Efficient algebraic representation of quantum circuits

Abstract

A novel and powerful method for representing the unitary matrix of a quantum circuit as an algebraic equation is presented. The method forms a product of sum of Kronecker products (POSOK’s) equation whereby simple mathematical properties can be used to manipulate the algebraic equation to reduce the quantum circuit and prove known circuit equivalences. The method is simple enough to be done by hand or simple automation. The benefits of such a method apply to quantum simulation where the quantum circuit can be easily parsed and reduction techniques can reduce simulation time. Also, having an algebraic expression that can be manipulated through a set of mathematical rules has applications in quantum logic synthesis and quantum computational theory.

Keywords and phrases:

• Quantum circuits
• quantum logic
• quantum simulation