Abstract:
The Gottesman-Neill theorem states that stabilizer circuits can be efficiently simulated on classical computers. We discuss a specific method for reducing stabilizer circuits to classical ones. By fixing a set of rules for rewriting quantum operations into classical ones, we construct a context-free hidden variable model for stabilizer circuits of the Calderbank-Shor-Steane class. For arbitrary stabilizer circuits, context-free models do not exist. We introduce a frame of reference formalism based on the theory of quadratic forms, which allows us to construct a context-dependent hidden variable model for stabilizer operations.
