Qubits, Weyl spinors, quantum NOT gates, and dynamical decoupling

Abstract

An equivalence is established between orthogonal pure state qubits on the Bloch sphere and massless Weyl spinors, when the Bloch vector is taken as the physical three-momentum. A family of unitary, coordinate dependent transformations is obtained which connects orthogonal combinations of the basis states of a two-level quantum system. It is shown that a subset of these transformations possesses the novel feature of effecting a point inversion by means of a rotation. For qubits, these transformations act as quantum NOT/parity gates, and also as flipping operators that exactly cancel decoherence in a dynamical decoupling setting. For Weyl spinors they provide, at the relativistic quantum level, a unitary symmetry transformation for the Weyl equations.

Improved version with added results in dynamical decoupling and added references, sections reorganized and a new one added. Title and abstract modified to reflect the changes. 11 pages, 1 figure, and 1 table