Subsystem bivariate bicycle codes achieve high-rate BB logical qubits with local four-qubit gauge checks, yielding examples such as [[108,12,6]] that outperform surface-code alternatives.
Coupled-Layer Construction of Quantum Product Codes
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abstract
Product codes are a class of quantum error correcting codes built from two or more constituent codes. They have recently gained prominence for a breakthrough yielding quantum low-density parity-check (qLDPC) codes with favorable scaling of both code distance and encoding rate. However, despite its powerful algebraic formulation, the physical mechanism for assembling a general product code from its constituents remains unclear. In this letter, we show that the tensor and balanced product codes admit an intuitive coupled-layer construction by taking a stack of one code and condensing a set of excitations in the pattern given by the checks of the other code. We also make a connection to concatenated codes by showing that the tensor product code can be obtained by gauging large-weight logicals in concatenated codes, making them qLDPC. Our framework accommodates both classical or quantum CSS input codes, unifies known physical mechanisms for constructing higher dimensional topological phases via anyon condensation, and naturally extends to non-topological codes.
fields
quant-ph 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Compactification of a single higher-dimensional hypergraph-product fracton model yields a broad family of translation-invariant quantum LDPC codes that includes fracton models and all A2BGA codes such as BB codes.
citing papers explorer
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Topological subsystem bivariate bicycle codes with four-qubit check operators
Subsystem bivariate bicycle codes achieve high-rate BB logical qubits with local four-qubit gauge checks, yielding examples such as [[108,12,6]] that outperform surface-code alternatives.
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Translation-invariant quantum low-density parity-check codes from compactified fracton models
Compactification of a single higher-dimensional hypergraph-product fracton model yields a broad family of translation-invariant quantum LDPC codes that includes fracton models and all A2BGA codes such as BB codes.