Graded paraparticle algebra of Majorana fields for multidimensional quantum computing with structured light

We present a theoretical framework that integrates Majorana's infinite-component relativistic equation within the algebraic structure of paraparticles through the minimal nontrivial <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi mathvariant="double-struck">Z</a:mi> <a:mn>2</a:mn> </a:msub> <a:mo>×</a:mo> <a:msub> <a:mi mathvariant="double-struck">Z</a:mi> <a:mn>2</a:mn> </a:msub> </a:mrow> </a:math> -graded Lie algebras and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mi>R</d:mi> </d:math> -matrix quantization. By mapping angular momentum-dependent mass spectra of the Majorana Tower to graded sectors associated with generalized quantum statistics, we derive an equation describing Majorana quasiparticles of structured light carrying spin and orbital angular momentum. These quanta in the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:msub> <e:mi mathvariant="double-struck">Z</e:mi> <e:mn>2</e:mn> </e:msub> <e:mo>×</e:mo> <e:msub> <e:mi mathvariant="double-struck">Z</e:mi> <e:mn>2</e:mn> </e:msub> </e:mrow> </e:math> -graded algebras and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mi>R</h:mi> </h:math> -matrix formulations extend the previous results from superconducting qubits to photonic platforms and set up deterministic two-photon gates involving at least two qubits encoded in a single photon without nonlinear effects. This makes feasible the writing of general quantum computing pathways exploiting fractional statistics through Nelson's quantum mechanics and implementing a procedure for error correction in photonic platforms. Furthermore, this approach makes possible to set paraparticle-based quantum information processing, beyond fermions and bosons, using graded qudits.