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

TL;DR

This paper establishes a link between qubits and Weyl spinors, introduces unitary transformations acting as quantum gates and decoherence cancelers, and explores their implications in relativistic quantum mechanics.

Contribution

It introduces a family of coordinate-dependent unitary transformations connecting qubits and Weyl spinors, demonstrating their role as quantum gates and symmetry transformations.

Findings

Transformations act as quantum NOT and parity gates.

They can cancel decoherence in dynamical decoupling.

Provide a unitary symmetry for Weyl equations.

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.