Joint Optimization of Clifford-Deformed Surface Codes and Neural Decoders

Quantum error correction can exponentially suppress physical qubit error rates, with the rotated surface code being one of the leading candidates. However, realizing this advantage requires a large number of physical qubits per logical qubit. Recent work [Dua et al., PRX Quantum 5, 010347 (2024)] demonstrated that Clifford-deforming the surface code stabilizers under high noise bias can substantially reduce this overhead. Building on this idea, we identify two key challenges that arise when applying Clifford deformations: (1) the exponentially large search space of possible deformations, and (2) the suboptimal performance of conventional decoders on deformed codes.

We present a joint learning framework that simultaneously narrows the search space over Clifford-deformed codes and trains a neural-network decoder. This coupled optimization efficiently discovers high-performing code-decoder pairs, achieving improved logical error rates while reducing the computational cost of exploring the deformation space.