Contextuality supplies the magic for quantum computation

Mark Howard, IQC Waterloo
Event Date and Time: 
Tue, 2014-03-25 14:00 - 15:00
Hennings 309B
Local Contact: 
Robert Raussendorf
Intended Audience: 
Quantum information enables dramatic new advantages for computation, such as Shor's factoring algorithm and quantum simulation algorithms. This naturally raises the fundamental question: what unique resources of the quantum world enable the advantages of quantum information? There have been many attempts to answer this question, with proposals including the hypothetical "quantum parallelism" some associate with quantum superposition, the necessity of large amounts of entanglement, and much ado about quantum discord. Unfortunately none of these proposals have proven satisfactory, and, in particular, none have helped resolve outstanding challenges confronting the field. For example, on the theoretical side, the most general classes of problems for which quantum algorithms might offer an exponential speed-up over classical algorithms are poorly understood. On the experimental side, there remain significant challenges to designing robust, large-scale quantum computers, and an important open problem is to determine the minimal physical requirements of a useful quantum computer. A framework identifying relevant resources for quantum computation should help clarify these issues, for example, by identifying new efficient simulation schemes for classes of quantum algorithms and by clarifying the trade-offs between the distinct physical requirements for achieving robust quantum computation. Here we establish that quantum contextuality, a generalization of nonlocality identified by Bell and Kochen-Specker almost 50 years ago, is a critical resource for quantum speed-up within the leading model for fault-tolerant quantum computation, magic state distillation. We prove our results by finding the exact value of the independence number in an infinite family of graphs, which is a particular instance of an NP-hard problem. Ref: arXiv:1401.4174
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