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Self-concordant Schr\"odinger operators: spectral gaps and optimization without condition numbers
Sander Gribling, Simon Apers, Harold Nieuwboer, Michael Walter
https://arxiv.org/abs/2510.06115

Self-concordant Schrödinger operators: spectral gaps and optimization without condition numbers
Spectral gaps play a fundamental role in many areas of mathematics, computer science, and physics. In quantum mechanics, the spectral gap of Schrödinger operators has a long history of study due to its physical relevance, while in quantum computing spectral gaps are an important proxy for efficiency, such as in the quantum adiabatic algorithm. Motivated by convex optimization, we study Schrödinger operators associated with self-concordant barriers over convex domains and prove non-asymptotic …