Near-Optimal Bounds on the Density of Low-Energy States of k-Local Hamiltonians and Faster Quantum Algorithms

arXiv:2609.34532 · quant-ph, cs.CC, cs.DS · Submitted 2026-09-28 · Read on arXiv

quant-ph, cs.CC, cs.DS

Submitted: 2026-09-28

Updated: 2026-09-28

Terminology

• Accuracy — 4× in this paper · explained in 1 episode
• Trace — 3× in this paper · explained in 2 episodes
• Benchmark — 2× in this paper · explained in 2 episodes
• Spectral Gap — 2× in this paper · explained in 5 episodes
• Accountability — 1× in this paper · explained in 2 episodes
• BQP — 1× in this paper · explained in 2 episodes
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Electronic Colloquium on Computational Complexity — 1× in this paper
• Fidelity — 1× in this paper · explained in 2 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes
• Quantum Phase Estimation (QPE) — 1× in this paper · explained in 3 episodes
• Quantum Physics — 1× in this paper · explained in 10 episodes
• Quantum Strong Exponential-Time Hypothesis — 1× in this paper
• Variational Quantum Eigensolver — 1× in this paper
• Variational Quantum Eigensolver (VQE) — 1× in this paper · explained in 5 episodes

Sources

• An Entropy-Governed Speedup for Quantum Algorithms on Local Hamiltonians
• Optimal Lower Bound for Ground-State Energy Estimation with a Guiding State

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