Logical Gates in qLDPC
summary
Claims a concrete method to get transversal Clifford gates on hypergraph-product LDPC codes by choosing a kernel basis, folding paired qubits and applying local unitaries so stabilizers stay preserved. Implements Hadamard+swap on diagonal logicals, realizes logical S and S† on diagonal plus CZ between paired logicals, and shows global H on all logicals with a swap pattern. Requires either the same classical parity-check twice or a parity-check whose row- and column-spans match. Gate application is cheap and transversal; targeted CZ between individual logicals needs a round-robin that costs time scaling with code distance.
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