12,074 research outputs found
Unique Continuation for Stochastic Heat Equations
We establish a unique continuation property for stochastic heat equations
evolving in a bounded domain . Our result shows that the value of the
solution can be determined uniquely by means of its value on an arbitrary open
subdomain of at any given positive time constant. Further, when 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
- …