Grassmann representation in qubit informatics and superlogic

TL;DR

This paper introduces a Grassmann algebra-based superlogic framework for representing qubits and quantum gates, providing a novel algebraic and path integral approach to quantum automata with memory.

Contribution

It develops a new superlogic representation of qubits using Grassmann algebra, including quantum gate representations and path integral formulations for quantum automata.

Findings

Superlogic effectively models quantum gates and logic operations.

Path integral in Grassmann algebra offers a new perspective on quantum automata.

Representation captures nonlinear dynamics in quantum systems with memory.

Abstract

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.