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.

翻译：我们提出了一种新颖的量子编程语言，该语言支持高阶程序和量子控制流，确保所有量子比特变换都是酉的。该语言拥有一套类型系统，同时保证酉性和多项式时间归一化。酉性通过使用一种特殊的叠加模态实现，同时要求叠加项之间具有正交性。多项式时间归一化则采用基于线性逻辑的类型规则，结合Barber与Plotkin对偶性以及一种特定模态来处理潜在的复制操作。该类型规则还能确保派生值的大小为多项式级。我们的语言无缝融合了这两种模态：量子电路程序保持酉性，所有程序均可在多项式时间内完成求值，从而保证其可行性。