On the geometry and invariants of qubits, quartits and octits

Abstract

Four level quantum systems, known as quartits, and their relation to two- qubit systems are investigated group theoretically. Following the spirit of Klein's lectures on the icosahedron and their relation to Hopf sphere bra- tions, invariants of complex re ection groups occuring in the theory of qubits and quartits are displayed. Then, real gates over octits leading to the Weyl group of E8 and its invariants are derived. Even multilevel systems are of interest in the context of solid state nuclear magnetic resonance.

version to be published in International Journal of Geometric Methods in Modern Physics (IJGMMP)

References in corpus (9)

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• Projective Ring Line of an Arbitrary Single Qudit
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Cited by in corpus (4)

• Pauli graphs when the Hilbert space dimension contains a square: why the Dedekind psi function ?
• Majorana representation of adiabatic and superadiabatic processes in three-level systems
• Majorana representation, qutrit Hilbert space and NMR implementation of qutrit gates
• A Sequence of Qubit-Qudit Pauli Groups as a Nested Structure of Doilies