Researchers at IQM Quantum Computers and the Universidad Autónoma de Madrid have achieved arbitrary code distance in fermion-to-qubit encodings, a development published on September 30, 2026, in Quantum Science and Technology. The team embedded low-distance encodings into the surface code using topological defects, scaling the code distance without increasing stabilizer weights, which was previously a significant limitation in quantum error correction. This work details a family of Ladder Encodings, optimal in relating code distance to the weights of operators in a one-dimensional Fermi-Hubbard model.

Ladder Encodings Scale Code Distance to Arbitrary Values

This scaling is achieved by embedding lower-distance encodings directly into the surface code structure, manifesting as topological defects within the system. The team demonstrated that the code distance within these Ladder Encodings is equivalent to the weights of both density and nearest-neighbor hopping operators, a precise relationship previously difficult to achieve. This optimization extends beyond one dimension; the researchers also showed how to scale the code distance for Ladder Encodings, alongside other low-distance encodings like Verstraete-Cirac and Derby-Klassen, in two-dimensional systems.

Expanding on these possibilities, they introduced Perforated Encodings, a method for locally encoding two fermionic spin modes within the same surface code structure. The applicability of this approach is not limited to surface codes. The study explicitly embeds the Ladder Encoding into a 6.6.6 color code, demonstrating the strategy’s extendability to other topological codes. The paper was received on June 2, 2026, underwent revision on September 2, 2026, and was accepted for publication on September 17, 2026. This research represents a step toward building quantum computers capable of handling increasingly complex calculations.

Source: https://iopscience.iop.org/article/10.1088/2058-9565/aea92c

More like this