  Quantum computers promise dramatic advantages over their classical
counterparts, but the answer to the most basic question "What is the source of
the power in quantum computing?" has remained elusive. Here we prove a
remarkable equivalence between the onset of contextuality and the possibility
of universal quantum computation via magic state distillation. This is a
conceptually satisfying link because contextuality provides one of the
fundamental characterizations of uniquely quantum phenomena and, moreover,
magic state distillation is the leading model for experimentally realizing
fault-tolerant quantum computation. Furthermore, this connection suggests a
unifying paradigm for the resources of quantum information: the nonlocality of
quantum theory is a particular kind of contextuality and nonlocality is already
known to be a critical resource for achieving advantages with quantum
communication. In addition to clarifying these fundamental issues, this work
advances the resource framework for quantum computation, which has a number of
practical applications, such as characterizing the efficiency and trade-offs
between distinct theoretical and experimental schemes for achieving robust
quantum computation and bounding the overhead cost for the classical simulation
of quantum algorithms.
