An Algebra of Pure Quantum Programming
  We develop a sound and complete equational theory for the functional quantum programming language QML. The soundness and completeness of the theory are with respect to the previously-developed denotational semantics of QML. The completeness proof also gives rise to a normalisation algorithm following the normalisation by evaluation approach. The current work focuses on the pure fragment of QML omitting measurements. 
Thorsten Altenkirch and Jonathan Grattage and Juliana K. Vizzotto and   Amr Sabry