Symbolic bisimulation for quantum processes

TL;DR

This paper introduces a symbolic bisimulation method for quantum processes that avoids the infeasible state instantiation, enabling more practical verification of quantum process equivalence.

Contribution

It presents a novel symbolic operational semantics for quantum processes, establishing an equivalence with existing bisimulation notions and providing an algorithm for checking bisimilarity.

Findings

Symbolic bisimulation is equivalent to open bisimulation for quantum processes.

An algorithm for checking symbolic ground bisimilarity is developed.

A modal logical framework characterizing quantum bisimilarity is proposed.

Abstract

With the previous notions of bisimulation presented in literature, to check if two quantum processes are bisimilar, we have to instantiate the free quantum variables of them with arbitrary quantum states, and verify the bisimilarity of resultant configurations. This makes checking bisimilarity infeasible from an algorithmic point of view because quantum states constitute a continuum. In this paper, we introduce a symbolic operational semantics for quantum processes directly at the quantum operation level, which allows us to describe the bisimulation between quantum processes without resorting to quantum states. We show that the symbolic bisimulation defined here is equivalent to the open bisimulation for quantum processes in the previous work, when strong bisimulations are considered. An algorithm for checking symbolic ground bisimilarity is presented. We also give a modal logical characterisation for quantum bisimilarity based on an extension of Hennessy-Milner logic to quantum processes.