Variable-Cliff Nielsen Geometry and an Exponent-4/3 Lower Bound for the Infinite-Cliff Diameter

arXiv:2609.03323 · quant-ph, math-ph, math.MP, math.PR · Submitted 2026-09-03 · Read on arXiv

quant-ph, math-ph, math.MP, math.PR

Submitted: 2026-09-03

Updated: 2026-09-16

Comments: Minor revision: corrected a citation and the corresponding bibliographic entry. No changes to the mathematical results

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Trace — 9× in this paper · explained in 2 episodes
• Hilbert Space — 3× in this paper · explained in 2 episodes
• Regularization — 2× in this paper · explained in 3 episodes
• Admissibility — 1× in this paper · explained in 2 episodes
• Homogeneity — 1× in this paper · explained in 2 episodes

Sources

• A Quantum Complexity Lowerbound from Differential Geometry
• Nielsen complexity with multiple cost factors
• Conjugate points on Lie groups with left-invariant metrics

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