Exact Quantum Algorithms for the Leader Election Problem

TL;DR

This paper demonstrates that quantum algorithms can exactly solve the leader election problem in anonymous networks, a task impossible for classical algorithms, by leveraging quantum communication to achieve polynomial-time solutions.

Contribution

It provides the first quantum algorithms that exactly solve leader election in anonymous networks with polynomial complexity, surpassing classical limitations.

Findings

Quantum algorithms solve leader election exactly in polynomial time.

Classical algorithms cannot solve leader election exactly in anonymous networks.

Quantum communication enables solving an unsolvable classical problem.

Abstract

This paper gives the first separation of quantum and classical pure (i.e., non-cryptographic) computing abilities with no restriction on the amount of available computing resources, by considering the exact solvability of a celebrated unsolvable problem in classical distributed computing, the ``leader election problem'' on anonymous networks. The goal of the leader election problem is to elect a unique leader from among distributed parties. The paper considers this problem for anonymous networks, in which each party has the same identifier. It is well-known that no classical algorithm can solve exactly (i.e., in bounded time without error) the leader election problem in anonymous networks, even if it is given the number of parties. This paper gives two quantum algorithms that, given the number of parties, can exactly solve the problem for any network topology in polynomial rounds and polynomial communication/time complexity with respect to the number of parties, when the parties are connected by quantum communication links.