An example of universal braiding in Links--Gould topological quantum computation

Abstract:We construct a universal quantum computational encoding via braiding in Links--Gould fusion spaces associated to $U_q^H(\mathfrak{sl}(2|1))$ where $q$ is on the unit circle and is not a root of unity. The construction uses only neglectons and is realized in the morphism spaces $\mathrm{Hom}_{U_q^H}(V(0,\alpha),V(0,-\frac{1}{2})^{\otimes 2N}\otimes V(0,\alpha)).$ Under explicit positivity and arithmetic constraints these spaces admit a $2^N$-dimensional computational subspace with a positive definite Hermitian form. We prove single-qubit density in $\mathrm{U}(2,1)$ and approximate arbitrary unitary operators on $N$-qubit computational subspaces with arbitrarily small leakage. The calculations use explicit inclusions, projections, and Hermitian pairings without requiring $F$-matrices.

Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el); Quantum Algebra (math.QA)

arXiv:2611.04290 [quant-ph]

(or arXiv:2611.04290v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2611.04290 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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