Realizing three logical qubits in a qLDPC code with superconducting circuits, Part 1: Theory

Recent work has shown that quantum error correcting codes with non-local connectivity may significantly reduce the qubit overhead required to reach algorithmically relevant logical error rates [1]. However, realizing these so-called quantum low-density parity-check (qLDPC) codes with superconducting qubits seems challenging since this platform most naturally supports 2D local connectivities. In this two-part talk, we outline our theoretical and experimental efforts toward realizing a small-scale qLDPC code using superconducting qubits, encoding three logical qubits at distance-two with only six data qubits and two long-range connections. The results presented in this talk, combined with discussions on how our techniques extend to larger code architectures, provide evidence for a path to low-overhead quantum error correction with superconducting qubits.

Part 1 will theoretically introduce our novel [[6,3,2]] code, featuring X, Z, and Y stabilizers, which are measured repeatedly. We discuss the implications of operating on three logical qubits within one code block and present schemes such as logical cluster-state preparation and logical teleportation between our three logical qubits.



[1] S. Bravyi, et al., Nature, 2024