Compiling quantamorphisms for the IBM Q Experience

TL;DR

This paper introduces 'quantamorphisms', a category-theoretic approach to constructing correct quantum circuits for IBM Q devices, leveraging Haskell and Quipper to automate quantum program generation and execution.

Contribution

It extends classical program algebra to quantum programming by defining quantamorphisms, enabling correct-by-construction quantum circuits with recursive reversibility and quantum cycle implementation.

Findings

Quantum programs exhibit expected quantum effects.

Large quantum circuits can be generated and tested.

Error rates are high but expected to improve with device evolution.

Abstract

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.