Spins associated to single defects in solids provide promising qubits for quantum information processing and quantum networks. Recent experiments have demonstrated long coherence times, high-fidelity operations and long-range entanglement. However, control has so far been limited to a few qubits, with entangled states of three spins demonstrated. Realizing larger multi-qubit registers is challenging due to the need for quantum gates that avoid crosstalk and protect the coherence of the complete register. In this paper, we present novel decoherence-protected gates that combine dynamical decoupling of an electron spin with selective phase-controlled driving of nuclear spins. We use these gates to realize a 10-qubit quantum register consisting of the electron spin of a nitrogen-vacancy center and 9 nuclear spins in diamond. We show that the register is fully connected by generating entanglement between all 45 possible qubit pairs, and realize genuine multipartite entangled states with up to 7 qubits. Finally, we investigate the register as a multi-qubit memory. We show coherence times up to 63(2) seconds -the longest reported for a single solid-state qubit -and demonstrate that two-qubit entangled states can be stored for over 10 seconds. Our results enable the control of large quantum registers with long coherence times and therefore open the door to advanced quantum algorithms and quantum networks with solid-state spin qubits.

Nuclear magnetic resonance (NMR) is a powerful method for determining the structure of molecules and proteins [1]. While conventional NMR requires averaging over large ensembles, recent progress with single-spin quantum sensors [2][3][4][5][6][7][8][9] has created the prospect of magnetic imaging of individual molecules [10][11][12][13]. As an initial step towards this goal, isolated nuclear spins and spin pairs have been mapped [14][15][16][17][18][19][20][21]. However, large clusters of interacting spins -such as found in molecules -result in highly complex spectra. Imaging these complex systems is an outstanding challenge due to the required high spectral resolution and efficient spatial reconstruction with sub-angstrom precision. Here we develop such atomic-scale imaging using a single nitrogen-vacancy (NV) centre as a quantum sensor, and demonstrate it on a model system of 27 coupled 13 C nuclear spins in a diamond. We present a new multidimensional spectroscopy method that isolates individual nuclearnuclear spin interactions with high spectral resolution (< 80 mHz) and high accuracy (2 mHz). We show that these interactions encode the composition and inter-connectivity of the cluster, and develop methods to extract the 3D structure of the cluster with sub-angstrom resolution. Our results demonstrate a key capability towards magnetic imaging of individual molecules and other complex spin systems [9][10][11][12][13].The nitrogen-vacancy (NV) centre in diamond has emerged as a powerful quantum sensor [2-13, 22, 23]. The NV electron spin provides long coherence times [5, 6,20] and high-contrast optical readout [5,24,25], enabling high sensitivity over a large range of temperatures [5, 6,20,25,26]. Pioneering experiments with near-surface NV centers have demonstrated spectroscopy of small ensembles of nuclear spins in nano-scale volumes [2, 3,[5][6][7][8], and electron-spin labelled proteins [4]. Furthermore, single nuclear spin sensitivity has been demonstrated and isolated individual nuclear spins and spin pairs have been mapped [14][15][16][17][18][19][20][21]. Together, these results have established the NV center as a promising platform * T.H.Taminiau@TUDelft.nl for magnetic imaging of complex spin systems and single molecules [10][11][12][13].In this work, we realise a key ability towards that goal: the 3D imaging of large nuclear-spin structures with atomic resolution. The main idea of our method is to obtain structural information by accessing the couplings between individual nuclear spins. The key open challenges are: (1) to realize high spectral resolution so that small couplings can be accessed, (2) to isolate such couplings from complex spectra, and (3) to transform the revealed connectivity into the 3D spatial structure with sub-angstrom precision.The basic elements of our experiment are illustrated in Fig. 1a. We consider a cluster of 13 C nuclear spins in the vicinity of a single NV centre in diamond at 4 K. This cluster provides a model system for the magnetic imaging of single molecules and spin ...

Society increasingly relies on machine learning models for automated decision making. Yet, efficiency gains from automation have come paired with concern for algorithmic discrimination that can systematize inequality. Recent work has proposed optimal post-processing methods that randomize classification decisions for a fraction of individuals, in order to achieve fairness measures related to parity in errors and calibration. These methods, however, have raised concern due to the information inefficiency, intra-group unfairness, and Pareto sub-optimality they entail. The present work proposes an alternative active framework for fair classification, where, in deployment, a decision-maker adaptively acquires information according to the needs of different groups or individuals, towards balancing disparities in classification performance. We propose two such methods, where information collection is adapted to group-and individual-level needs respectively. We show on real-world datasets that these can achieve: 1) calibration and single error parity (e.g., equal opportunity); and 2) parity in both false positive and false negative rates (i.e., equal odds). Moreover, we show that by leveraging their additional degree of freedom, active approaches can substantially outperform randomization-based classifiers previously considered optimal, while avoiding limitations such as intra-group unfairness.

Figure 1: Diagram of data processing and analysis fow in VizML, starting from (1) the original Plotly Community Feed API endpoints, proceeding to (2) the deduplicated dataset-visualization pairs, (3a) features describing each individual column, pair of columns, and dataset, (3b) design choices extracted from visualizations, (4) task-specifc models trained on these features, and (5) potential recommended design choices.