Barbell Codes: qLDPC Codes for Superconducting Quantum Hardware

The major challenge on the way to fault-tolerant quantum computing comes from the insufficient quality of hardware components and the difficulty of scaling their number without further compromising fidelity. Quantum Low-Density Parity-Check (qLDPC) codes offer a promising solution by encoding logical qubits with low overhead and at a comparatively high code distance. However, it remains an open question how to scalably implement efficient qLDPC codes on fixed-connectivity quantum chips without increasing hardware complexity to enable the non-local interactions in their underlying QEC cycles. We resolve this challenge for the first time by introducing a family of qLDPC "barbell" codes accompanied by a realistic chip layout that natively supports all required two-qubit interactions. Crucially, the hardware complexity required to implement barbell codes remains constant as code distance increases. We provide a detailed investigation into the feasibility of all required hardware components and simulate a specific family of barbell codes against circuit-level noise. We find that, with a modest overhead of $<30$ data qubits per logical qubit, barbell codes can preserve information at a physical noise strength of $10^{-4}$ for several trillion QEC cycles. Simulations of logical multi-Pauli measurements, performed with circuits tailored to the chip, yield similar logical performance per QEC round, indicating that entangling gates between logical qubits in barbell codes can be realized fault-tolerantly.