My research is in the areas of quantum computation, quantum complexity theory, and quantum information. I am particularly interested in the mathematical theory of quantum tomography, as well as related problems concerning testing, certifying, and learning quantum states with low sample complexity and computational complexity. I like to apply a wide range of mathematical tools (representation theory, probability, combinatorics, Fourier analysis) when attacking problems in the theory of quantum computation and quantum information.
- "Optimal Inapproximability Results for MAX‐CUT and Other 2‐Variable CSPs?," Subhash Khot, Guy Kindler, Elchanan Mossel, and Ryan O’Donnell, SIAM J. Comput.,37, 319 (2007)
- "Analysis of Boolean Functions," Ryan O’Donnell,Cambridge University Press (2014).
- "Noise stability of functions with low influences: invariance and optimality,"Elchanan Mossel, Ryan O'Donnell, Krzysztof Oleszkiewicz, FOCS 171, 295 (2005).
- "Learning functions of k relevant variables," Elchanan Mossel, Ryan O’Donnell, and Rocco A. Servedioc, Journal of Computer and System Sciences 69, 421 (2004).
- "Learning intersections and thresholds of halfspaces," Adam R. Klivans, Ryan O’Donnell, and Rocco A. Servedio, Journal of Computer and System Sciences 68, 808 (2004).
- "The Weakness of CTC Qubits and the Power of Approximate Counting," Ryan O’Donnell, A. C. Cem Say, ACM Transactions on Computation Theory 10, 2 (2018).
- "A log-Sobolev inequality for the multislice, with applications," Yuval Filmus, Ryan O’Donnell, Xinyu Wu, arXiv:1809.03546v1 (2018).
- "SOS lower bounds with hard constraints: think global, act local," Pravesh K. Kothari, Ryan O’Donnell, Tselil Schramm, arXiv:1809.01207v (2018).
- "Fooling Polytopes," Ryan O’Donnell, Rocco A. Servedio, Li-Yang Tan, arXiv:1808.04035v1 (2018).
- "On closeness to k-wise uniformity," Ryan O’Donnell, Yu Zhao, arXiv:1806.03569v1 (2018).