to drive Rabi oscillations, and a Hahn echo pulse sequence reveals a spin coherence time exceeding 200 µs. This time should be even longer in isotopically enriched (28)Si samples. Combined with a device architecture that is compatible with modern integrated circuit technology, the electron spin of a single phosphorus atom in silicon should be an excellent platform on which to build a scalable quantum computer.

Single-shot readout of an electron spin in silicon.

The size of silicon transistors used in microelectronic devices is shrinking to the level at which quantum effects become important. Although 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 silicon can represent a well-isolated quantum bit with long coherence times because of the weak spin-orbit coupling and the possibility of eliminating nuclear spins from the bulk crystal. However, the control of single electrons in silicon has proved challenging, and so far the observation and manipulation of a single spin has been impossible. Here we report the demonstration of single-shot, time-resolved readout of an electron spin in silicon. 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 of ∼6 seconds at a magnetic field of 1.5 tesla, and achieved a spin readout fidelity better than 90 per cent. High-fidelity single-shot spin readout in silicon opens the way to the development of a new generation of quantum computing and spintronic devices, built using the most important material in the semiconductor industry.

Single-shot readout and relaxation of singlet and triplet states in exchange-coupled 31P electron spins in silicon.

We present the experimental observation of a large exchange coupling J ≈ 300 µeV 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) ≈ 4 ms at zero magnetic field agrees with the theoretical prediction for J-coupled 31P dimers in silicon. The time evolution of the two-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 two-qubit quantum logic gates with spins in silicon and highlight the necessity to adopt gating schemes compatible with weak J-coupling strengths.

Coherent control of a single ²9Si nuclear spin qubit.

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 semiconductor materials, the spin-bearing nuclei are sufficiently rare that it is possible to identify and control individual host nuclear spins. This Letter presents the first experimental detection and manipulation of a single ²9Si nuclear spin. The quantum nondemolition single-shot readout of the spin is demonstrated, and a Hahn echo measurement reveals a coherence time of T2=6.3(7) ms­in excellent agreement with bulk experiments. Atomistic modeling combined with extracted experimental parameters provides possible lattice sites for the ²9Si atom under investigation. These results demonstrate that single ²9Si nuclear spins could serve as a valuable resource in a silicon spin-based quantum computer.

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

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

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

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

Deterministic Shallow Dopant Implantation in Silicon with Detection Confidence Upper-Bound to 99.85% by Ion-Solid Interactions.

Silicon chips containing arrays of single dopant atoms can be the material of choice for classical and quantum devices that exploit single donor spins. For example, group-V donors implanted in isotopically purified 28 Si crystals are attractive for large-scale quantum computers. Useful attributes include long nuclear and electron spin lifetimes of 31 P, hyperfine clock transitions in 209 Bi or electrically controllable 123 Sb nuclear spins. Promising architectures require the ability to fabricate arrays of individual near-surface dopant atoms with high yield. Here, an on-chip detector electrode system with 70 eV root-mean-square noise (≈20 electrons) is employed to demonstrate near-room-temperature implantation of single 14 keV 31 P+ ions. The physics model for the ion-solid interaction shows an unprecedented upper-bound single-ion-detection confidence of 99.85 ± 0.02% for near-surface implants. As a result, the practical controlled silicon doping yield is limited by materials engineering factors including surface gate oxides in which detected ions may stop. For a device with 6 nm gate oxide and 14 keV 31 P+ implants, a yield limit of 98.1% is demonstrated. Thinner gate oxides allow this limit to converge to the upper-bound. Deterministic single-ion implantation can therefore be a viable materials engineering strategy for scalable dopant architectures in silicon devices.

Transport spectroscopy of single phosphorus donors in a silicon nanoscale transistor.

We have developed nanoscale 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.

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

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

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

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

A dressed spin qubit in silicon.

Coherent dressing of a quantum two-level system provides access to a new quantum system with improved properties-a different and easily tunable 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 assess its potential as a 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, frequency modulation of the driving field or a simple detuning pulse. We measure coherence times of and , one order of magnitude longer than those of the undressed spin. Furthermore, the use of the dressed states enables coherent coupling of the solid-state spins to electric fields and mechanical oscillations.

Coherent population trapping in diamond N-V centers at zero magnetic field.

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.

GEANT4 models for the secondary radiation flux in the collimation system of a 300MeV proton microbeam.

In Harbin, we are developing a 300MeV proton microbeam for many applications in space science including upset studies in microelectronic devices, radiation hardness of materials for satellites and radiation effects in human tissues. There are also applications of this facility proposed for proton therapy. The microbeam system will employ a purpose-built proton synchrotron to provide the beam. However there are many challenges to be addressed in the design, construction and operation of this facility. Here we address two important design aspects for which we apply GEANT4 modeling. First, the high energy proton beam interacts strongly with beam line materials, especially the collimation slits, to produce showers of secondary particles which could introduce significant background signals and degrade the resolution of the proton microbeam. Second, the beam transport within the residual vacuum of the beam line may also introduce undesirable background radiation. In both cases mitigation strategies need to be incorporated during the design phase of the new system. We study the use of a dipole magnet following the aperture collimator to reduce the flux of secondary particles incident on the analysis chamber. Monte Carlo simulations are performed using GEANT4 and SRIM. By inserting the dipole magnet, we find as expected a significant reduction in the scattering of protons and other particles, such as neutrons and gamma rays, at the collimation system exit position. Secondary radiation from the residual gas pressure within the beam line vacuum system are also modelled and found to be negligible under the standard operating conditions.

Bell's inequality violation with spins in silicon.

Bell's theorem proves 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, and provides a single-number benchmark for the performance of devices that use such states for quantum computing. We demonstrate a Bell/ Clauser-Horne-Shimony-Holt inequality violation with Bell signals up to 2.70(9), using the electron and the nuclear spins of a single phosphorus atom embedded in a silicon nanoelectronic device. Two-qubit state tomography 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 highlight the important function of the nuclear qubit to expand the computational basis and maximize the readout fidelity.

Electrically controlling single-spin qubits in a continuous microwave field.

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 (31)P 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.

Storing quantum information for 30 seconds in a nanoelectronic device.

The spin of an electron or a nucleus in a semiconductor naturally implements the unit of quantum information--the qubit. In addition, because semiconductors are currently used in the electronics industry, developing qubits in semiconductors would be a promising route to realize scalable quantum information devices. The solid-state environment, however, may provide deleterious interactions between the qubit and the nuclear spins of surrounding atoms, or charge and spin fluctuations arising from defects in oxides and interfaces. For materials such as silicon, enrichment of the spin-zero (28)Si isotope drastically reduces spin-bath decoherence. Experiments on bulk spin ensembles in (28)Si crystals have indeed demonstrated extraordinary coherence times. 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. The (31)P nuclear spin sets the new benchmark coherence time (>30 s with Carr-Purcell-Meiboom-Gill (CPMG) sequence) of any single qubit in the solid state and reaches >99.99% control fidelity. The electron spin CPMG coherence time exceeds 0.5 s, and detailed noise spectroscopy indicates that--contrary to widespread belief--it is not limited by the proximity to an interface. Instead, decoherence is probably dominated by thermal and magnetic noise external to the device, and is thus amenable to further improvement.