Asynchronous Quantum Distributed Computing: Causality, Snapshots, and Global Operations

TL;DR

This paper introduces the study of asynchronous quantum distributed systems, presenting a quantum algorithm for implementing global operations like snapshots, and analyzing causality in quantum contexts.

Contribution

It develops a formal model for quantum distributed computing and designs a quantum snapshot algorithm inspired by classical methods, highlighting causality preservation.

Findings

The quantum snapshot algorithm successfully implements global operations in asynchronous systems.

Causality arguments from classical distributed computing remain valid in quantum systems despite entanglement.

A formal model of quantum distributed computing is proposed, applicable to classical randomized algorithms.

Abstract

We initiate the study of asynchronous quantum distributed systems, focusing on the case of implementing atomic quantum global operations that can be decomposed into a collection of local operations on the components of the system. A simple example of such an operation is a quantum snapshot in which the whole system is instantaneously measured. Based on the classical snapshot algorithm of Chandy and Lamport, we design a quantum distributed algorithm to implement such decomposable global operations, which we call the QGO Algorithm. The analysis of our algorithm shows that arguments based on Lamport's computational causality remain valid in the quantum world, even though, due to entanglement, causality is not manifest from the standard description of the system in terms of a (global) quantum state. Our other contributions include a formal model of quantum distributed computing, and a formal specification for the desired behavior of a global operation, which may be of interest even in classical settings (such as in the setting of randomized algorithms).