operations research and operations management applications―by bringing ideas and methods from algebraic geometry, geometry of numbers and algebraic topology to quantum computing. The research program has several thrusts: Use computational algebraic geometry and Knuth–Bendix completion algorithm to compile on quantum computers (both AQC and NISQ). Develop novel hybrid quantum-classical algorithms and quantum-inspired classical Graver Augmented Multi-seed Algorithm (GAMA) for non-linear integer optimization with non-convex objective functions. The group has conducted numerical testing on D-Wave of their new hybrid quantum-classical algorithm to compute Graver basis, which is known to be useful in many applications of non-linear integer optimization and game theory and use it for optimization. The group has applied the above algorithms to Cancer Genomics to study acute myeloid leukemia. The group is also the first to introduce Morse theory, Cerf theory (from algebraic topology), and Gauss–Bonnet theorem (from differential geometry) to understand adiabatic quantum computation at a fundamental level by studying the deformation of Hamiltonian surface and evolution of (and around) anti-crossings. In collaboration with NASA's Quantum Artificial Intelligence Lab (QuAIL), the group has developed mathematical programming methods for minor-embedding in quantum annealers such as D-Wave. In 2020, with support from National Science Foundation and in partnership with Universities Space Research Association and Amazon, he co-developed and co-taught a course on Quantum Integer Programming, which is freely available to students and researchers around the globe. In 2021, this course was expanded to include Quantum Machine Learning. Tayur's work on quantum computing has been covered by Ars Technica and Notices of the American Mathematical Society. In 2020, he was inducted into Pittsburgh Quantum Institute, as the first business school professor to join as a member. In a 2020 interview with Fortune, he endorsed the White House's proposed budget that doubled the Federal spending for artificial intelligence and quantum computing, citing the governments' crucial role in fueling basic research and that major tech firms such as Alphabet and Facebook “are doing research in A.I. that benefits their business models.” He is an executive committee member of Pittsburgh Quantum Institute. Unconventional computing Tayur's TEDxCMU2020 talk discusses "Magical Unconventional Computing beyond Quantum." He is currently developing and supporting research on room-temperature Ising machines with collaborators from IIT Madras and National University of Singapore. Quantum communications Quantum queue-channels arise naturally in the context of buffering in quantum networks. Collaborating with researchers at IIT-Madras, Tayur has studied Unital Qubit (that includes the important case of