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

2025/05/29 by Tamburini, Fabrizio, Leone, Nicolò, Sanna, Matteo +1 · 2 citations
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2505.23232

Abstract

We present a theoretical framework that integrates Majorana's infinite-component relativistic equation within the algebraic structure of paraparticles through the minimal nontrivial ℤ₂ × ℤ₂--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 ℤ₂ × ℤ₂--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.

Citations

• Monitoring the generation of photonic linear cluster states with partial measurements
• A Majorana Relativistic Quantum Spectral Approach to the Riemann Hypothesis in (1+1)-Dimensional Rindler Spacetimes
• On the detectability of paraparticles beyond bosons and fermions
• Para-particle oscillator simulations on a trapped ion quantum computer
• On the spectral density of the wavelet coefficients of long memory time series with application to the log-regression estimation of the memory parameter

Cited by

• Braided QM and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework
• Random-projector quantum diagnostics of Ramsey numbers and a prime-factor heuristic for R(5,5)=45

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