  It has been shown that non-stabilizer eigenstates of permutation gates are
appropriate for allowing $d$-dimensional universal quantum computing (uqc)
based on minimal informationally complete POVMs. The relevant quantum gates may
be built from subgroups of finite index of the modular group
$\Gamma=PSL(2,\mathbb{Z})$ [M. Planat, Entropy 20, 16 (2018)] or more generally
from subgroups of fundamental groups of $3$-manifolds [M. Planat, R. Aschheim,
M.~M. Amaral and K. Irwin, arXiv 1802.04196(quant-ph)]. In this paper, previous
work is encompassed by the use of torsion-free subgroups of Bianchi groups for
deriving the quantum gate generators of uqc. A special role is played by a
chain of Bianchi congruence $n$-cusped links starting with Thurston's link.
