Melvin Mathews, Lukas Pahl, David Pahl, Vaishnavi L. Addala, Catherine Tang, William D. Oliver, Jeffrey A. Grover (Aug 01 2025).

Abstract: Quantum error correcting codes (QECCs) with asymptotically lower overheads than the surface code require non-local connectivity. Leveraging multi-layer routing and long-range coupling capabilities in superconducting qubit hardware, we develop Hardware-Aware Layout, HAL: a robust, runtime-efficient heuristic algorithm that automates and optimizes the placement and routing of arbitrary QECCs. Using HAL, we perform a comparative study of hardware cost across various families of QECCs, including the bivariate bicycle codes, the open-boundary tile codes, and the constant-depth-decodable radial codes. The layouts produced by HAL confirm that open boundaries significantly reduce the hardware cost, while incurring reductions in logical efficiency. Among the best-performing codes were low-weight radial codes, despite lacking topological structure. Overall, HAL provides a valuable framework for evaluating the hardware feasibility of existing QECCs and guiding the discovery of new codes compatible with realistic hardware constraints.

Arxiv: https://arxiv.org/abs/2507.23011