# Grassmann representation in qubit informatics and superlogic. (arXiv:1802.01392v1 [quant-ph])

The Grassmann representation for the system of qubits, is considered. The
treatment is based on natural description of the qubits system as fermions and
uses coherent states of fermions. The quantum logic gates are represented in
two forms - by symbols of operations and by partial differential operators on
the symbols of the states. The considered representation of quantum logic is
called as superlogic. The examples are given for classical logic operations of
negation, conjunction, disjunction and for reversible three-bit Toffoli gate
and its quantum generalization - three-qbit Deutsch gate. The representation
for composite gates is also considered. Path integral represenatation in
Grassmann algebra for quantum automaton with qubits memory is described. In
particular for the autonomous automaton corresponding to the special case of
general dynamic system this description differ from path integral
representation in commutative memory phase space by the specific nonliner term
in superaction.