Negative quasi-probability as a resource for quantum computation
Victor Veitch, Christopher Ferrie, David Gross, Joseph Emerson · New Journal of Physics · 2012
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 computation.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.