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.

Present-day implementations of quantum information processing rely on two widely different types of quantum bits (qubits). On the one hand, microscopic systems such as atoms or spins are naturally well decoupled from their environment and as such can reach extremely long coherence times [1,2]; on the other hand, more macroscopic objects such as superconducting circuits are strongly coupled to electromagnetic fields, making them easy to entangle [3,4] although with shorter coherence times [5,6]. It thus seems appealing to combine the two types of systems in hybrid structures that could possibly take the best of both worlds. Here we report the first experimental realization of a hybrid quantum circuit in which a superconducting qubit of the transmon type [5,7] is coherently coupled to a spin ensemble consisting of nitrogen-vacancy (NV) centers in a diamond crystal [8] via a frequency-tunable superconducting resonator [9] acting as a quantum bus. Using this circuit, we prepare arbitrary superpositions of the qubit states that we store into collective excitations of the spin ensemble and retrieve back later on into the qubit. We demonstrate that this process preserves quantum coherence by performing quantum state tomography of the qubit. These results constitute a first proof of concept of spin-ensemble based quantum memory for superconducting qubits [10][11][12]. As a landmark of the successful marriage between a superconducting qubit and electronic spins, we detect with the qubit the hyperfine structure of the NV center.Superconducting qubits have been successfully coupled to electromagnetic [13] as well as mechanical [14] resonators; but coupling them to microscopic systems in a controlled way has up to now remained an elusive perspective -even though qubits sometimes turn out to be coupled to unknown and uncontrolled microscopic degrees of freedom with relatively short coherence times [15]. Whereas the coupling constant g of one individual microscopic system to a superconducting circuit is usually too weak for quantum information applications, ensembles of N such systems are coupled with a constant g √ N enhanced by collective effects.This makes possible to reach a regime of strong coupling between one collective variable of the ensemble and the circuit. This collective variable, which behaves in the low excitation limit as a harmonic oscillator, has been proposed [10-12] as a quantum memory for storing the state of superconducting qubits. Experimentally, the strong coupling between an ensemble of electronic spins and a superconducting resonator has been demonstrated 2 spectroscopically [16][17][18], and the storage of a microwave field into collective excitations of a spin ensemble has been observed very recently [19,20]. These experiments were however carried out in a classical regime since the resonator and spin ensemble behaved as two coupled harmonic oscillators driven by large microwave fields. In the perspective of building a quantum memory, it is instead necessary to perform experiments at the level of a...

Spin defects in silicon carbide have exceptional electron spin coherence with a nearinfrared spin-photon interface in a material amenable to modern semiconductor fabrication. Leveraging these advantages, we successfully integrate highly coherent single neutral divacancy spins in commercially available p-i-n structures and fabricate diodes to modulate the local electrical environment of the defects. These devices enable deterministic charge state control and broad Stark shift tuning exceeding 850 GHz. Surprisingly, we show that charge depletion results in a narrowing of the optical linewidths by over 50 fold, approaching the lifetime limit. These results demonstrate a method for mitigating the ubiquitous problem of spectral diffusion in solid-state emitters by engineering the electrical environment while utilizing classical semiconductor devices to control scalable spin-based quantum systems.

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.

International audienceA quantum memory at microwave frequencies, able to store the state of multiple superconducting qubits for long times, is a key element for quantum information processing. Electronic and nuclear spins are natural candidates for the storage medium as their coherence time can be well above 1 s. Benefiting from these long coherence times requires one to apply the refocusing techniques used in magnetic resonance, a major challenge in the context of hybrid quantum circuits. Here, we report the first implementation of such a scheme, using ensembles of nitrogen-vacancy centers in diamond coupled to a superconducting resonator, in a setup compatible with superconducting qubit technology. We implement the active reset of the nitrogen-vacancy spins into their ground state by optical pumping and their refocusing by Hahn-echo sequences. This enables the storage of multiple microwave pulses at the picowatt level and their retrieval after up to 35 μs, a 3 orders of magnitude improvement compared to previous experiments