Quantum-assisted Rendezvous on Graphs: Explicit Algorithms and Quantum Computer Simulations

TL;DR

This paper investigates quantum advantage in one-step rendezvous games on graphs, demonstrating protocols that achieve optimal bounds and testing them on NISQ processors with mixed results.

Contribution

It provides explicit quantum protocols for rendezvous games on graphs, extends them to larger graphs, and experimentally tests quantum advantage on NISQ hardware.

Findings

Quantum protocols achieve optimal bounds on small graphs.

NISQ experiments show quantum advantage on K3.

Hardware performance varies with graph complexity.

Abstract

We study quantum advantage in one-step rendezvous games on simple graphs analytically, numerically, and using noisy intermediate-scale quantum (NISQ) processors. Our protocols realise the recently discovered [arXiv:2207.14404] optimal bounds for small cycle graphs and cubic graphs. In the case of cycle graphs, we generalise the protocols to arbitrary graph size. The NISQ processor experiments realise the expected quantum advantage with high accuracy for rendezvous on the complete graph K3. In contrast, for the graph 2K4, formed by two disconnected 4-vertex complete graphs, the performance of the NISQ hardware is sub-classical, consistent with the deeper circuit and known qubit decoherence and gate error rates.