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).
- "Quantum state certification," C Badescu, R O'Donnell, and J Wright. 51st Annual ACM SIGACT Symposium on Theory of Computing (2019)
- "The SDP value for random two-eigenvalue CSP's," S Mohanty, R O'Donnell, and P Paredes. arXiv 1906.06732 (2019)
- "Lower bounds for testing complete positivity and quantum separability," C Badescu and R O'Donnell. arXiv 1905.01542 (2019)
- "X-Ramanujan Graph," S Mohanty and R O'Donnell. arXiv 1904.03500
- "Optimal mean-based algorithms for trace reconstruction." De, Anindya, Ryan O’Donnell, and Rocco A. Servedio. The Annals of Applied Probability 29, no. 2 (2019): 851-874.