A verified optimizer for Quantum circuits

We present VOQC, the first fully verified optimizer for quantum circuits, written using Coq proof assistant. Quantum circuits are expressed as programs in a simple, low-level language called SQIR, simple intermediate representation, which is deeply embedded Coq. Optimizations and other transformations functions, proved correct with respect to semantics of SQIR programs. uses matrices complex numbers, standard computation, but treats symbolically order reason about that use an arbitrary number bits. SQIR's careful design our provided automation make it possible write verify broad range optimizations including full-circuit from cutting-edge optimizers.