Quantum error correction in a solid-state hybrid spin register.

Error correction is important in classical and quantum computation. Decoherence caused by the inevitable interaction of quantum bits with their environment leads to dephasing or even relaxation. Correction of the concomitant errors is therefore a fundamental requirement for scalable quantum computation. Although algorithms for error correction have been known for some time, experimental realizations are scarce. Here we show quantum error correction in a heterogeneous, solid-state spin system. We demonstrate that joint initialization, projective readout and fast local and non-local gate operations can all be achieved in diamond spin systems, even under ambient conditions. High-fidelity initialization of a whole spin register (99 per cent) and single-shot readout of multiple individual nuclear spins are achieved by using the ancillary electron spin of a nitrogen-vacancy defect. Implementation of a novel non-local gate generic to our electron-nuclear quantum register allows the preparation of entangled states of three nuclear spins, with fidelities exceeding 85 per cent. With these techniques, we demonstrate three-qubit phase-flip error correction. Using optimal control, all of the above operations achieve fidelities approaching those needed for fault-tolerant quantum operation, thus paving the way to large-scale quantum computation. Besides their use with diamond spin systems, our techniques can be used to improve scaling of quantum networks relying on phosphorus in silicon, quantum dots, silicon carbide or rare-earth ions in solids.

Solid-state electron spin lifetime limited by phononic vacuum modes.

Longitudinal relaxation is the process by which an excited spin ensemble decays into its thermal equilibrium with the environment. In solid-state spin systems, relaxation into the phonon bath usually dominates over the coupling to the electromagnetic vacuum1-9. In the quantum limit, the spin lifetime is determined by phononic vacuum fluctuations 10 . However, this limit was not observed in previous studies due to thermal phonon contributions11-13 or phonon-bottleneck processes10, 14,15. Here we use a dispersive detection scheme16,17 based on cavity quantum electrodynamics18-21 to observe this quantum limit of spin relaxation of the negatively charged nitrogen vacancy (NV-) centre 22 in diamond. Diamond possesses high thermal conductivity even at low temperatures 23 , which eliminates phonon-bottleneck processes. We observe exceptionally long longitudinal relaxation times T1 of up to 8 h. To understand the fundamental mechanism of spin-phonon coupling in this system we develop a theoretical model and calculate the relaxation time ab initio. The calculations confirm that the low phononic density of states at the NV- transition frequency enables the spin polarization to survive over macroscopic timescales.

Critical Thermalization of a Disordered Dipolar Spin System in Diamond.

Statistical mechanics underlies our understanding of macroscopic quantum systems. It is based on the assumption that out-of-equilibrium systems rapidly approach their equilibrium states, forgetting any information about their microscopic initial conditions. This fundamental paradigm is challenged by disordered systems, in which a slowdown or even absence of thermalization is expected. We report the observation of critical thermalization in a three dimensional ensemble of ∼10^{6} electronic spins coupled via dipolar interactions. By controlling the spin states of nitrogen vacancy color centers in diamond, we observe slow, subexponential relaxation dynamics and identify a regime of power-law decay with disorder-dependent exponents; this behavior is modified at late times owing to many-body interactions. These observations are quantitatively explained by a resonance counting theory that incorporates the effects of both disorder and interactions.

Indistinguishable photons from separated silicon-vacancy centers in diamond.

We demonstrate that silicon-vacancy (SiV) centers in diamond can be used to efficiently generate coherent optical photons with excellent spectral properties. We show that these features are due to the inversion symmetry associated with SiV centers. The generation of indistinguishable single photons from separated emitters at 5 K is demonstrated in a Hong-Ou-Mandel interference experiment. Prospects for realizing efficient quantum network nodes using SiV centers are discussed.

Experimental implementation of assisted quantum adiabatic passage in a single spin.

Quantum adiabatic passages can be greatly accelerated by a suitable control field, called a counter-diabatic field, which varies during the scan through resonance. Here, we implement this technique on the electron spin of a single nitrogen-vacancy center in diamond. We demonstrate two versions of this scheme. The first follows closely the procedure originally proposed by Demirplak and Rice [J. Phys. Chem. A 107, 9937 (2003)]. In the second scheme, we use a control field whose amplitude is constant but whose phase varies with time. This version, which we call the rapid-scan approach, allows an even faster passage through resonance and therefore makes it applicable also for systems with shorter decoherence times.

Detecting and polarizing nuclear spins with double resonance on a single electron spin.

We report the detection and polarization of nuclear spins in diamond at room temperature by using a single nitrogen-vacancy (NV) center. We use Hartmann-Hahn double resonance to coherently enhance the signal from a single nuclear spin while decoupling from the noisy spin bath, which otherwise limits the detection sensitivity. As a proof of principle, we (i) observe coherent oscillations between the NV center and a weakly coupled nuclear spin and (ii) demonstrate nuclear-bath cooling, which prolongs the coherence time of the NV sensor by more than a factor of 5. Our results provide a route to nanometer scale magnetic resonance imaging and novel quantum information processing protocols.

Negative-U system of carbon vacancy in 4H-SiC.

Using electron paramagnetic resonance (EPR), energy levels of the carbon vacancy (V(C)) in 4H-SiC and its negative-U properties have been determined. Combining EPR and deep-level transient spectroscopy we show that the two most common defects in as-grown 4H-SiC--the Z(1/2) lifetime-limiting defect and the EH(7) deep defect--are related to the double acceptor (2-|0) and single donor (0|+) levels of V(C), respectively.

Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble.

We report the experimental realization of a hybrid quantum circuit combining a superconducting qubit and an ensemble of electronic spins. The qubit, of the transmon type, is coherently coupled to the spin ensemble consisting of nitrogen-vacancy centers in a diamond crystal via a frequency-tunable superconducting resonator acting as a quantum bus. Using this circuit, we prepare a superposition of the qubit states that we store into collective excitations of the spin ensemble and retrieve back into the qubit later on. These results constitute a proof of concept of spin-ensemble based quantum memory for superconducting qubits.

Multiple intrinsically identical single-photon emitters in the solid state.

Emitters of indistinguishable single photons are crucial for the growing field of quantum technologies. To realize scalability and increase the complexity of quantum optics technologies, multiple independent yet identical single-photon emitters are required. However, typical solid-state single-photon sources are inherently dissimilar, necessitating the use of electrical feedback or optical cavities to improve spectral overlap between distinct emitters. Here we demonstrate bright silicon vacancy (SiV(-)) centres in low-strain bulk diamond, which show spectral overlap of up to 91% and nearly transform-limited excitation linewidths. This is the first time that distinct single-photon emitters in the solid state have shown intrinsically identical spectral properties. Our results have impact on the application of single-photon sources for quantum optics and cryptography.

Nuclear magnetic resonance spectroscopy with single spin sensitivity.

Nuclear magnetic resonance spectroscopy and magnetic resonance imaging at the ultimate sensitivity limit of single molecules or single nuclear spins requires fundamentally new detection strategies. The strong coupling regime, when interaction between sensor and sample spins dominates all other interactions, is one such strategy. In this regime, classically forbidden detection of completely unpolarized nuclei is allowed, going beyond statistical fluctuations in magnetization. Here we realize strong coupling between an atomic (nitrogen-vacancy) sensor and sample nuclei to perform nuclear magnetic resonance on four (29)Si spins. We exploit the field gradient created by the diamond atomic sensor, in concert with compressed sensing, to realize imaging protocols, enabling individual nuclei to be located with Angstrom precision. The achieved signal-to-noise ratio under ambient conditions allows single nuclear spin sensitivity to be achieved within seconds.

Identification of the carbon antisite-vacancy pair in 4H-SiC.

The metastability of vacancies was theoretically predicted for several compound semiconductors alongside their transformation into the antisite-vacancy pair counterpart; however, no experiment to date has unambiguously confirmed the existence of antisite-vacancy pairs. Using electron paramagnetic resonance and first principles calculations we identify the S15 center as the carbon antisite-vacancy pair in the negative charge state (C(Si)V-(C)) in 4H-SiC. We suggest that this defect is a strong carrier-compensating center in n-type or high-purity semi-insulating SiC.