We present VOQC, the first fully verified optimizer for quantum circuits, written using the Coq
proof assistant. Quantum circuits are expressed as programs in a simple, low-level language
called SQIR, a simple quantum intermediate representation, which is deeply embedded in
Coq. Optimizations and other transformations are expressed as Coq functions, which are
proved correct with respect to a semantics of SQIR programs. SQIR uses a semantics of
matrices of complex numbers, which is the standard for quantum computation, but treats …

We present voqc, the first verified optimizer for quantum circuits, written using the Coq proof
assistant. Quantum circuits are expressed as programs in a simple, low-level language
called sqir, a small quantum intermediate representation, which is deeply embedded in Coq.
Optimizations and other transformations are expressed as Coq functions, which are proved
correct with respect to a semantics of sqir programs. sqir programs denote complex-valued
matrices, as is standard in quantum computation, but we treat matrices symbolically to …