Year: 2026
Type: preprint
Abstract: We show that one-way one-round quantum-LOCAL algorithms cannot $4$-color directed cycles with high probability. This is the first lower bound in the high-probability quantum LOCAL setting that goes beyond the non-signaling and bounded-dependence models, exploiting the structure of distributed quantum algorithms. Our proof establishes a bidirectional connection between distributed quantum computing and extremal combinatorics. We obtain our lower bound by proving a Mantel-type stability theorem for weighted matrix spaces.
Source: arXiv (Cornell University)
Authors: Gur, Tom, Li, Longcheng
Institution: University of Cambridge
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: UK Research and Innovation
Award: G6654660187
OpenAlex ID: W7212048109