Quantum error correction is essential for reliably storing and manipulating information in quantum devices. In this talk, I will review dynamical quantum error-correcting codes, which involve sequences of non-commuting measurements. The dynamical nature of these codes offers several advantages over static codes, but also introduces new challenges, since errors must now be tracked across both space and time.
I will show that the measurement sequences underlying dynamical stabilizer codes can be understood as non-invertible symmetries of certain topological quantum field theories. In this framework, a sequence of measurements corresponds to the fusion of these topological symmetry operators. Using this approach, I will present a characterization of both error detectors and detectable errors in dynamical codes, entirely in terms of the braiding of specific topological operators.
