LEGO_HQEC: Automating the Analysis, Construction, and Decoding of Holographic Quantum Codes

Quantum error correction (QEC) is a crucial prerequisite for future large-scale quantum computation. Finding and analyzing new QEC codes, along with efficient decoding and fault-tolerance protocols, is central to this effort. Holographic codes are a recent class of generalized concatenated codes derived from holographic bulk/boundary dualities. In addition to exploring the physics of such dualities, these codes possess useful QEC properties such as tunable encoding rates, distance scaling competitive with other well-studied code classes,and excellent recovery thresholds. To allow for a comprehensive analysis of holographic code constructions, we introduce LEGO_HQEC, a software package utilizing the quantum LEGO formalism. This package allows for the construction and analysis of holographic codes on regular hyperbolic tilings, computing their stabilizer generators and logical operators for a specified number of seed codes and layers. Three decoders are included: an erasure decoder based on Gaussian elimination; an integeroptimization decoder; and a tensor-network decoder. With these tools, LEGO_HQEC enables systematic studies of both previously known holographic codes and novel variants. As a demonstration, we provide new numerical results on the holographic blackhole pentagon code, establishing its threshold behavior under the erasure channel as a benchmark example.