A symbolic calculus for a class of quantum computing circuits

Abstract

This paper introduces a symbolic calculus to evaluate the output signals at the target line(s) of quantum computing subcircuits using controlled negations and controlled-Q gates, where Q represents the k-th root of [0 1; 1 0], the unitary matrix of NOT, and k is a power of two. The controlling signals are GF(2) expressions possibly including Boolean expressions. The method does not require operating with complex-valued matrices. The method may be used to verify the functionality and to check for possible minimization of a given quantum computing circuit using target lines. The method does not apply for a whole circuit if there are interactions among target lines. In this case the method applies for the independent subcircuits.