Placing and Routing Non-Local Quantum Error Correcting Codes in Multi-Layer Superconducting Qubit Hardware

  1. Melvin Mathews,
  2. Lukas Pahl,
  3. David Pahl,
  4. Vaishnavi L. Addala,
  5. Catherine Tang,
  6. William D. Oliver,
  7. and Jeffrey A. Grover
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 pdf

leave comment