Computing efficiently in QLDPC codes.

Quantum error correction is essential for building utility-scale quantum computers that outperform classical machines, yet leading approaches incur substantial physical qubit overhead. Quantum low-density parity check (QLDPC) codes offer a promising alternative by significantly reducing the number of physical qubits required per logical qubit. However, existing work on QLDPC codes has focused primarily on quantum memories, with no efficient method known for implementing arbitrary logical Clifford operations at low circuit depth. Here, we introduce a new family of QLDPC codes that enables efficient implementation of the full Clifford group via transversal operations, allowing any m-qubit Clifford operation to be executed in at most O(m) syndrome extraction rounds. We run circuit-level simulations of depth-126 logical circuits to demonstrate the near-memory logical performance of these logical operations. In combination with known methods for implementing T gates, these results establish QLDPC codes as a viable route toward resource-efficient universal quantum computation.