Experimental realization of a universal set of quantum logic gates is the central requirement for the implementation of a quantum computer. In an 'all-geometric' approach to quantum computation, the quantum gates are implemented using Berry phases and their non-Abelian extensions, holonomies, from geometric transformation of quantum states in the Hilbert space. Apart from its fundamental interest and rich mathematical structure, the geometric approach has some built-in noise-resilience features. On the experimental side, geometric phases and holonomies have been observed in thermal ensembles of liquid molecules using nuclear magnetic resonance; however, such systems are known to be non-scalable for the purposes of quantum computing. There are proposals to implement geometric quantum computation in scalable experimental platforms such as trapped ions, superconducting quantum bits and quantum dots, and a recent experiment has realized geometric single-bit gates in a superconducting system. Here we report the experimental realization of a universal set of geometric quantum gates using the solid-state spins of diamond nitrogen-vacancy centres. These diamond defects provide a scalable experimental platform with the potential for room-temperature quantum computing, which has attracted strong interest in recent years. Our experiment shows that all-geometric and potentially robust quantum computation can be realized with solid-state spin quantum bits, making use of recent advances in the coherent control of this system.

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Pressure alters the physical, chemical, and electronic properties of matter. The diamond anvil cell enables tabletop experiments to investigate a diverse landscape of high-pressure phenomena. Here, we introduce and use a nanoscale sensing platform that integrates nitrogen-vacancy (NV) color centers directly into the culet of diamond anvils. We demonstrate the versatility of this platform by performing diffraction-limited imaging of both stress fields and magnetism as a function of pressure and temperature. We quantify all normal and shear stress components and demonstrate vector magnetic field imaging, enabling measurement of the pressure-driven a ↔ D phase transition in iron and the complex pressure-temperature phase diagram of gadolinium. A complementary NV-sensing modality using noise spectroscopy enables the characterization of phase transitions even in the absence of static magnetic signatures.3 of 6 Fig. 2. Full tensorial reconstruction of the stresses in a (111)-cut diamond anvil. (A) Spatially resolved maps of the loading stress (left) and mean lateral stress (right), s ⊥ ¼ 1 2 ðs XX þ s YY Þ, across the culet surface.In the inner region, where the culet surface contacts the pressure-transmitting medium (16:3:1 methanol/ ethanol/water), the loading stress is spatially uniform, whereas the lateral stress is concentrated toward the center; this qualitative difference is highlighted by a linecut (taken along the white-dashed line) of the two stresses (below), and reconstructed by finite-element analysis (orange and purple dashed lines). The black pixels indicate where the NV spectrum was obfuscated by the ruby microsphere. (B) Comparison of all stress tensor components in the fluid-contact region at P ¼ 4:9 GPa and P ¼ 13:6 GPa. At P ¼ 13:6 GPa, the pressure-transmitting medium has entered its glassy phase, and we observe a spatial gradient in the loading stress s ZZ (inset).

We report the first state-independent experimental test of quantum contextuality on a single photonic qutrit (three-dimensional system), based on a recent theoretical proposal [Phys. Rev. Lett. 108, 030402 (2012)]. Our experiment spotlights quantum contextuality in its most basic form, in a way that is independent of either the state or the tensor product structure of the system.

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