Adapt analog message passing for dimensionality-reduced GKP-LDLCs

Determine whether dimensionality-reduced GKP-LDLCs with two additional dense checks can be decoded effectively using message-passing algorithms, and, if so, develop the necessary decoder modifications.

Background

The dimensionality-reduction procedure converts a sparse GKP-LDLC generator into a single-qubit code by adding two dense checks. These codes exhibit promising distances and logical-error probabilities compared with mode-matched concatenated surface-code constructions, but the dense checks create short cycles in the decoding graph. The authors report that exact closest-vector decoding is computationally feasible only for relatively small instances, making an efficient approximate decoder necessary for practically relevant mode numbers.

The paper tests analog message-passing decoders as a natural candidate, but the resulting dense checks cause poor performance and no simple adaptation is found. Consequently, it remains unresolved whether these reduced codes can retain their coding advantages while admitting efficient message-passing-based decoding.

References

As a consequence, it is not clear at this stage if the resulting codes are still suitable for decoding through message-passing, and, if so, how the decoder would need to be modified.

— Quantum low-density lattice codes  (2609.03021 - Hillmann et al., 2 Sep 2026) in Section 3, subsection “Distance and logical error probability of the reduced codes”

At this point, we do not yet understand how to modify the decoder to achieve highly accurate decoding across a large class of codes.

— Quantum low-density lattice codes  (2609.03021 - Hillmann et al., 2 Sep 2026) in Section 4, subsection “Decoding concatenated codes with analog message-passing decoders”