PreprintCC BY 4.0arXiv
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 UqH(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 HomUqH(V(0,α),V(0,−1/2)⊗ 2N⊗ V(0,α)). Under explicit positivity and arithmetic constraints these spaces admit a 2N-dimensional computational subspace with a positive definite Hermitian form. We prove single-qubit density in 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.
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BibTeX
@misc{harper2026example,
title = {{An example of universal braiding in Links--Gould topological quantum computation}},
author = {Matthew Harper and Ben-Michael Kohli},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04290},
eprint = {2611.04290},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04290},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An example of universal braiding in Links--Gould topological quantum computation
AU - Matthew Harper
AU - Ben-Michael Kohli
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04290
UR - https://arxiv.org/abs/2611.04290
AB - We construct a universal quantum computational encoding via braiding in Links--Gould fusion spaces associated to U_q^H(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 Hom_U_q^H(V(0,α),V(0,−1/2)^⊗ 2N⊗ V(0,α)). 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 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.
ER -