Unique Continuation for Stochastic Heat Equations

We establish a unique continuation property for stochastic heat equations evolving in a bounded domain $G$. Our result shows that the value of the solution can be determined uniquely by means of its value on an arbitrary open subdomain of $G$ at any given positive time constant. Further, when $G$ is convex and bounded, we also give a quantitative version of the unique continuation property. As applications, we get an observability estimate for stochastic heat equations, an approximate result and a null controllability result for a backward stochastic heat equation

Universal quantum gates between nitrogen-vacancy centers in a levitated nanodiamond

We propose a scheme to realize universal quantum gates between nitrogen-vacancy (NV) centers in an optically trapped nanodiamond, through uniform magnetic field induced coupling between the NV centers and the torsional mode of the levitated nanodiamond. The gates are tolerant to the thermal noise of the torsional mode. By combining the scheme with dynamical decoupling technology, it is found that the high fidelity quantum gates are possible for the present experimental conditions. The proposed scheme is useful for NV-center-based quantum network and distributed quantum computationComment: 7 pages, 6 figure