A first step to the categorical logic of quantum programs

Abstract

The long-term goal of our research is to develop a powerful quantum logic which is useful in the formal verification of quantum programs and protocols. In this paper we introduce the basic idea of our categorical logic of quantum programs (CLQP): It combines the logic of quantum programming (LQP) and categorical quantum mechanics (CQM) such that the advantages of both LQP and CQM are preserved while their disadvantages are overcome. We present the syntax, semantics and proof system of CLQP. As a proof-of-concept, we apply CLQP to verify the correctness of Deutsch's algorithm and the concealing property of quantum bit commitment.