  Quantum computer is the key to controlling complex processes. If its
hardware, in general is successfully created on the basis of the physical
baggage of the 20th century, the mathematical software is fundamentally lagging
behind. Feynman's user interface in the form of quantum gate arrays, cannot be
used for the control because it gives the solution of Schr\"odinger equation
with quadratic slowdown compared to the real process. The software must then
imitate the real process using appropriate program primitives written as the
programs for classical supercomputer. The decoherence will be reflected by some
constant - the number of basic states that can fit into the limited of memory
available to software. The real value of this constant can be found in the
experimental realization of Grover search algorithm. Rough estimates of this
constant are given based on the simplest processes of quantum electrodynamics
and nuclear decay.
