Beijing Institute of Mathematical Sciences and Applications

Song Cheng , Dawei Ding , Jinpeng Liu , Zhengwei Liu , Ziwen Liu

Yijia Xu

Friday, October 31, 2025 4:00 PM - 5:30 PM

Shuangqing-B627

Zoom 230 432 7880 (BIMSA)

Continuous-variable cat codes are encodings into a single photonic or phononic mode that offer a promising avenue for hardware-efficient fault-tolerant quantum computation. Protecting information in a cat code requires measuring the mode’s occupation number modulo two, but this can be relaxed to a linear occupation-number constraint using the alternative two-mode pair-cat encoding. We construct multimode codes with similar linear constraints using any two integer matrices satisfying a CSS-like homological condition of a quantum rotor code. Just like the pair-cat code, syndrome extraction can be performed in tandem with stabilizing dissipation using current superconducting-circuit designs. The framework includes codes with various finite- or infinite-dimensional codespaces, and codes with finite or infinite Fock-state support. It encompasses two-component cat, pair-cat, dual-rail, two-mode binomial, various bosonic repetition codes, and aspects of chi-squared encodings while also yielding codes from homological products, lattices, generalized coherent states, and algebraic varieties. Among our examples are analogues of repetition codes, the Shor code, and a surface-like code that is not a concatenation of a known cat code with the qubit surface code. Codewords are coherent states projected into a Fock-state subspace defined by an integer matrix, and their overlaps are governed by Gelfand-Kapranov-Zelevinsky hypergeometric functions. [To appear in PRX]