Problem
Research questions and friction points this paper is trying to address.
one-way one-round quantum LOCAL algorithms
4-coloring
directed cycles
Impossibility of One-Way One-Round Quantum 4-Coloring via Matrix-Space Stability
🤖 AI Summary
本文证明了单向单轮量子LOCAL算法无法以高概率对有向环进行4着色，通过将分布式量子计算与非交换极值组合学联系起来解决问题。
📝 Abstract
We show that one-way one-round quantum LOCAL algorithms cannot $4$-color directed cycles with high probability, even with unbounded local computation and quantum message length. 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 connects distributed quantum computing with noncommutative extremal combinatorics by identifying local collision probabilities with the weighted multiplicative energy of matrix-space decompositions. We obtain our lower bound by proving a dimension-independent weighted stability theorem for a directed noncommutative analogue of Mantel's theorem.
Innovation
Methods, ideas, or system contributions that make the work stand out.
quantum LOCAL algorithms
noncommutative extremal combinatorics
weighted stability theorem
matrix-space decompositions
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