Comparison of state assignment methods for “quantum circuit” model of permutative quantum state machines

The design of state machines for quantum algorithms remains a largely unexplored topic. The abstract models for quantum computation proposed by Feynman, Deutsch etc have been related to the theory of Quantum Turing Machines (QTM) and the work was later expanded by Bernstein and Vazirani to lay the foundations of quantum complexity theory. However, no papers deal with the following problem: “how to realize the quantum state machine in hardware as an operational quantum circuit that the internal states of which can be measured and used as inputs in a system of such machines”. This is an equivalent to the fundamental problem of “structural synthesis of FSM”. This paper creates models of quantum state machines that are useful from an engineering perspective. The objective of the paper is to propose models that can be used for circuit-level implementation. We restrict our study to binary logic realized in quantum, the so-called binary permutative quantum circuits; the “permutative machines”. The presented synthesis procedure is analogous to classical logic circuits synthesis and is a necessary step in the entire design procedure of quantum automata. Thus state minimization, state assignment and excitation function realization aspects are also of interest and some preliminary experimental results are presented.