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On Incorrectness Logic for quantum Programs

PROCEEDINGS OF THE ACM ON programming languages-PACMPL 2022年第OOPSLA期6卷 1–28页

作者： Yan, Peng Jiang, Hanru Yu, Nengkun Univ Technol Sydney Ctr Quantum Software & Informat Sydney NSW Australia Yanqi Lake Beijing Inst Math Sci & Applicat Beijing Peoples R China

Bug-catching is important for developing quantum programs. Motivated by the incorrectness logic for classical programs, we propose an incorrectness logic towards a logical foundation for static bug-catching in quantum programming. The validity of formulas in this logic is dual to that of quantum Hoare logics. We justify the formulation of validity by an intuitive explanation from a reachability point of view and a comparison against several alternative formulations. Compared with existing works focusing on dynamic analysis, our logic provides sound and complete arguments. We further demonstrate the usefulness of the logic by reasoning several examples, including Grover's search, quantum teleportation, and a repeat-until-success program. We also automate the reasoning procedure by a prototyped static analyzer built on top of the logic rules.

关键词： Incorrectness Logic quantum programming languages Projective quantum Predicates

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OpenQASM3: A Broader and Deeper quantum Assembly Language

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ACM TRANSACTIONS ON quantum COMPUTING 2022年第3期3卷 1–50页

作者： Cross, Andrew Javadi-Abhari, Ali Alexander, Thomas de Beaudrap, Niel Bishop, Lev S. Heidel, Steven Ryan, Colm A. Sivarajah, Prasahnt Smolin, John Gambetta, Jay M. Johnson, Blake R. IBM Quantum IBM TJ Watson Res Ctr 1101 Kitchawan Rd Yorktown Hts NY 10598 USA Univ Sussex Dept Informat Brighton England AWS Ctr Quantum Comp 391 S Holliston Ave Pasadena CA 91106 USA

quantum assembly languages are machine-independent languages that traditionally describe quantum computation in the circuit model. Open quantum assembly language (OpenQASM 2) was proposed as an imperative programming language for quantum circuits based on earlier QASM dialects. In principle, any quantum computation could be described using OpenQASM 2, but there is a need to describe a broader set of circuits beyond the language of qubits and gates. By examining interactive use cases, we recognize two different timescales of quantum-classical interactions: real-time classical computations that must be performed within the coherence times of the qubits, and near-time computations with less stringent timing. Since the near-time domain is adequately described by existing programming frameworks, we choose in OpenQASM 3 to focus on the real-time domain, which must be more tightly coupled to the execution of quantum operations. We add support for arbitrary control flow as well as calling external classical functions. In addition, we recognize the need to describe circuits at multiple levels of specificity, and therefore we extend the language to include timing, pulse control, and gate modifiers. These new language features create a multi-level intermediate representation for circuit development and optimization, as well as control sequence implementation for calibration, characterization, and error mitigation.

关键词： quantum computing quantum programming languages quantum circuits dynamic circuits circuit scheduling

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A Blueprint for Q-CS1, an Introductory quantum programming Course 56

A Blueprint for Q-CS1, an Introductory Quantum Programming C...

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56th Annual SIGCSE Technical Symposium on Computer Science Education, SIGCSE TS 2025

作者： Adams, Austin J. Borela, Rodrigo Young, Jeffrey S. Conte, Thomas M. Georgia Institute of Technology Atlanta GA United States

ISBN: (纸本)9798400705328

Despite the need to build a quantum workforce, current courses that introduce quantum programming are rooted in quantum notation that students may find intimidating. We propose Q-CS1, a quantum equivalent of CS1 that begins with hands-on quantum programming. Q-CS1 is enabled by the Qwerty quantum programming language, which allows for reasoning about qubit behavior without physics notation or quantum circuits. An outline of Q-CS1 is provided along with plans for assessing its effectiveness. © 2025 Copyright held by the owner/author(s).

关键词： computer science education quantum education quantum programming languages

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Boolean satisfiability in quantum compilation

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PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 2020年第2164期378卷 20190161-20190161页

作者： Soeken, Mathias Meuli, Giulia Schmitt, Bruno Mozafari, Fereshte Riener, Heinz De Micheli, Giovanni Ecole Polytech Fed Lausanne Lausanne Switzerland

quantum compilation is the task of translating a quantum algorithm implemented in a high-level quantum programming language into a technology-dependent instructions flow for a physical quantum computer. To tackle the large gap between the quantum program and the low-level instructions, quantum compilation is split into a multi-stage flow consisting of several layers of abstraction. Several different individual tasks have been proposed for the layers in the flow, many of them are NP-hard. In this article, we will describe the flow and we will propose algorithms based on Boolean satisfiability, which is a good match to tackle such computationally complex problems. This article is part of the theme issue 'Harmonizing energy-autonomous computing and intelligence'.

关键词： quantum computing quantum programming languages quantum compilation Boolean satisfiability logic synthesis

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On the Source Code Structure of quantum Code: Insights from Q# and QDK 13th

On the Source Code Structure of Quantum Code: Insights from ...

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13th International Conference on the Quality of Information and Communications Technology (QUATIC)

作者： Sicilia, Miguel-Angel Sanchez-Alonso, Salvador Mora-Cantallops, Marcal Garcia-Barriocanal, Elena Univ Alcala Dept Comp Sci Polytech BldgCtra Barcelona Km 33-6 Alcala De Henares 28871 Madrid Spain

ISBN: (纸本)9783030587925;9783030587932

A considerable number of high-level quantum programming languages have been proposed and implemented in the last years. This fact opens the possibility to study the structure of the source code of quantum software, using initially the same metrics typically used in classical software. Here we report a preliminary study in module structure and use of quantum gates in the libraries of Microsoft's quantum development platform QDK (quantum Developer Kit) that uses a specific language, Q#. The structure of dependencies and the use of primitives is analyzed across all the source code available in the Github repositories related to the platform to date.

关键词： quantum programming languages Software metrics Dependency structures

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A Tutorial Introduction to quantum Circuit programming in Dependently Typed Proto-Quipper 12th

A Tutorial Introduction to Quantum Circuit Programming in De...

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12th International Conference on Reversible Computation (RC)

作者： Fu, Peng Kishida, Kohei Ross, Neil J. Selinger, Peter Dalhousie University Halifax NS Canada University of Illinois Urbana-Champaign IL United States

ISBN: (纸本)9783030524814;9783030524821

We introduce dependently typed Proto-Quipper, or ProtoQuipper-D for short, an experimental quantum circuit programming language with linear dependent types. We give several examples to illustrate how linear dependent types can help in the construction of correct quantum circuits. Specifically, we show how dependent types enable programming families of circuits, and how dependent types solve the problem of type-safe uncomputation of garbage qubits. We also discuss other language features along the way.

关键词： quantum programming languages Linear dependent types Proto-Quipper-D

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Full abstraction for the quantum lambda-Calculus

Full abstraction for the quantum lambda-Calculus

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Proceedings of the ACM on programming languages

作者： Clairambault, Pierre De Visme, Marc Univ Lyon EnsL UCBL CNRS LIP LYON LYON Cedex 07F-69364 France

quantum programming languages permit a hardware independent, high-level description of quantum algorithms. In particular, the quantum γ-calculus is a higher-order language with quantum primitives, mixing quantum data and classical control. Giving satisfactory denotational semantics to the quantum γ-calculus is a challenging problem that has attracted significant interest. In the past few years, both static (the quantum relational model) and dynamic (quantum game semantics) denotational models were given, with matching computational adequacy results. However, no model was known to be fully abstract. Our first contribution is a full abstraction result for the games model of the quantum γ-calculus. Full abstraction holds with respect to an observational quotient of strategies, obtained by summing valuations of all states matching a given observable. Our proof method for full abstraction extends a technique recently introduced to prove full abstraction for probabilistic coherence spaces with respect to probabilistic PCF. Our second contribution is an interpretation-preserving functor from quantum games to the quantum relational model, extending a long line of work on connecting static and dynamic denotational models. From this, it follows that the quantum relational model is fully abstract as well. Altogether, this gives a complete denotational landscape for the semantics of the quantum γ-calculus, with static and dynamic models related by a clean functorial correspondence, and both fully abstract. © 2020 Copyright held by the owner/author(s).

关键词： Calculations Abstracting Algebra Differentiation (calculus) High level languages quantum theory Semantics Computational adequacy Full abstraction Game semantics High level description Higher order languages quantum programming quantum programming languages Static and dynamic models

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Formalization of Metatheory of the Quipper quantum programming Language in a Linear Logic

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JOURNAL OF AUTOMATED REASONING 2019年第4期63卷 967-1002页

作者： Mahmoud, Mohamed Yousri Felty, Amy P. Univ Ottawa Sch Elect Engn & Comp Sci Ottawa ON Canada

We develop a linear logical framework within the Hybrid system and use it to reason about the type system of a quantum lambda calculus. In particular, we consider a practical version of the calculus called Proto-Quipper, which contains the core of Quipper. Quipper is a quantum programming language under active development and recently has gained much popularity among the quantum computing communities. Hybrid is a system that is designed to support the use of higher-order abstract syntax for representing and reasoning about formal systems implemented in the Coq Proof Assistant. In this work, we extend the system with a linear specification logic (SL) in order to reason about the linear type system of Quipper. To this end, we formalize the semantics of Proto-Quipper by encoding the typing and evaluation rules in the SL, and prove type soundness.

关键词： Proto-Quipper quantum programming languages Linear logic Hybrid Higher-order abstract syntax Coq

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Advantages of a modular high-level quantum programming framework

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MICROPROCESSORS AND MICROSYSTEMS 2019年 66卷 81-89页

作者： Steiger, Damian S. Haner, Thomas Troyer, Matthias Swiss Fed Inst Technol Theoret Phys CH-8093 Zurich Switzerland

We review some of the features of the ProjectQ software framework and quantify their impact on the resulting circuits. The concise high-level language facilitates implementing even complex algorithms in a very time-efficient manner while, at the same time, providing the compiler with additional information for optimization through code annotation - so-called meta-instructions. We investigate the impact of these annotations for the example of Shor's algorithm in terms of logical gate counts. Furthermore, we analyze the effect of different intermediate gate sets for optimization and how the dimensions of the resulting circuit depend on a smart choice thereof. Finally, we demonstrate the benefits of a modular compilation framework by implementing mapping procedures for one- and two-dimensional nearest neighbor architectures which we then compare in terms of overhead for different problem sizes. (C) 2019 Published by Elsevier B.V.

关键词： quantum computing Compilers quantum programming languages

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QPCF: Higher-Order languages and quantum Circuits

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JOURNAL OF AUTOMATED REASONING 2019年第4期63卷 941-966页

作者： Paolini, Luca Piccolo, Mauro Zorzi, Margherita Univ Torino Dept Comp Sci Turin Italy Univ Verona Dept Comp Sci Verona Italy

qPCF is a paradigmatic quantum programming language that extends PCF with quantum circuits and a quantum co-processor. quantum circuits are treated as classical data that can be duplicated and manipulated in flexible ways by means of a dependent type system. The co-processor is essentially a standard QRAM device, albeit we avoid to store permanently quantum states in between two co-processor's calls. Despite its quantum features, qPCF retains the classic programming approach of PCF. We introduce qPCF syntax, typing rules, and its operational semantics. We prove fundamental syntactic properties of the system. Moreover, we provide some higher-order examples of circuit encoding.

关键词： PCF quantum computing quantum programming languages

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