Author

Guneykan Ozgul

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Preprint Sep 2026

Super-Quadratic Quantum Speedups for Combinatorial Optimization via Tilted Walks

We introduce quantum tilted walks, a quantum algorithmic framework for solving exact combinatorial optimization problems. The framework applies an average of powers of a tilted Hamiltonian that biases the discriminant matrix of a base Markov chain (mixer) with the objective function. Our starting point is quantum short...

Guneykan Ozgul, Shouvanik Chakrabarti · 0 citations

Preprint Sep 2026

Near-Optimal Quantum Lower Bounds for Convex Optimization via Fourier Rank

We establish a near-linear quantum query lower bound for high-accuracy convex optimization over an explicit family of $n$-dimensional ellipsoids. We focus on linear optimization with an explicitly given objective, where the feasible set is accessed through a membership oracle. We show that any algorithm that, for every...

Brandon Augustino, Shouvanik Chakrabarti, Enrico Fontana et al. · 1 citation

#machine learning Apr 2025

Quantum Speedups for Sampling and Non-Convex Optimization with Stochastic Oracles

This framework accelerates classical stochastic Langevin Monte Carlo and Hamiltonian Monte Carlo algorithms by replacing stochastic gradient estimators with variance-controlled quantum mean estimation and gradient estimation subroutines, and develops gradient estimators robust to noisy function evaluations, yielding im...

Guneykan Ozgul, Xian-Tao Li, Mehrdad Mahdavi et al. · Theory of Quantum Computatio... · 6 citations · ⚡1