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. Quantum LDPC codes can shield quantum computers from decoherence with minimal overhead. In this work, the authors describe a new QLDPC family, SHYPS, as a path to practical fault tolerance with efficient Clifford circuit implementation on encoded states.

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Nature

A new family of quantum low-density parity check (QLDPC) codes called SHYPS is introduced, enabling efficient implementation of the full Clifford group via transversal operations. Any m-qubit Clifford operation can be executed in at most O(m) syndrome extraction rounds, addressing a key gap where prior QLDPC work focused only on quantum memories without efficient logical gate implementations. Circuit-level simulations of depth-126 logical circuits demonstrate near-memory logical performance. Combined with known T gate methods, this establishes QLDPC codes as a viable path to resource-efficient universal quantum computation with reduced physical qubit overhead.

Computing efficiently in QLDPC codes