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

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