Logical operations for layer-code memories

Determine which logical operations layer codes admit beyond quantum storage and characterize how their implementations compare with surface-code lattice surgery, beginning with transversal CNOT operations.

Background

The paper studies layer codes exclusively as memories: it develops syndrome-extraction circuits, evaluates thresholds and idle robustness, and does not implement logical gates. The authors identify the characterization of logical operations as a separate unresolved direction.

The comparison with surface codes is intended to assess not only which operations are possible, but also their implementation cost relative to lattice surgery. Transversal CNOT is singled out as the natural first operation to investigate, with throughput under explicit connectivity and workspace constraints proposed as an additional performance metric.

References

A second direction is logical operations, of which this paper measures none: which ones a layer code admits beyond storage, and how they compare with the lattice surgery a surface code would use, are open.

— Layer codes as quantum memories: syndrome extraction, thresholds and idle robustness  (2609.39522 - Sun et al., 30 Sep 2026) in Section 6.2, “Outlook”

Whether the better parameters carry over to a circuit-level advantage is open, since the construction's check weight $3(D-1)$ and qubit degree $2D$ force a deeper extraction round, and depth is the cost that dominates the threshold gap we measure in three dimensions.

— Layer codes as quantum memories: syndrome extraction, thresholds and idle robustness  (2609.39522 - Sun et al., 30 Sep 2026) in Section 6.2, “Outlook”