Communicating Quantum Processes

TL;DR

This paper introduces CQP, a formal language combining quantum and classical communication primitives, with a type system ensuring proper ownership and enabling modeling of quantum communication systems.

Contribution

It defines the syntax, semantics, and type system of CQP, facilitating formal analysis of quantum-classical systems and ensuring unique ownership of qubits.

Findings

CQP can model quantum communication protocols.

Type system guarantees qubit ownership.

Semantics preserve typing and correctness.

Abstract

We define a language CQP (Communicating Quantum Processes) for modelling systems which combine quantum and classical communication and computation. CQP combines the communication primitives of the pi-calculus with primitives for measurement and transformation of quantum state; in particular, quantum bits (qubits) can be transmitted from process to process along communication channels. CQP has a static type system which classifies channels, distinguishes between quantum and classical data, and controls the use of quantum state. We formally define the syntax, operational semantics and type system of CQP, prove that the semantics preserves typing, and prove that typing guarantees that each qubit is owned by a unique process within a system. We illustrate CQP by defining models of several quantum communication systems, and outline our plans for using CQP as the foundation for formal analysis and verification of combined quantum and classical systems.