  We introduce a novel quantum programming language featuring higher-order
programs and quantum controlflow which ensures that all qubit transformations
are unitary. Our language boasts a type system guaranteeingboth unitarity and
polynomial-time normalization. Unitarity is achieved by using a special
modality forsuperpositions while requiring orthogonality among superposed
terms. Polynomial-time normalization isachieved using a linear-logic-based type
discipline employing Barber and Plotkin duality along with a specificmodality
to account for potential duplications. This type discipline also guarantees
that derived values havepolynomial size. Our language seamlessly combines the
two modalities: quantum circuit programs upholdunitarity, and all programs are
evaluated in polynomial time, ensuring their feasibility.
