Strongly correlated quantum many-body systems may exhibit exotic phases, such as spin liquids and supersolids. Although their numerical simulation becomes intractable for as few as 50 particles, quantum simulators offer a route to overcome this computational barrier. However, proposed realizations either require stringent conditions such as low temperature/ultra-high vacuum, or are extremely hard to scale. Here, we propose a new solid-state architecture for a scalable quantum simulator that consists of strongly interacting nuclear spins attached to the diamond surface. Initialization, control and read-out of this quantum simulator can be accomplished with nitrogen-vacancy centers implanted in diamond. The system can be engineered to simulate a wide variety of strongly correlated spin models. Owing to the superior coherence time of nuclear spins and nitrogen-vacancy centers in diamond, our proposal offers new opportunities towards large-scale quantum simulation at ambient conditions of temperature and pressure.
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We are grateful for valuable communications with M. Troyer, L. Pollet and B. Capogrosso-Sansone about the properties of supersolids and QMC simulations with ALPS. We also thank R. Rosenbach and J. Almeida for their help in numerical simulations. The work was supported by the Alexander von Humboldt Foundation, the EU Integrating Project Q-ESSENCE, the EU STREP PICC and DIAMANT, the BMBF Verbundprojekt QuOReP, DFG (FOR 1482, FOR 1493, SFB/TR 21) and DARPA. J.C. was also supported by a Marie-Curie Intra-European Fellowship (FP7). Computations were performed on the bwGRiD.