Computing on Anonymous Quantum Network

TL;DR

This paper demonstrates that distributed quantum computing on anonymous networks enables efficient leader election and exact computation of Boolean functions, surpassing classical algorithms in certain scenarios.

Contribution

It introduces a quantum leader election algorithm with improved efficiency and shows that any n-qubit state can be shared on an anonymous quantum network with optimal complexity.

Findings

Quantum leader election runs in O(n) rounds.

Exact computation of any Boolean function with improved complexity.

Sharing any n-qubit state efficiently on anonymous networks.

Abstract

This paper considers distributed computing on an anonymous quantum network, a network in which no party has a unique identifier and quantum communication and computation are available. It is proved that the leader election problem can exactly (i.e., without error in bounded time) be solved with at most the same complexity up to a constant factor as that of exactly computing symmetric functions (without intermediate measurements for a distributed and superposed input), if the number of parties is given to every party. A corollary of this result is a more efficient quantum leader election algorithm than existing ones: the new quantum algorithm runs in O(n) rounds with bit complexity O(mn^2), on an anonymous quantum network with n parties and m communication links. Another corollary is the first quantum algorithm that exactly computes any computable Boolean function with round complexity O(n) and with smaller bit complexity than that of existing classical algorithms in the worst case over all (computable) Boolean functions and network topologies. More generally, any n-qubit state can be shared with that complexity on an anonymous quantum network with n parties.