Together with Marco Timpanella (University of Perugia) and Giovanni Zini (University of Modena and Reggio Emilia), the research group organize monthly seminars.
15 April 2026 [5.00 pm - Italian time] - Giuseppe Cotardo (Virginia Tech, US)
Title: Quantum Anticodes
Abstract: Quantum error-correcting codes are essential for protecting quantum information in large-scale quantum architectures. While most experimentally implemented codes, encode a single logical qubit, scalable quantum systems require codes capable of encoding multiple logical qubits. In this setting, different logical qubits may exhibit distinct local distances that are not captured by standard quantum coding theory. In this talk, we introduce a symplectic framework for quantum error-correcting codes that analyzes the local structure of a code from an anticode perspective. Codes are modeled as symplectic spaces, and anticodes arise as maximal symplectic subspaces supported on prescribed sets of components, providing a natural quantum analogue of classical anticodes. This framework encompasses several families of quantum codes, including stabilizer and subsystem codes, extends the notion of generalized distances in quantum coding theory, and yields new invariants that capture local algebraic and combinatorial features. Moreover, this approach naturally leads to operations such as puncturing and shortening, offering algebraic interpretations of phenomena such as the cleaning lemma, complementary recovery, and new descriptions of quantum weight enumerators. The results presented in this talk are joint work with C. Cao and B. Lackey.