Contextuality supplies the ‘magic’ for quantum computation

Quantum computers promise dramatic advantages over their classical counterparts, but 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, which is the leading model for experimentally realizing a fault-tolerant quantum computer. This is a conceptually satisfying link, because contextuality, which precludes a simple ‘hidden variable’ model of quantum mechanics, provides one of the fundamental characterizations of uniquely quantum phenomena. Furthermore, this connection suggests a unifying paradigm for the resources of quantum information: the non-locality of quantum theory is a particular kind of contextuality, and non-locality 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 putting bounds on the overhead cost for the classical simulation of quantum algorithms. Quantum computing promises advantages over classical computing for certain problems; now ‘quantum contextuality’ — a generalization of the concept of quantum non-locality — is shown to be a critical resource that gives the most promising class of quantum computers their power. Quantum computing in context It is widely appreciated that quantum computing promises advantages over classical computing in certain circumstances and for certain problems. But what are the specific features of quantum mechanics that are ultimately responsible for this enhanced potential? Mark Howard and colleagues identify 'quantum contextuality' — a generalization of the concept of quantum non-locality — as the critical resource that gives quantum computers their power. This finding not only provides clarification of the theoretical basis of quantum computing, it also provides a framework for directing experimental efforts to most effectively harness the weirdness of quantum mechanics for computational tasks.