turkmath.org

A central question in quantum information theory is to determine physical resources required for quantum computational speedup. Such resources are characterized in terms of intrinsic features of quantum states which include various notions such as quantum contextuality, quasiprobability representations and topological phases. Each of these notions correspond to a different perspective taken on the question of where the computational power is hidden. We take a topological approach based on the recently established connection between classifying spaces from algebraic topology and the study of quantum contextuality from quantum foundations. I will describe this new topological approach to quantum contextuality and a recently developed classical simulation algorithm for quantum computation with magic states. The simulation algorithm will be used to motivate possible ways of extending the role of topology in the study of quantum computational resources.