Gibbs Sampling in the Shattered Phase by Decoded Quantum Interferometry

arXiv:2609.40345 · quant-ph, cond-mat.dis-nn, cs.CC, cs.DS, math.PR · Submitted 2026-09-30 · Read on arXiv

quant-ph, cond-mat.dis-nn, cs.CC, cs.DS, math.PR

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Hypergraph — 21× in this paper · explained in 2 episodes
• Hamming Distance — 12× in this paper · explained in 2 episodes
• Decoded Quantum Interferometry — 9× in this paper
• Symmetry Breaking — 9× in this paper · explained in 3 episodes
• Phase Transitions — 7× in this paper · explained in 2 episodes
• Annual Symposium on Foundations of Computer Science — 6× in this paper
• Wasserstein Distance — 6× in this paper · explained in 4 episodes
• Generalization — 4× in this paper · explained in 13 episodes
• Clustering — 2× in this paper · explained in 2 episodes
• Decoded Quantum Interferometry (DQI) — 2× in this paper · explained in 2 episodes
• Quantum Circuits — 2× in this paper · explained in 2 episodes
• Unambiguous State Discrimination — 2× in this paper
• Adam — 1× in this paper · explained in 2 episodes
• Combinatorial Optimization — 1× in this paper · explained in 2 episodes
• Decode — 1× in this paper · explained in 2 episodes
• Diffusion Processes — 1× in this paper · explained in 2 episodes
• Gibbs State — 1× in this paper · explained in 2 episodes
• Langevin Dynamics — 1× in this paper · explained in 2 episodes

Sources

• Spin Glass Transitions Obstruct Decoded Quantum Interferometry
• Local algorithms and the failure of log-depth quantum advantage on sparse random CSPs
• The Quantum Decoding Problem
• The Quantum Approximate Optimization Algorithm Needs to See the Whole Graph: A Typical Case
• Efficiently constructing a quantum uniform superposition over bit strings near a binary linear code
• Regev's reduction as a candidate quantum algorithm for the discrete logarithm problem in finite abelian groups
• Full replica symmetry breaking in the Sherrington-Kirkpatrick model
• The Polynomial-Time Low-Degree Conjecture is False
• Hamiltonian Decoded Quantum Interferometry
• Optimization Using Locally-Quantum Decoders
• Computational Complexity of Statistics: New Insights from Low-Degree Polynomials
• Average-case quantum complexity from glassiness

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