Quantum registers of nuclear spins coupled to electron spins of individual solid-state defects are a promising platform for quantum information processing [1][2][3][4][5][6][7][8][9][10][11][12][13]. Pioneering experiments selected defects with favourably located nuclear spins having particularly strong hyperfine couplings [4][5][6][7][8][9][10]. For progress towards large-scale applications, larger and deterministically available nuclear registers are highly desirable. Here we realize universal control over multi-qubit spin registers by harnessing abundant weakly coupled nuclear spins. We use the electron spin of a nitrogen-vacancy centre in diamond to selectively initialize, control and read out carbon-13 spins in the surrounding spin bath and construct high-fidelity single-and two-qubit gates. We exploit these new capabilities to implement a three-qubit quantum-error-correction protocol [14][15][16][17] and demonstrate the robustness of the encoded state against applied errors. These results transform weakly coupled nuclear spins from a source of decoherence into a reliable resource, paving the way towards extended quantum networks and surface-code quantum computing based on multi-qubit nodes [11,18,19].Electron and nuclear spins associated with defects in solids provide natural hybrid quantum registers [3][4][5][6][7][8][9][10][11]. Fullycontrolled registers of multiple spins hold great promise as building blocks for quantum networks [18] and fault-tolerant quantum computing [19]. The defect electron spin enables initialization and readout of the register and coupling to other (distant) electron spins [11,18], whereas the nuclear spins provide well-isolated qubits and memories with long coherence times [8,9,11]. Previous experiments relied on selected defects having nuclear spins with strong hyperfine couplings that exceed the inverse of the electron spin dephasing time (1/T * 2 ). With these strongly coupled spins, singleshot readout [9,10,[20][21][22] and entanglement [9,11] were demonstrated. However, the number of strongly coupled spins varies per defect and is intrinsically limited, so that universal control has so far been restricted to two-qubit registers [4,7] and the required control of multi-qubit registers has remained an open challenge.Here we overcome this challenge by demonstrating universal control of weakly coupled nuclear spins (unresolved hyperfine coupling 1/T * 2 ). We use the electron spin of single nitrogen-vacancy (NV) centres in room-temperature diamond to selectively control multiple carbon-13 ( 13 C) nuclear spins in the surrounding spin bath (Fig. 1a). With this new level of control we realize multi-qubit registers by constructing high-fidelity unconditional and electroncontrolled gates, implementing initialization and readout, and creating nuclear-nuclear entangling gates through the electron spin. Finally, we demonstrate the power of this approach by implementing the first quantum-error-correction protocol with individual solid-state spins.We have used dynamical decoupling spect...

We experimentally isolate, characterize, and coherently control up to six individual nuclear spins that are weakly coupled to an electron spin in diamond. Our method employs multipulse sequences on the electron spin that resonantly amplify the interaction with a selected nuclear spin and at the same time dynamically suppress decoherence caused by the rest of the spin bath. We are able to address nuclear spins with interaction strengths that are an order of magnitude smaller than the electron spin dephasing rate. Our results provide a route towards tomography with single-nuclear-spin sensitivity and greatly extend the number of available quantum bits for quantum information processing in diamond.

The magnetic fields generated by spins and currents provide a unique window into the physics of correlatedelectron materials and devices. Proposed only a decade ago, magnetometry based on the electron spin of nitrogen-vacancy (NV) defects in diamond is emerging as a platform that is excellently suited for probing condensed matter systems: it can be operated from cryogenic temperatures to above room temperature, has a dynamic range spanning from DC to GHz, and allows sensor-sample distances as small as a few nanometres. As such, NV magnetometry provides access to static and dynamic magnetic and electronic phenomena with nanoscale spatial resolution. Pioneering work focused on proof-of-principle demonstrations of its nanoscale imaging resolution and magnetic field sensitivity. Now, experiments are starting to probe the correlatedelectron physics of magnets and superconductors and to explore the current distributions in low-dimensional materials. In this Review, we discuss the application of NV magnetometry to the exploration of condensed matter physics, focusing on its use to study static and dynamic magnetic textures, and static and dynamic current distributions. Box 1| Measuring static fieldsHere we describe elementary considerations for the use of nitrogen-vacancy (NV) centres for imaging magnetic fields generated by static magnetic textures and current distributions. Reconstructing a vector magnetic field by measuring a single field componentBecause the NV electron spin resonance splitting is first-order sensitive to the projection of the magnetic field B on the NV spin quantization axis, B||, this is the quantity typically measured in an NV magnetometry measurement 16 . It is therefore convenient to realize that the full vector field B can be reconstructed by measuring any of its components in a plane positioned at a distance d from the sample, where d is the NV-sample distance (provided this component is not parallel to the measurement plane). This results from the linear dependence of the components of B̂ in Fourier space 24,25 , which follows from the fact that B can be expressed as the gradient of a scalar magnetostatic potential. Moreover, by measuring B||(x, y; z = d) we can reconstruct B at all distances d + h through the evanescent-field analogue of Huygens' principle, a procedure known as upward propagation 24 . As an example, the out-of-plane stray field component Bz(x, y; z = d + h) can be reconstructed from B||(x, y; z = d) using ̂( ; + ℎ) = − ℎ̂| | ( ; ) NV •

rates. Here we present the integration of dynamical decoupling into quantum gates for a paradigmatic hybrid system, the electron-nuclear spin register. Our design harnesses the internal resonance in the coupled-spin system to resolve the conflict between gate operation and decoupling. We experimentally demonstrate these gates on a two-qubit register in diamond operating at room temperature. Quantum tomography reveals that the qubits involved in the gate operation are protected as accurately as idle qubits. We further illustrate the power of our design by executing .Decoherence is a major hurdle towards realizing scalable quantum technologies in the solid state. The inter-qubit dynamics that implement the quantum logic are unavoidably affected by uncontrolled couplings to the solid-state environment, preventing high-fidelity gate performance (Fig 1a). Dynamical decoupling 4 , a technique that employs fast qubit flips to average out the interactions with the environment, is a powerful and practical tool for mitigating decoherence [5][6][7][8][9][10][11][12]24,25 . This approach is particularly promising for the emerging class of hybrid quantum architectures [13][14][15][16][17][18][19][20][21][22][23] in which different types of qubits, such as electron and nuclear spins, superconducting resonators, and nanomechanical oscillators, perform different functions. Dynamical 2 decoupling allows for each qubit type to be decoupled at its own appropriate rate, ensuring uniform coherence protection.However, combining dynamical decoupling with quantum gate operations is generally problematic, since decoupling does not distinguish the desired inter-qubit interaction from the coupling to the decohering environment, and in general cancels both (Fig. 1b). For hybrid systems, where large difference in coherence and control timescales among the different qubit types make the encoding-based schemes 11 or synchronized application of decoupling pulses 4,12 fail, a solution has thus far remained elusive.Here we present a design that enables the integration of decoupling into gate operation for hybrid quantum architectures. We demonstrate such decoherence-protected gates on a prototype hybrid quantum system: a two-qubit register consisting of an electron and a nuclear spin (Fig. 1c). The key idea is to precisely adapt the time intervals between the electron decoupling pulses to the nuclear spin dynamics. When combined with continuous nuclear spin driving, this synchronization yields selective rotations of the nuclear spin while the electron spin is dynamically protected, as explained below. This design preserves all of the advantages of dynamical decoupling without requiring additional qubits or controllable inter-qubit couplings. It can be readily implemented to yield decoherence-protected quantum gates in a range of hybrid systems, such as various electron-nucleus spin registers [13][14][15][16][17]20 , and interface gates between the qubits and a spinchain quantum databus 22,23 .We experimentally demonstrate the scheme on ...

The spin chemical potential characterizes the tendency of spins to diffuse. Probing this quantity could provide insight into materials such as magnetic insulators and spin liquids and aid optimization of spintronic devices. Here we introduce single-spin magnetometry as a generic platform for nonperturbative, nanoscale characterization of spin chemical potentials. We experimentally realize this platform using diamond nitrogen-vacancy centers and use it to investigate magnons in a magnetic insulator, finding that the magnon chemical potential can be controlled by driving the system's ferromagnetic resonance. We introduce a symmetry-based two-fluid theory describing the underlying magnon processes, measure the local thermomagnonic torque, and illustrate the detection sensitivity using electrically controlled spin injection. Our results pave the way for nanoscale control and imaging of spin transport in mesoscopic systems.

We investigate spin-dependent decay and intersystem crossing in the optical cycle of single negatively-charged nitrogen-vacancy (NV) centres in diamond. We use spin control and pulsed optical excitation to extract both the spin-resolved lifetimes of the excited states and the degree of optically-induced spin polarization. By optically exciting the centre with a series of picosecond pulses, we determine the spin-flip probabilities per optical cycle, as well as the spin-dependent probability for intersystem crossing. This information, together with the indepedently measured decay rate of singlet population provides a full description of spin dynamics in the optical cycle of NV centres. The temperature dependence of the singlet population decay rate provides information on the number of singlet states involved in the optical cycle.

Pushing the frontiers of condensed-matter magnetism requires the development of tools that provide real-space, few-nanometre-scale probing of correlated-electron magnetic excitations under ambient conditions. Here we present a practical approach to meet this challenge, using magnetometry based on single nitrogen-vacancy centres in diamond. We focus on spin-wave excitations in a ferromagnetic microdisc, and demonstrate local, quantitative and phase-sensitive detection of the spin-wave magnetic field at ∼50 nm from the disc. We map the magnetic-field dependence of spin-wave excitations by detecting the associated local reduction in the disc's longitudinal magnetization. In addition, we characterize the spin–noise spectrum by nitrogen-vacancy spin relaxometry, finding excellent agreement with a general analytical description of the stray fields produced by spin–spin correlations in a 2D magnetic system. These complementary measurement modalities pave the way towards imaging the local excitations of systems such as ferromagnets and antiferromagnets, skyrmions, atomically assembled quantum magnets, and spin ice.

Understanding and mitigating decoherence is a key challenge for quantum science and technology. The main source of decoherence for solid-state spin systems is the uncontrolled spin bath environment. Here, we demonstrate quantum control of a mesoscopic spin bath in diamond at room temperature that is composed of electron spins of substitutional nitrogen impurities. The resulting spin bath dynamics are probed using a single nitrogen-vacancy (NV) centre electron spin as a magnetic field sensor. We exploit the spin bath control to dynamically suppress dephasing of the NV spin by the spin bath. Furthermore, by combining spin bath control with dynamical decoupling, we directly measure the coherence and temporal correlations of different groups of bath spins. These results uncover a new arena for fundamental studies on decoherence and enable novel avenues for spin-based magnetometry and quantum information processing.