Cihan Okay

Contextuality and Wigner-function negativity in qubit quantum computation

We describe schemes of quantum computation with magic states on qubits for which contextuality and negativity of the Wigner function are necessary resources possessed by the magic states. These schemes satisfy a constraint. Namely, the non-negativity of Wigner functions must be preserved under all available measurement operations. Furthermore, we identify stringent consistency conditions on such computational schemes, revealing the general structure by which negativity of Wigner functions, hardness of classical simulation of the computation, and contextuality are connected.

Homotopy colimits of classifying spaces of abelian subgroups of a finite group

The classifying space BG of a topological group

Equivalence between contextuality and negativity of the Wigner function for qudits

G

Colimits of abelian groups

can be filtered by a sequence of subspaces

Spherical posets from commuting elements

B(q,G)

Contextuality as a Resource for Models of Quantum Computation with Qubits

, using the descending central series of free groups. If

Contextuality as a resource for qubit quantum computation

G

Topological proofs of contextuality in quantum mechanics

is finite, describing them as homotopy colimits is convenient when applying homotopy theoretic methods. In this paper we introduce natural subspaces

The cohomological and the resource-theoretic perspective on quantum contextuality: common ground through the contextual fraction

B(q,G)_p

A computationally universal phase of quantum matter

of