We present voqc, the first fully verified compiler for quantum circuits, written using the Coq proof assistant. Quantum circuits are expressed as programs in a simple, low-level language called sqir, 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. We evaluate voqc's verified optimizations on a series of benchmarks, and it performs comparably to industrial-strength compilers. voqc's optimizations reduce total gate counts on average by 17.7% on a benchmark of 29 circuit programs compared to a 10.7% reduction when using IBM's Qiskit compiler.

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@MISC{hietala19voqc,
  AUTHOR = {Kesha Hietala and Robert Rand and Shih-Han Hung and Xiaodi Wu and Michael Hicks},
  TITLE = {A Verified Optimizer for Quantum Circuits},
  MONTH = NOV,
  YEAR = {2019},
  SUBMITTED = {yes}
}