Bad Qubits — Learn Quantum by Doing

Multiple choice

Why are anyons possible in two spatial dimensions but not in three or more? The lesson attributes the difference to the fundamental group of the configuration space of n distinct points.

In d >= 3 the braid group B_n applies, while in d = 2 the permutation group S_n applies
In d >= 3 the relevant group is the (finite) permutation group S_n, forcing exchange eigenvalues +-1; in d = 2 it is the infinite, noncommutative braid group B_n, allowing fractional and non-abelian statistics
Anyons require zero temperature, which is only achievable in two dimensions
In d = 2 there are simply fewer particles, so more exotic statistics fit