Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Negative Quasi-Probability as a Resource for Quantum Computation   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 analog
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.

10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas