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arXiv:quant-ph/0602156

Quantum Predicative Programming

Anya Tafliovich, Eric C. R. Hehner

Published Feb 17, 2006• 0 citations
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Abstract

The subject of this work is quantum predicative programming -- the study of developing of programs intended for execution on a quantum computer. We look at programming in the context of formal methods of program development, or programming methodology. Our work is based on probabilistic predicative programming, a recent generalisation of the well-established predicative programming. It supports the style of program development in which each programming step is proven correct as it is made. We inherit the advantages of the theory, such as its generality, simple treatment of recursive programs, time and space complexity, and communication. Our theory of quantum programming provides tools to write both classical and quantum specifications, develop quantum programs that implement these specifications, and reason about their comparative time and space complexity all in the same framework.

DOI
10.48550/arxiv.quant-ph/0602156

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The subject of this work is quantum predicative programming -- the study of developing of programs intended for execution on a quantum computer. We look at programming in the context of formal methods of program development, or programming methodology. Our work is based on probabilistic predicative programming, a recent generalisation of the well-established predicative programming. It supports the style of program development in which each programming step is proven correct as it is made. We inherit the advantages of the theory, such as its generality, simple treatment of recursive programs, time and space complexity, and communication. Our theory of quantum programming provides tools to write both classical and quantum specifications, develop quantum programs that implement these specifications, and reason about their comparative time and space complexity all in the same framework.
Over the past 27 years, quantum computing has seen a huge rise in interest from both academia and industry. At the current rate, quantum computers are growing in size rapidly backed up by the increase of research in the field. Significant efforts are being made to improve the reliability of quantum hardware and to develop suitable software to program quantum computers. In contrast, the verification of quantum programs has received relatively less attention. Verifying programs is especially important in the quantum setting due to how difficult it is to program complex algorithms correctly on resource-constrained and error-prone quantum hardware. Research into creating verification frameworks for quantum programs has seen recent development, with a variety of tools implemented using a collection of theoretical ideas. This survey aims to be a short introduction into the area of formal verification of quantum programs, bringing together theory and tools developed to date. Further, this survey examines some of the challenges that the field may face in the future, namely the development of complex quantum algorithms.
Quantum computer programming is emerging as a new subject domain from multidisciplinary research in quantum computing, computer science, mathematics (especially quantum logic, lambda calculi, and linear logic), and engineering attempts to build the first non-trivial quantum computer. This paper briefly surveys the history, methods, and proposed tools for programming quantum computers circa late 2007. It is intended to provide an extensive but non-exhaustive look at work leading up to the current state-of-the-art in quantum computer programming. Further, it is an attempt to analyze the needed programming tools for quantum programmers, to use this analysis to predict the direction in which the field is moving, and to make recommendations for further development of quantum programming language tools.
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected that recursion will become one of the fundamental paradigms of quantum programming. Several program logics have been developed for verification of non-recursive quantum programs. However, there are as yet no general methods for reasoning about recursive procedures in quantum computing. We fill the gap in this paper by presenting a logic for recursive quantum programs. This logic is an extension of quantum Hoare logic for quantum While-programs. The (relative) completeness of the logic is proved, and its effectiveness is shown by a running example: fixed-point Grover's search.
The verification of quantum computing algorithms presents a significant hurdle due to the probabilistic nature of quantum mechanics and the complex entanglement inherent in quantum computations. This paper proposes a novel approach to address this challenge by developing a formal language and a corresponding verification tool tailored explicitly for quantum algorithm specification and verification. The system leverages concepts from quantum information theory and formal methods to provide a rigorous framework for ensuring the correctness of quantum algorithms. We introduce a new formalism that allows for precise description of quantum circuits and their operations, combined with automated theorem proving techniques to systematically verify the algorithm's behavior against a given specification. The key innovation lies in the ability to reason about quantum states and measurements within a formal setting, enabling a more comprehensive understanding and validation of these algorithms. This work lays the foundation for increased confidence in the development and deployment of quantum computing technologies.