Verification of Distributed Quantum Programs

TL;DR

This paper introduces a new formal language and logic for specifying and verifying distributed quantum programs, addressing key challenges in ensuring correctness in quantum internet systems.

Contribution

It presents a CSP-like programming language with semantics and a Hoare-style logic for distributed quantum systems, including proofs of soundness and completeness.

Findings

Verified quantum teleportation correctness

Verified local implementation of non-local CNOT gates

Demonstrated effectiveness of the logic in distributed quantum algorithms

Abstract

Distributed quantum systems and especially the Quantum Internet have the ever-increasing potential to fully demonstrate the power of quantum computation. This is particularly true given that developing a general-purpose quantum computer is much more difficult than connecting many small quantum devices. One major challenge of implementing distributed quantum systems is programming them and verifying their correctness. In this paper, we propose a CSP-like distributed programming language to facilitate the specification and verification of such systems. After presenting its operational and denotational semantics, we develop a Hoare-style logic for distributed quantum programs and establish its soundness and (relative) completeness with respect to both partial and total correctness. The effectiveness of the logic is demonstrated by its applications in the verification of quantum teleportation and local implementation of non-local CNOT gates, two important algorithms widely used in distributed quantum systems.