Louvre: Relaxing Hardware Requirements of Quantum LDPC Codes by Routing with Expanded Quantum Instruction Set

Abstract Generalized bicycle codes (GB codes) represent a promising family of quantum low-density parity-check codes, characterized by high code rates and relatively local qubit connectivity. A subclass of the GB code called bivariate bicycle codes (BB codes) has garnered significant interest due to its compatibility with two-layer connectivity architectures on superconducting quantum processors. However, one key limitation of BB codes is the high qubit connectivity degree requirements (degree 6), which exacerbates the noise susceptibility of the system. Building on the recent progress in implementing multiple two-qubit gates on a single chip, this work introduces Louvre—a routing-based framework designed to reduce qubit connectivity requirements in GB codes. Specifically, Louvre-7 achieves degree reduction while preserving the depth of the syndrome extraction circuit, whereas Louvre-8 further minimizes the connectivity by slightly increasing the circuit depth. When applied to BB codes, these two schemes could reduce the average degree to 4.5 and 4, respectively. Crucially, Louvre eliminates some of the long-range, error-prone connections, which is a distinct advantage over prior approaches. Numerical simulations demonstrate that Louvre-7 has an logical error rate indistinguishable from that of the standard syndrome extraction circuits of GB codes, while Louvre-8 only incurs a slight error rate penalty.