Controlling the interaction of a single quantum system with its environment is a fundamental challenge in quantum science and technology. We strongly suppressed the coupling of a single spin in diamond with the surrounding spin bath by using double-axis dynamical decoupling. The coherence was preserved for arbitrary quantum states, as verified by quantum process tomography. The resulting coherence time enhancement followed a general scaling with the number of decoupling pulses. No limit was observed for the decoupling action up to 136 pulses, for which the coherence time was enhanced more than 25 times compared to that obtained with spin echo. These results uncover a new regime for experimental quantum science and allow us to overcome a major hurdle for implementing quantum information protocols.

Crystal defects can confine isolated electronic spins and are promising candidates for solid-state quantum information. Alongside research focusing on nitrogen-vacancy centres in diamond, an alternative strategy seeks to identify new spin systems with an expanded set of technological capabilities, a materials-driven approach that could ultimately lead to ‘designer’ spins with tailored properties. Here we show that the 4H, 6H and 3C polytypes of SiC all host coherent and optically addressable defect spin states, including states in all three with room-temperature quantum coherence. The prevalence of this spin coherence shows that crystal polymorphism can be a degree of freedom for engineering spin qubits. Long spin coherence times allow us to use double electron–electron resonance to measure magnetic dipole interactions between spin ensembles in inequivalent lattice sites of the same crystal. Together with the distinct optical and spin transition energies of such inequivalent states, these interactions provide a route to dipole-coupled networks of separately addressable spins.

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...

Phase coherence is a fundamental concept in quantum mechanics. Understanding the loss of coherence is paramount for future quantum information processing. We studied the coherent dynamics of a single central spin (a nitrogen-vacancy center) coupled to a bath of spins (nitrogen impurities) in diamond. Our experiments show that both the internal interactions of the bath and the coupling between the central spin and the bath can be tuned in situ, allowing access to regimes with surprisingly different behavior. The observed dynamics are well explained by analytics and numerical simulations, leading to valuable insight into the loss of coherence in spin systems. These measurements demonstrate that spins in diamond provide an excellent test bed for models and protocols in quantum information.

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.

We demonstrate fluorescence thermometry techniques with sensitivities approaching 10 mK·Hz −1/2 based on the spin-dependent photoluminescence of nitrogen vacancy (NV) centers in diamond. These techniques use dynamical decoupling protocols to convert thermally induced shifts in the NV center's spin resonance frequencies into large changes in its fluorescence. By mitigating interactions with nearby nuclear spins and facilitating selective thermal measurements, these protocols enhance the spin coherence times accessible for thermometry by 45-fold, corresponding to a 7-fold improvement in the NV center's temperature sensitivity. Moreover, we demonstrate these techniques can be applied over a broad temperature range and in both finite and near-zero magnetic field environments. This versatility suggests that the quantum coherence of single spins could be practically leveraged for sensitive thermometry in a wide variety of biological and microscale systems.spintronics | electron spin resonance | quantum control T hermometry based on thermally driven changes in fluorescence lifetimes or intensities is an essential technique in many environments that preclude electrical probes (1). Although typical fluorescence thermometers use millimeter-scale optical probes (2), the desire to noninvasively monitor intracellular thermal gradients has motivated efforts to develop analogous methods at the nanoscale (3,4). This interest has stimulated the development of nanoscale fluorescence thermometers based on quantum dots (5), rare-earth ions (6), and nanogels (7), with recent studies suggesting that intracellular temperature gradients are on the order of 1 K (8). However, the application of conventional fluorescence thermometry techniques in biological settings is limited by temperature resolutions of ∼0.2 K or worse (8-10), motivating the development of more advanced nanoscale thermometers.In recent years, solid-state electronic spins have gained considerable attention for applications in nanoscale sensing. In particular, the diamond nitrogen vacancy (NV) center (Fig. 1A) has garnered attention for its optical spin initialization and fluorescence-based spin readout (11), the ability to isolate and measure single defects (12), and the ability to manipulate its spin using microwave electron spin resonance techniques (13). NV center sensing is based on monitoring shifts in the spin resonance frequencies through the defect's fluorescence as a function of external perturbations such as magnetic fields (14-17), electric fields (18), or temperature (19,20), with the sensitivity of these techniques scaling as 1= ffiffiffiffiffiffi T C p , where T C is the relevant spin coherence time (21). These coherence times can be enhanced by two to three orders of magnitude for perturbations amenable to timeperiodic (AC) modulation through the use of dynamical decoupling techniques that periodically invert the spin state and the signal being sensed to mitigate the effects of low-frequency magnetic noise (22-24). These methods have enabled the detection...

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 ...

We present joint theoretical-experimental study of the correlation effects in the electronic structure of (pyH)3[Mn4O3Cl7(OAc)3]·2MeCN molecular magnet (Mn4). Describing the many-body effects by cluster dynamical mean-field theory, we find that Mn4 is predominantly Hubbard insulator with strong electron correlations. The calculated electron gap (1.8 eV) agrees well with the results of optical conductivity measurements, while other methods, which neglect many-body effects or treat them in a simplified manner, do not provide such an agreement. Strong electron correlations in Mn4 may have important implications for possible future applications.PACS numbers: 75.50. Xx,71.15.Mb, Single molecule magnets (SMMs), made of exchangecoupled magnetic ions surrounded by large organic ligands, represent a novel interesting class of magnetic materials. They are of fundamental interest as test systems for studying magnetism at nanoscale, and interplay between the structural, electronic, and magnetic properties. SMMs demonstrate fascinating mixture of clasiscal and quantum properties: as classical superparamagnets, they possess large anisotropy and magnetic moment, but also exhibit interesting mesoscopic quantum spin effects [1,2,3]. Moreover, recent experiments on the electron transport through SMMs [4], and predicted connection between the transport and spin tunneling [5], make SMMs good candidates for interesting spintronics studies. Progress in this area -synthesis of novel SMMs with optimized properties, design and analysis of the transport experiments, possible uses in information processing -demands detailed theoretical investigations of the magnetic and electronic structure of SMMs [6,7,8,9,10]. Among other factors, the many-body correlations caused by the Coulomb repulsion between electrons, may be important. E.g., in transition metal-oxide systems [11], which share many similarities with SMMs, strong correlations may form the Mott-Hubbard insulating state [12], where the nature of the charge and spin excitations is drastically different from the predictions of standard band-insulator theory. This affects the basic properties of the system (e.g., exchange interactions), and drastically changes charge and spin transport.In this joint experimental-theoretical work, we present a detailed study of the many-body effects in electronic structure of SMMs (pyH) 3 [Mn 4 O 3 Cl 7 (OAc) 3 ]·2MeCN (denoted below as Mn 4 for brevity) [19]. We use the cluster LDA+DMFT method [13] which combines the realistic ab initio calculations based on the local density approximation (LDA), and the accurate description of the correlation effects within the cluster dynamical mean field theory (CDMFT). Using the electron gap as a most convenient benchmark, we show that the gap value (1.8 eV) calculated within LDA+CDMFT is in good agreement with the optical conductivity measurements (showing the peak corresponding to vertical transitions at ∼1.8 eV). The approaches which neglect the electron correlations (LDA), or treat these correlation in a simplifi...