Placing and routing quantum LDPC codes in multilayer superconducting hardware
ORAL
Abstract
Quantum error-correcting codes with asymptotically lower overheads than the surface code require nonlocal connectivity [1]. Leveraging multilayer 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 codes. Using HAL, we generate around 150 explicit layouts of quantum low-density parity-check (qLDPC) codes with topological structure—such as the bivariate bicycle codes [2, 3] and the open-boundary tile codes [4, 5]—and find that removing the periodic boundaries significantly lowers the hardware complexity with only a moderate reduction of logical efficiency. We also lay out highly nonlocal qLDPC code families— quantum radial [6] and Tanner codes [7]—that achieve competitive tradeoffs between hardware complexity and logical efficiency. Based on our findings, we anticipate many novel qLDPC codes to be realizable on near-term superconducting qubit hardware and inform future directions for the co-design of quantum devices and fault-tolerant architectures.
[1] S. Bravyi et al., Phys. Rev. Lett. 104, 050503 (2010).
[2] Z. Liang et al., PRX Quantum 6, 020357 (2025).
[3] S. Bravyi et al., Nature 627, 778 (2024).
[4] V. Steffan et al., arXiv:2504.09171 (2025).
[5] Z. Liang et al., arXiv:2504.08887 (2025).
[6] T. R. Scruby et al., arXiv:2406.14445 (2024).
[7] R. K. Radebold et al., arXiv:2508.05095 (2025).
*This material is based upon work supported in part by the U.S. Army Research Laboratory and the U.S. Army Research Office under contract/grant number W911NF2310255, and in part by IARPA and the Army Research Office, under the Entangled Logical Qubits program, and was accomplished under Cooperative Agreement Number W911NF-23-2-0212. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the U.S. Government.
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Publication:Melvin Mathews, Lukas Pahl, David Pahl, Vaishnavi L. Addala, Catherine Tang, William D. Oliver, & Jeffrey A. Grover. (2025). Placing and routing quantum LDPC codes in multilayer superconducting hardware. [Manuscript submitted for publication].
