We're familiar with Clifford gates for qubits, which have attracted a lot of attention and research effort. Clifford circuits normalize Pauli strings, i.e., under conjugation, Clifford circuits map Pauli strings to other Pauli strings. This enables efficient classical simulations of Clifford circuits.
It's natural to think about Clifford gates for higher-dimensional representations of SU(2). Say, for example, we have a collection of spin-1 degrees of freedom. These still have a notion of Pauli string where each Pauli $X, Y, Z$ now has dimension 3. My questions are
- Have the generating sets for normalizers of higher-spin Pauli groups been worked out?
- Have these "higher dimensional Clifford circuits" attracted much interest? They'd probably be interesting from the perspective of many-body theorists (my area of specialty) but I haven't heard anything about them.
Any references you could point me towards which address these subjects would be very helpful. Thanks in advance.
