Corrigendum: Negative quasi-probability as a resource for quantum computation

Victor Veitch, Christopher Ferrie, David Gross, Joseph Emerson
2013 New Journal of Physics  
Quasi-probability representations of quantum theory with applications to quantum information science Christopher Ferrie Fundamentals of universality in one-way quantum computation M Van den Nest, W Dür, A Miyake et al. Framed Hilbert space: hanging the quasi-probability pictures of quantum theory Abstract. A central problem in quantum information is to determine the minimal physical resources that are required for quantum computational speedup and, in particular, for fault-tolerant quantum
more » ... tation. We establish a remarkable connection between the potential for quantum speed-up and the onset of negative values in a distinguished quasi-probability representation, a discrete analogue of the Wigner function for quantum systems of odd dimension. This connection allows us to resolve an open question on the existence of bound states for magic state distillation: we prove that there exist mixed states outside the convex hull of stabilizer states that cannot be distilled to non-stabilizer target states using stabilizer operations. We also provide an efficient simulation protocol for Clifford circuits that extends to a large class of mixed states, including bound universal states.
doi:10.1088/1367-2630/15/3/039502 fatcat:ipshie65azfeder5b3tpc45hni