Any distributed quantum algorithm guaranteeing a perfect 3-coloring on a cycle of computers demands Ω(n) communication rounds. This establishes a definitive limit, demonstrating quantum computation offers no speed-up for this symmetry-breaking problem, unlike previous bounds reliant on physical causality. This work presents the first genuinely quantum lower bound, distinguishing quantum from classically-simulatable distributions.
Algorithms Require at Least N Rounds to Colour Cycles with Quantum Computers
Any distributed quantum algorithm guaranteeing a perfect 3-coloring on a cycle of computers demands Ω(n) communication rounds. This establishes a definitive limit, demonstrating quantum computation offers no speed-up for this symmetry-breaking problem, unlike previous bounds reliant on physical causality. This work presents the first genuinely quantum lower bound, distinguishing quantum from classically-simulatable distributions.