  We study the effects of noise and decoherence for a double-potential well
system, suitable for the fabrication of qubits and quantum logic elements. A
random noise term is added to the hamiltonian, the resulting wavefunction found
numerically and the density matrix obtained by averaging over noise signals.
Analytic solutions using the two-state model are obtained and found to be
generally in agreement.
  In particular, a simple formula for the decoherence rate in terms of the
noise parameters in the two-state model is reviewed and verified for the full
simulation with the multi-level system. The formalism is extended to describe
multiple sources of noise or different "dephasing" axes at the same time.
Furthermore, the old formula for the "Turing-Watched Pot" effect is generalized
to the case where the environmental interactions do not conserve the "quality"
in question.
  Various forms for the noise signal are investigated. An interesting result is
the importance of the noise power at low frequency. If it vanishes there is, in
leading order, no decoherence. This is verified in a numerical simulation where
two apparently similar noise signals, but differing in the power at zero
frequency, give strikingly different decoherence effects. A short discussion of
situations dominated by low frequency noise is given.
