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This research establishes that distributed quantum algorithms for 3-coloring cycles require Ω(n) communication rounds, proving no speed-up exists over classical methods for this specific symmetry-breaking problem. By deriving the first genuinely quantum lower bound independent of physical causality assumptions, the work clarifies the intrinsic limits of quantum advantage in networked computing scenarios.

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Algorithms Require at Least N Rounds to Colour Cycles with Quantum Computers

Quantum ZeitgeistAugust 17, 20265 min read

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.

A new lower bound demonstrates that any distributed quantum algorithm solving a 3-coloring problem on a cycle of computers with probability 1 requires Ω(n) communication rounds. Xavier Coiteux-Roy of the University of Waterloo and colleagues have shown that quantum computers offer no speed advantage when solving the 3-coloring of a cycle, a network where computers are connected in a closed loop. The team's findings isolate quantum computational power, as they do not rely on previous assumptions about the fundamental limits of information transfer. Xavier Coiteux-Roy and colleagues developed a new method to differentiate between…

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