Quantum Advantage for Distributed Symmetry Breaking

arXiv:2609.26788 · quant-ph, cs.DC · Submitted 2026-09-22 · Read on arXiv

quant-ph, cs.DC

Submitted: 2026-09-22

Updated: 2026-09-22

Terminology

• Trace — 6× in this paper · explained in 2 episodes
• Hilbert Space — 4× in this paper · explained in 2 episodes
• Local Optimization — 2× in this paper · explained in 2 episodes
• Symmetry Breaking — 2× in this paper · explained in 3 episodes
• AI Agents — 1× in this paper · explained in 2 episodes
• Entanglement — 1× in this paper · explained in 4 episodes
• Generalization — 1× in this paper · explained in 13 episodes

Sources

• Distributed Quantum Algorithms Cannot Color Cycles with Probability 1
• Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
• No Distributed Quantum Advantage for 3-Coloring Rooted Trees and 2-Coloring Even Cycles
• Impossibility of One-Way One-Round Quantum 4-Coloring via Matrix-Space Stability
• Non-trivial lower bound for 3-coloring the ring in the quantum LOCAL model

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