ON THE GEOMETRY AND INVARIANTS OF QUBITS, QUARTITS AND OCTITS

DOI10.1142/S0219887811005142zbMath1216.81051arXiv1005.1997MaRDI QIDQ3007735

Michel Planat

Publication date: 17 June 2011

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.1997

zbMATH Keywords

finite groupsinvariant theorymultilevel systems\(E_{8}\) Weyl groupquartits

Mathematics Subject Classification ID

Quantum computation (81P68) Statistical mechanics of solids (82D20) Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) (14D21) Applications of group representations to physics and other areas of science (20C35)

Related Items (2)

Molien generating functions and integrity bases for the action of the \(\mathrm{SO}(3)\) and \(\mathrm{O}(3)\) groups on a set of vectors ⋮ Universal quantum computing and three-manifolds

Cites Work

• Unnamed Item
• A survey of finite algebraic geometrical structures underlying mutually unbiased quantum measurements
• Multi-line geometry of qubit-qutrit and higher-order Pauli operators
• Three-qubit entangled embeddings of \(CPT\) and Dirac groups within \(E_8\) Weyl group
• An algorithm to calculate optimal homogeneous systems of parameters
• Modular invariance property of association schemes, type II codes over finite rings and finite abelian groups and reminiscences of François Jaeger (a survey)
• The Magma algebra system. I: The user language
• Self-dual codes and invariant theory
• Exact polynomial eigenmodes for homogeneous spherical 3-manifolds
• An angular momentum approach to quadratic Fourier transform, Hadamard matrices, Gauss sums, mutually unbiased bases, the unitary group and the Pauli group
• Geometry of entangled states, Bloch spheres and Hopf fibrations
• Projective ring line of an arbitrary single qudit
• The invariants of the Clifford groups
• Experimental evidence for the occurrence of \(E_8\) in nature and the radii of the Gosset circles.

This page was built for publication: ON THE GEOMETRY AND INVARIANTS OF QUBITS, QUARTITS AND OCTITS