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 spinzero 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][7][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.It is well known that the Si/SiO 2 interface hosts a variety of defects that act as charge and spin fluctuators. Spin resonance experiments have documented the deleterious effects of the Si/SiO 2 interface on the coherence of donors in 28 Si, implanted at different depths [10]. Theoretical models suggest that magnetic fluctuation from paramagnetic spins at the interface cause the decohering noise [4], and recent work advocates the use of 'clock transitions' in 209 Bi donors [11] to obtain a spin qubit that is to first-order insensitive to magnetic noise. Fluctuations of interface charges or gate voltages can also cause decoherence, if there is a physical mechanism for electric fields to couple to the spin qubit states. Evidence of such effects was found for instance in carbon nanotube valley-spin qubits [12]. For donors in silicon, fluctuating electric fields can couple to the spin states by modulating the hyperfine coupling [13, 14] or the g-factor [15]. Here we operate single-atom spin qubits in isotopically purified 28 Si, with a residual 29 Si concentration of 800 ppm. Minimizing the effect 29 Si nuclear spin fluctuations allowed us not only to set new benchmarks for qubit performance in solid state, but also to uncover the microscopic origin of residual decoherence mechanisms, specific to a gated nanostructure.A substitutional P atom in Si behaves to a good approximation like hydrogen in vacuum, with energy levels renormalized by the effective mass and the dielectric constant of the host material [16]. Both the bound electron (e − ) and the nucleus ( 31 P) possess a spin 1/2 and constitute natural qubits with simple spin up/down eigenstates, which we denote ...

Control of individual spin qubits through local electric fields, suitable for large-scale silicon quantum computers.

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

We present two strategies for performing two-qubit operations on the electron spins of an exchange-coupled pair of 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 two 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 resonant excitation. The latter requires no dynamic tuning of the exchange interaction at all, and offers a very attractive scheme to implement two-qubit logic gates under realistic experimental conditions.

State of the art qubit systems are reaching the gate fidelities required for scalable quantum computation architectures. Further improvements in the fidelity of quantum gates demands characterization and benchmarking protocols that are efficient, reliable and extremely accurate. Ideally, a benchmarking protocol should also provide information on how to rectify residual errors. Gate set tomography (GST) is one such protocol designed to give detailed characterization of as-built qubits. We implemented GST on a high-fidelity electron-spin qubit confined by a single 31 P atom in 28 Si. The results reveal systematic errors that a randomized benchmarking analysis could measure but not identify, whereas GST indicated the need for improved calibration of the length of the control pulses. After introducing this modification, we measured a new benchmark average gate fidelity of ( ) 99.942 8 %, an improvement on the previous value of ( ) 99.90 2 %. Furthermore, GST revealed high levels of non-Markovian noise in the system, which will need to be understood and addressed when the qubit is used within a fault-tolerant quantum computation scheme.

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.

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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.