Graded Paraparticle Algebra of Majorana Fields for Multidimensional Quantum Computing with Structured Light

• URL: http://arxiv.org/abs/2505.23232v1
• Date: Thu, 29 May 2025 08:34:29 GMT
• Title: Graded Paraparticle Algebra of Majorana Fields for Multidimensional Quantum Computing with Structured Light
• Authors: Fabrizio Tamburini, Nicolò Leone, Matteo Sanna, Roberto Siagri,
• Abstract summary: We present a framework that integrates Majorana's infinite-component relativistic equation within the algebraic structure of paraparticles.<n>By mapping spin-dependent mass spectra to graded sectors associated with generalized quantum statistics, we derive an equation embodying Majorana's mass-spin relation.<n>This approach makes possible to set paraparticle-based quantum information processing, beyond fermions and bosons, using graded qudits.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a theoretical framework that integrates Majorana's infinite-component relativistic equation within the algebraic structure of paraparticles through the minimal nontrivial $\mathbb{Z}_2 \times \mathbb{Z}_2$--graded Lie algebras and $R$-matrix quantization. By mapping spin-dependent mass spectra to graded sectors associated with generalized quantum statistics, we derive an equation embodying Majorana's mass-spin relation describing Majorana quasiparticles of structured light carrying spin and orbital angular momentum. These quanta in the $\mathbb{Z}_2 \times \mathbb{Z}_2$--graded algebras and $R$-matrix formulations extend the previous results from superconducting qubits to photonic platforms and set up deterministic 2-photon gates involving at least two qubits encoded in a single photon without nonlinear effects. This makes feasible general quantum computing pathways exploiting fractional statistics through Nelson's quantum mechanics and implement a novel 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.

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