As quantum mechanics ventures into the world of applications and engineering, materials science faces the necessity to design matter to quantum grade purity. For such materials, quantum effects define their physical behaviour and open completely new (quantum) perspectives for applications. Carbon-based materials are particularly good examples, highlighted by the fascinating quantum properties of, for example, nanotubes or graphene. Here, we demonstrate the synthesis and application of ultrapure isotopically controlled single-crystal chemical vapour deposition (CVD) diamond with a remarkably low concentration of paramagnetic impurities. The content of nuclear spins associated with the (13)C isotope was depleted to 0.3% and the concentration of other paramagnetic defects was measured to be <10(13) cm(-3). Being placed in such a spin-free lattice, single electron spins show the longest room-temperature spin dephasing times ever observed in solid-state systems (T2=1.8 ms). This benchmark will potentially allow observation of coherent coupling between spins separated by a few tens of nanometres, making it a versatile material for room-temperature quantum information processing devices. We also show that single electron spins in the same isotopically engineered CVD diamond can be used to detect external magnetic fields with a sensitivity reaching 4 nT Hz(-1/2) and subnanometre spatial resolution.

Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. It is well known that out-of-equilibrium systems can display a rich array of phenomena, ranging from self-organized synchronization to dynamical phase transitions1,2. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter3-6. As a particularly striking example, the interplay of periodic driving, disorder, and strong interactions has recently been predicted to result in exotic "time-crystalline" phases7, which spontaneously break the discrete time-translation symmetry of the underlying drive8-11. Here, we report the experimental observation of such discrete time-crystalline order in a driven, disordered †

Measuring local temperature with a spatial resolution on the order of a few nanometers has a wide range of applications from semiconductor industry over material to life sciences [1]. When combined with precision temperature measurement it promises to give excess to small temperature changes caused e.g. by chemical reactions or biochemical processes [2]. However, nanoscale temperature measurements and precision have excluded each other so far owing to the physical processes used for temperature measurement of limited stability of nanoscale probes [3]. Here we experimentally demonstrate a novel nanoscale temperature sensing technique based on single atomic defects in diamonds. Sensor sizes range from millimeter down to a few tens of nanometers. Utilizing the sensitivity of the optically accessible electron spin level structure to temperature changes [4] we achieve a temperature noise floor of 5 mK/ √ Hz for single defects in bulk sensors. Using doped nanodiamonds as sensors yields temperature measurement with 130 mK/ √ Hz noise floor and accuracies down to 1 mK at length scales of a few ten nanometers. The high sensitivity to temperature changes together with excellent spatial resolution combined with outstanding sensor stability allows for nanoscale precision temperature determination enough to measure chemical processes of few or single molecules by their reaction heat even in heterogeneous environments like cells.Several kinds of nanoscale temperature sensing techniques have been developed in the recent past [1]. These are scanning thermal microscopes (SThM) [5], dispersed or scanned individual nanoprobes [3,6], direct methods like micro-Raman spectroscopy [7] or near-field optical temperature measurements [8]. SThMs have temperature sensitive elements at a scanning tip (e.g. thermocouple), the nanoprobes have temperature dependent properties (e.g. fluorescence spectrum) which can be accessed without direct contact.In this study utilize a single quantum system in a solid state matrix as a temperature nanoprobe, namely the negatively charged nitrogen-vacancy (NV) center in diamond, which allows probe sizes down to ∼ 5 nm [9]. High fidelity control of its ground state electronic and nuclear spins has been demonstrated for various quantum information test experiments [10-15] as well as for nanometer scale metrology purposes [16][17][18][19] e.g. measuring small magnetic and electric fields. Here we show that it also allows tracking temperature with high precision. Temperature nanoprobes can be either dispersed in the specimen to be investigated or used in scanning probe geometry (see fig. 1a).The NV center is a molecular impurity in diamond comprising a substitutional nitrogen impurity and an adjacent carbon vacancy. Optical excitation in a wavelength range from 460 nm to 580 nm yields intense fluorescence emission [20]. Excitation also leads to a high degree of ground state electron spin polarization (S = 1, the actual sensor level) into its m S = 0 (|0 ) sublevel [21]. Furthermore the fluorescence decreases upo...

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.

NV defect centres in diamond are promising solid-state magnetometers. Single centres allow for high spatial resolution field imaging but are limited in their magnetic field sensitivity to around 𝟏𝟎 𝐧𝐓/√𝐇𝐳 at room temperature. Using defect centre ensembles sensitivity can be scaled as √𝑵 when 𝑵 is the number of defects. In the present work, we use an ensemble of 10 11 defect centres for sensing. By carefully eliminating all noise sources like laser intensity fluctuations, microwave amplitude and phase noise we achieve a photon shot noise limited field sensitivity of 𝟎. 𝟗 𝐩𝐓/√𝐇𝐳 at room-temperature with an effective sensor volume of 𝟖. 𝟓𝐞-𝟒 𝐦𝐦 𝟑 . The smallest field we measured with our device is 𝟏𝟎𝟎 𝐟𝐓. While this denotes the best diamond magnetometer sensitivity so far, further improvements using decoupling sequences and material optimization could lead to 𝐟𝐓/√𝐇𝐳 sensitivity.