Reasoning About Imperative Quantum Programs

Chadha, Rohit; Mateus, Paulo; Sernadas, Amı́lcar

doi:10.1016/j.entcs.2006.04.003

Cited by 58 publications

(59 citation statements)

References 19 publications

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“…We aim to investigate Hoare-style reasoning and dynamic logics for quantum programming. Towards this end, we have already designed logics for reasoning about individual quantum states [19,5] and a sound Hoare logic for basic quantum imperative programs [4].…”

Section: Discussionmentioning

confidence: 99%

Reasoning About States of Probabilistic Sequential Programs

Chadha¹,

Mateus²,

Sernadas³

2006

Computer Science Logic

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Abstract. A complete and decidable propositional logic for reasoning about states of probabilistic sequential programs is presented. The state logic is then used to obtain a sound Hoare-style calculus for basic probabilistic sequential programs. The Hoare calculus presented herein is the first probabilistic Hoare calculus with a complete and decidable state logic that has truth-functional propositional (not arithmetical) connectives. The models of the state logic are obtained exogenously by attaching sub-probability measures to valuations over memory cells. In order to achieve complete and recursive axiomatization of the state logic, the probabilities are taken in arbitrary real closed fields.

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Section: Discussionmentioning

confidence: 99%

Reasoning About States of Probabilistic Sequential Programs

Chadha¹,

Mateus²,

Sernadas³

2006

Computer Science Logic

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“…Another quantum Hoare logic is given by Chadha et al in [12]. Also their logic is based on a probabilistic Hoare logic.…”

Section: Related Workmentioning

confidence: 99%

“…• is 1/2 under Γ = q : qbit and A = H E 0 H. Unlike the logic in [12], we cannot describe a state of a quantum bit directly. We describe only a property on probability through measurement.…”

Section: γ a V |= φ Is Defined Inmentioning

confidence: 99%

A Logic for Formal Verification of Quantum Programs

Kakutani

2009

Advances in Computer Science - ASIAN 2009. Information Security and Privacy

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Abstract. This paper provides a Hoare-style logic for quantum computation. While the usual Hoare logic helps us to verify classical deterministic programs, our logic supports quantum probabilistic programs. Our target programming language is QPL defined by Selinger, and our logic is an extension of the probabilistic Hoare-style logic defined by den Hartog. In this paper, we demonstrate how the quantum Hoare-style logic proves properties of well-known algorithms.

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“…Brunet and Jorrand [35] introduced a way of applying Birkhoff and von Neumann's quantum logic in reasoning about quantum programs. Chadha et al [36] proposed a Hoare-style proof system for reasoning about imperative quantum programs in which only bounded iterations are allowed. Some useful proof rules were proposed in [37] for purely quantum programs.…”

Section: Proof Systemsmentioning

confidence: 99%

Quantum programming: From theories to implementations

et al. 2012

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This paper surveys the new field of programming methodology and techniques for future quantum computers, including design of sequential and concurrent quantum programming languages, their semantics and implementations. Several verification methods for quantum programs and communication protocols are also reviewed. The potential applications of programming techniques and related formal methods in quantum engineering are pointed out. Chin Sci Bull, 2012, 57: 1903-1909, doi: 10.1007 Even though quantum hardware is still in its infancy, people widely believe that building a large-scale and functional quantum computer is merely a matter of time and concentrated effort. As the techniques of quantum devices progress, architectural studies will become critical for designing and implementing bigger quantum computing systems. Indeed, a research group from top US universities, including MIT and UC Berkeley, has conducted their research on quantum computing architecture, with support from the DARPA Quantum Information Program [1]. On the other hand, once quantum computers come into being, quantum software will play the key role in exploiting the power of quantum computers. However, today's software development methodologies and techniques are purely classical, and they are not suited to quantum computers. In the last 15 years, researchers began to realize the importance of quantum software. In fact, quantum software engineering was listed as a grand challenge in UK Grand Challenges in Computing Research, and the goal of research on quantum software is explained clearly by The challenge is to rework and extend the whole of classical software engineering into the quantum domain so that programmers can manipulate quantum programs with the same ease and confidence that they manipulate today's classical programs. In US, EU and Canada there are already several research teams devoting to theoretical studies of quantum software, in particular quantum programming. More recently in 2010, IARPA in US initiated a Quantum Computer Science Program, and one of its major research issues is high-level quantum programming languages and quantum programming environments, including quantum compilers. Two excellent survey papers of quantum programming are [3,4], two newer surveys are [5] by one of the authors and [6], and [7,8] also contain a brief survey of quantum programming. This paper will further review the field of quantum programming, with emphasis on the authors' recent work conducted at Tsinghua (China) and UTS (Australia). Another quantum programming research group in China is led by Profs. Jiafu Xu and Fangmin Song at Nanjing University [9].

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Reasoning About Imperative Quantum Programs

Cited by 58 publications

References 19 publications

Reasoning About States of Probabilistic Sequential Programs

Reasoning About States of Probabilistic Sequential Programs

A Logic for Formal Verification of Quantum Programs

Quantum programming: From theories to implementations

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