Geometric algebra, qubits, geometric evolution, and all that

Abstract

The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that case. Generalization of formal complex plane to an an arbitrary plane in three dimensions and of usual Hopf fibration to the map generated by an arbitrary unit value element of even sub-algebra of the three-dimensional Geometric Algebra are resulting in more profound description of qubits compared to quantum mechanical Hilbert space formalism.

References in corpus (2)

• What quantum state really is?
• A tossed coin as quantum mechanical object

Cited by in corpus (6)

• State/observable interactions using basic geometric algebra solutions of the Maxwell equation
• The geometric algebra lift of qubits via basic solutions of Maxwell equation
• Quantum Computing with Variable Complex Plane. Light Beam Guide Implementation
• Anyons in three dimensions with geometric algebra
• Geometric phase in the G3+ quantum state evolution
• Quantum state evolution in C2 and G3+