Based on the connection between the categorical derivation of classical programs from specifications and the category-theoretic approach to quantum physics, this paper contributes to extending the laws of classical program algebra to quantum programming. This aims at building correct-by-construction quantum circuits to be deployed on quantum devices such as those available at the IBM Q Experience. Quantum circuit reversibility is ensured by minimal complements, extended recursively. Measurements are postponed to the end of such recursive computations, termed "quantamorphisms", thus maximising the quantum effect. Quantamorphisms are classical catamorphisms which, extended to ensure quantum reversibility, implement quantum cycles (vulg. for-loops) and quantum folds on lists. By Kleisli correspondence, quantamorphisms can be written as monadic functional programs with quantum parameters. This enables the use of Haskell, a monadic functional programming language, to perform the experimental work. Such calculated quantum programs prepared in Haskell are pushed through Quipper to the Qiskit interface to IBM Q quantum devices. The generated quantum circuits - often quite large - exhibit the predicted behaviour. However, running them on real quantum devices incurs into a significant amount of errors. As quantum devices are constantly evolving, an increase in reliability is likely in the near future, allowing for our programs to run more accurately.

中文翻译：

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为 IBM Q Experience 编译量化

基于从规范中分类推导经典程序与量子物理学的范畴论方法之间的联系，本文有助于将经典程序代数定律扩展到量子程序。这旨在构建正确构造的量子电路，以部署在量子设备上，例如 IBM Q Experience 中提供的那些设备。量子电路的可逆性是通过递归扩展的最小补码来确保的。测量被推迟到这种递归计算的末尾，称为“量子态”，从而最大化量子效应。Quantamorphisms 是经典的 catamorphisms，它扩展到确保量子可逆性，在列表上实现量子循环（vulg. for-loops）和量子折叠。通过 Kleisli 通信，量子态可以写成具有量子参数的一元函数程序。这使得可以使用 Haskell（一元函数式编程语言）来执行实验工作。此类在 Haskell 中准备的计算量子程序通过 Quipper 推送到 IBM Q 量子设备的 Qiskit 接口。生成的量子电路 - 通常非常大 - 表现出预测的行为。然而，在真正的量子设备上运行它们会导致大量错误。随着量子设备的不断发展，在不久的将来，可靠性可能会提高，从而使我们的程序能够更准确地运行。此类在 Haskell 中准备的计算量子程序通过 Quipper 推送到 IBM Q 量子设备的 Qiskit 接口。生成的量子电路 - 通常非常大 - 表现出预测的行为。然而，在真正的量子设备上运行它们会导致大量错误。随着量子设备的不断发展，在不久的将来，可靠性可能会提高，从而使我们的程序能够更准确地运行。此类在 Haskell 中准备的计算量子程序通过 Quipper 推送到 IBM Q 量子设备的 Qiskit 接口。生成的量子电路 - 通常非常大 - 表现出预测的行为。然而，在真正的量子设备上运行它们会导致大量错误。随着量子设备的不断发展，在不久的将来，可靠性可能会提高，从而使我们的程序能够更准确地运行。