Everyone is welcome to attend the N&O lecture of Arne Heimendahl, with the title: 'Faces of the stabilizer polytope and robustness measures'.
Abstract:
The stabiliser polytope plays an essential role in the magic state model of fault tolerant quantum computation. In this model all
unitary gates belong to the Clifford group and Non-Clifford operations are effectuated by injecting magic states.
The stabiliser polytope lives in the space of 2^n x 2^n Hermitian matrices with trace one. Its vertices are stabiliser states, which are rank one projectors onto the common +1 eigenspace of certain sets of Pauli matrices acting on n qubits. These sets are precisely abelian subgroups of order 2^n in the Pauli group acting on n qubits.
Applying a basis transformation, the stabiliser polytope can be embedded in a larger family of integral polytopes living in the (4^n -1)-dimensional real Euclidean space and I will investigate a certain type of its faces which are related to integral points in a dual version of these polytopes.
Besides, I will discuss the application of a hyperplane description of a polytope to the 'robustness of magic', a measure that is closely related to the robustness of entanglement and measures the utility of a state for the procedure of magic state distillation.
