Visibility

The following command changes the mode of the machine to the visibility mode in which the visibility of a unitary transformation can be calculated:
visibility mode;
The visibility of a quantum state $ \sigma$ with respect to a unitary transformation $ U$ is generally defined as

$\displaystyle v = \vert\mathrm{Tr} (U\sigma)\vert.$ (8)

No sooner the command ``visibility mode'' is input than the current state is copied to the state $ \sigma$. The subsequent quantum gates $ U$ is applied to $ \sigma$ without $ U^\dagger$ as well as to $ \rho$ with $ U^\dagger$ ($ \rho$ is the state for ordinary calculation), that is to say, both $ U\sigma$ and $ U\rho U^\dagger$ are calculated internally after that command. To see the visibility, one types the command:
visibility;
There are other commands related to the visibility. ``vtrace'' command is to show the matrix $ \mathrm{Tr}(U\sigma)$; ``vphase'' shows the phase $ \mathrm{Arg}\{\mathrm{Tr}(U\sigma)\}$.

root
2004-11-07