A logic for quantum circuits and protocols

Abstract

A logic for reasoning about quantum circuits and protocols is proposed. It incorporates the basic features of quantum theory-probability, unitary dynamics, tensor products and measurement. The underlying language could be used for verification and synthesis of quantum circuits. Important algorithms like the quantum search algorithm of Grover are discussed. The logic also forms the foundation on which more elaborate formal systems for reasoning about quantum protocols could be based. A sound and complete axiomatization is presented. Algorithms for circuit verification, circuit equivalence (exact and approximate) are outlined. Some related complexity issues are also discussed. © Springer-Verlag Berlin Heidelberg 2005.