The Commuting Local Hamiltonian Problem: Relativized Evidence Against BQP-Hardness

arXiv:2609.38957 · quant-ph, cs.CC · Submitted 2026-09-30 · Read on arXiv

quant-ph, cs.CC

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Verifier — 118× in this paper · explained in 2 episodes
• BQP — 11× in this paper · explained in 2 episodes
• Verification — 10× in this paper · explained in 2 episodes
• Query Complexity — 9× in this paper · explained in 2 episodes
• Ancilla Qubits — 5× in this paper · explained in 1 episode
• Trace — 5× in this paper · explained in 2 episodes
• Approximation Bound — 3× in this paper · explained in 1 episode
• Hamming Distance — 3× in this paper · explained in 2 episodes
• Core — 2× in this paper · explained in 2 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Adaptivity — 1× in this paper · explained in 1 episode
• Area Law — 1× in this paper · explained in 1 episode
• Entanglement — 1× in this paper · explained in 3 episodes
• Gibbs State — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Topological Order — 1× in this paper · explained in 2 episodes

Sources

• IQP circuits for 2-Forrelation

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