  All metal objects support fluctuating currents that are responsible for
evanescent-wave Johnson noise in their vicinity due both to thermal and quantum
effects. The noise fields can decohere qubits in their neighborhood. It is
quantified by the average value of $B(x,t)B(x',t')$ and its time Fourier
transform. We develop the formalism particularly for objects whose dimensions
are small compared with the skin depth, which is the appropriate regime for
nanoscale devices. This leads to a general and surprisingly simple formula for
the noise correlation function of an object of arbitrary shape. This formula
has a clear physical interpretation in terms of induced currents in the object.
It can also be the basis for straightforward numerical evaluation. For a
sphere, a solution is given in closed form in terms of a generalized multipole
expansion. Plots of the solution illustrate the physical principles involved.
We give examples of how the spatial pattern of noise can affect quantum
information processing in nearby qubits. The theory implies that if the qubit
system is miniaturized to a scale $D$, then decoherence rates of qubits scale
as $1/D$.
