Fold-Transversal Clifford Gates for Quantum Codes

Quantum 8, 1372 (2024).

https://doi.org/10.22331/q-2024-06-13-1372

We generalize the concept of folding from surface codes to CSS codes by considering certain dualities within them. In particular, this gives a general method to implement logical operations in suitable LDPC quantum codes using transversal gates and qubit permutations only.
To demonstrate our approach, we specifically consider a [[30, 8, 3]] hyperbolic quantum code called Bring’s code. Further, we show that by restricting the logical subspace of Bring’s code to four qubits, we can obtain the $full$ Clifford group on that subspace.