Towards quantum program calculation
Ana Neri · Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) · 2018
Based on the similarity between the categorial derivation of classical programs from their specification and the category theory approach to quantum physics, this dissertation aims at extending the laws of classical program algebra to quantum programming. In this context, the principles of the algebra of classical programs are applied to quantum programming, in order to verify the feasibility of creating correct-by-construction quantum circuits that can run on quantum devices available in the IBM Q Experience. The reversibility restrictions of quantum circuits are ensured by minimal complements. Moreover, measurements are postponed to the end of recursive computations called “quantamorphisms” to avoid the collapse of quantum states. Quantamorphisms are classical catamorphisms extended to ensure quantum reversibility. The derived quantamorphisms 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. The examples of the calculated quantum programs are simulated in Haskell, Quipper and QISKit and run on the quantum computers of the IBM Q Experience. The main conclusions of this work are that, while all the simulations produced correspond to the predicted results, running these programs on real quantum devices results in a significant amount of errors. As quantum devices are constantly evolving, it is likely that in the near future these devices will increase their reliability, allowing programs to run more accurately. The extension of the quantamorphism concept to more general input structures, such as finite trees, remains a challenge that is left for future work. Also relevant will be the study of conditional quantum control without measurements, which will extend the scope of quantamorphisms as quantum circuit specifications.