5 papers
Braided quantum mechanics and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework
Zhanna Kuznetsova, Francesco Toppan
We introduce color Heisenberg-Lie (super)algebras graded by the abelian groups , for , and investigate the properties of their associated multi-…
Braided Majorana qubits as a minimal setting for Topological Quantum Computation?
Francesco Toppan
I point out that a possible minimal setting to realize Kitaev's proposal of a Topological Quantum Computation which offers topological protection from decoherence could in principl…
On braid statistics versus parastatistics
Francesco Toppan
I report the recent advances in applying (graded) Hopf algebras with braided tensor product in two scenarios: i) paraparticles beyond bosons and fermions living in any space dimens…
On the Classification of the Lévy-Leblond Spinors
Luiza Miranda, Isaque P. de Freitas, Francesco Toppan
The first-order Lévy-Leblond differential equations (LLEs) are the non-relativistic analogous of the Dirac equation: they are the "square roots" of the Schrödinger equation in ($…
Volichenko-type metasymmetry of braided Majorana qubits
Francesco Toppan
This paper presents different mathematical structures connected with the parastatistics of braided Majorana qubits and clarifies their role; in particular, mixed-bracket Heisenberg…