Placing and routing quantum LDPC codes in multilayer superconducting hardware

Recent work has shown that quantum error correcting codes with nonlocal connectivity may significantly reduce the qubit overhead required to reach algorithmically relevant logical error rates. In this talk, we report on our efforts toward performing low-overhead quantum computation in a small-scale qLDPC code using superconducting qubits. Our code encodes three logical qubits at distance-two with only six data qubits. We realize the geometrically nonlocal connectivity of the X, Y, and Z stabilizers with transmission-line-cavity-based long-range couplers. We discuss the implications of operating three logical qubits within one code block and present schemes for hardware-tailored fault-tolerant logic. These results, combined with discussions on how our techniques extend to larger code architectures, demonstrate the potential for lowering overheads in fault-tolerant quantum computation with superconducting qubits.