Simulation of stabilizer quantum circuits and their reduction to classical Boolean circuits

Modern quantum computers suffer from noises, that is why a lot of effort is put in the theory of quantum error-correcting codes. Protocols of quantum fault-tolerance widely use a subclass of quantum computational processes called stabilizer circuits. Stabilizer circuits are most prone to error correction, they are capable of generating quantum entanglement, but they are also classically simulable.
The general theory of stabilizer circuits and their classical simulation, in addition to practical significance to error-correction, turns out to have close connection with wide range of topics, such as: Boolean circuits, Boolean linear algebra, projective representations of abelian groups and their cohomology, linear optics, and theories of reference frames and hidden variable models from quantum foundations.
In my talk, which is based on https://arxiv.org/abs/2511.05478, I will try to give an introduction to the subject and state some of my recent results.

The talk will be streamed through “Kontur Talk”: https://mian.ktalk.ru/ojolwic9po4h?pinCode=5195