Verification of Linear Optical Quantum Computing using Quantum Process Calculus

TL;DR

This paper demonstrates how quantum process calculus can be used to verify linear optical quantum computing models, specifically by proving behavioral equivalence between system models and specifications, including multi-photon states.

Contribution

It extends the theory of behavioral equivalence in Communicating Quantum Processes to include multiple photons and applies it to verify LOQC CNOT gate models for the first time.

Findings

Behavioral equivalence is a congruence in the extended calculus.

Successful verification of LOQC CNOT gate models.

Extension of process calculus to multi-photon states.

Abstract

We explain the use of quantum process calculus to describe and analyse linear optical quantum computing (LOQC). The main idea is to define two processes, one modelling a linear optical system and the other expressing a specification, and prove that they are behaviourally equivalent. We extend the theory of behavioural equivalence in the process calculus Communicating Quantum Processes (CQP) to include multiple particles (namely photons) as information carriers, described by Fock states or number states. We summarise the theory in this paper, including the crucial result that equivalence is a congruence, meaning that it is preserved by embedding in any context. In previous work, we have used quantum process calculus to model LOQC but without verifying models against specifications. In this paper, for the first time, we are able to carry out verification. We illustrate this approach by describing and verifying two models of an LOQC CNOT gate.