Reversibility for Quantum Programming Language QML

We present an extension of the denotational semantic model of the quantum programming language QML, to which computational reversibility is incorporated. The semantics of QML is defined in a functional setting which consider classical and quantum data, to which we add inverse functions. Additionally we incorporate into the semantics a history track which allows reversibility in QML. From the generation and processing of the history track and the final result of a program, the rules for executing reversibility allow to compute the original input data. This work contributes to the study of reversibility in quantum programming languages and considering that there is not yet a quantum computer in which the language can be implemented, this history and the proposed inverse functions are not trivial and allows us to determine that this language is reversible

Lenguaje de programación cuántico QML con historial, reversibilidad y cálculo lambda con mediciones

Research in quantum computing allows us to think about computing in a new and different way, having the ambition to solve problems more efficiently than with classical computing. Now a days, conventional tasks cannot be practically developed in a quantum computer, however, it is possible to think and develop abstractions of them, for example through quantum programming languages, being the core of this research, in particular the Quantum Meta Language (QML). We present a semantic model that incorporates reversibility via a history track for the quantum programming language QML, considering classical and quantum data, omitting measurements. With the history, the reversibility can be explicitly and naturally applied from the proposed rules. The language is worked first with classical data and extrapolated to quantum data. Also, the QML language and quantum lambda calculus were linked, giving as product a syntax with quantum measurements, operational semantics, typing rules and some formal proofs.La investigación en el cómputo cuántico permite pensar de una forma nueva y diferente la computación, teniendo la ambición de solucionar problemas de manera más eficiente que con el cómputo clásico. Por ahora, las tareas convencionales no se pueden desarrollar de manera práctica en una computadora cuántica, sin embargo, sí se puede pensar y desarrollar abstracciones de éstas, por ejemplo a través de lenguajes de programación cuánticos, siendo el núcleo de esta investigación, en particular el lenguaje Quantum Meta Language (QML). Se presenta un modelo semántico que incorpora reversibilidad a través de una pista de historial para el lenguaje de programación cuántico QML, considerando datos clásicos y cuánticos, omitiendo mediciones. Con la pila de historial, la reversibilidad puede aplicarse explícita y naturalmente a partir de las reglas propuestas. El lenguaje se trabaja gradualmente, inicialmente con datos clásicos y un procedimiento similar al clásico se extrapola con datos cuánticos. Además, se vincularon los lenguajes QML y cálculo lambda cuántico, dando como producto una sintaxis con mediciones cuánticas, semántica operacional, reglas de tipado y ciertas pruebas formales

A functional quantum programming language

This thesis introduces the language QML, a functional language for quantum computations on finite types. QML exhibits quantum data and control structures, and integrates reversible and irreversible quantum computations. The design of QML is guided by the categorical semantics: QML programs are interpreted by morphisms in the category FQC of finite quantum computations, which provides a constructive operational semantics of irreversible quantum computations, realisable as quantum circuits. The quantum circuit model is also given a formal categorical definition via the category FQC. QML integrates reversible and irreversible quantum computations in one language, using first order strict linear logic to make weakenings, which may lead to the collapse of the quantum wavefunction, explicit. Strict programs are free from measurement, and hence preserve superpositions and entanglement. A denotational semantics of QML programs is presented, which maps QML terms into superoperators, via the operational semantics, made precise by the category Q. Extensional equality for QML programs is also presented, via a mapping from FQC morphisms into the category Q

A functional quantum programming language

This thesis introduces the language QML, a functional language for quantum computations on finite types. QML exhibits quantum data and control structures, and integrates reversible and irreversible quantum computations. The design of QML is guided by the categorical semantics: QML programs are interpreted by morphisms in the category FQC of finite quantum computations, which provides a constructive operational semantics of irreversible quantum computations, realisable as quantum circuits. The quantum circuit model is also given a formal categorical definition via the category FQC. QML integrates reversible and irreversible quantum computations in one language, using first order strict linear logic to make weakenings, which may lead to the collapse of the quantum wavefunction, explicit. Strict programs are free from measurement, and hence preserve superpositions and entanglement. A denotational semantics of QML programs is presented, which maps QML terms into superoperators, via the operational semantics, made precise by the category Q. Extensional equality for QML programs is also presented, via a mapping from FQC morphisms into the category Q

Towards a formally verified functional quantum programming language

This thesis looks at the development of a framework for a functional quantum programming language. The framework is first developed in Haskell, looking at how a monadic structure can be used to explicitly deal with the side-effects inherent in the measurement of quantum systems, and goes on to look at how a dependently-typed reimplementation in Agda gives us the basis for a formally verified quantum programming language. The two implementations are not in themselves fully developed quantum programming languages, as they are embedded in their respective parent languages, but are a major step towards the development of a full formally verified, functional quantum programming language. Dubbed the “Quantum IO Monad”, this framework is designed following a structural approach as given by a categorical model of quantum computation

Quantum Control Machine: The Limits of Quantum Programs as Data

Quantum algorithms for factorization, search, and simulation obtain computational advantage by performing control flow such as branching and iteration based on the value of quantum data in superposition. Complicating realization of these algorithms is the fact that in predominant quantum machine models, all control flow as embodied by the program counter is classical, and cannot exist in superposition. In this work, we identify that an alternative model to enable a program counter in superposition faces an obstacle -- no such machine can correctly support control flow constructs with non-injective semantics, including the conventional conditional jump. In fact, prior attempts to support this instruction cause programs to inappropriately collapse the superposition of data, meaning that quantum advantage is lost. We present a quantum machine model that supports both quantum effects on data and data-dependent control flow, using variants of conditional jump with injective semantics. We identify the necessary condition for programs for such a machine to preserve superposition of data, and show that expressible programs coincide with the unitary quantum circuits.Comment: 12 pages, 8 figure

Formally Verified Quantum Programming

The field of quantum mechanics predates computer science by at least ten years, the time between the publication of the Schrodinger equation and the Church-Turing thesis. It took another fifty years for Feynman to recognize that harnessing quantum mechanics is necessary to efficiently simulate physics and for David Deutsch to propose the quantum Turing machine. After thirty more years, we are finally getting close to the first general-purpose quantum computers based upon prototypes by IBM, Intel, Google and others. While physicists and engineers have worked on building scalable quantum computers, theoretical computer scientists have made their own advances. Complexity theorists introduced quantum complexity classes like BQP and QMA; Shor and Grover developed their famous algorithms for factoring and unstructured search. Programming languages researchers pursued two main research directions: Small-scale languages like QPL and the quantum lambda-calculi for reasoning about quantum computation and large-scale languages like Quipper and Q# for industrial-scale quantum software development. This thesis aims to unify these two threads while adding a third one: formal verification. We argue that quantum programs demand machine-checkable proofs of correctness. We justify this on the basis of the complexity of programs manipulating quantum states, the expense of running quantum programs, and the inapplicability of traditional debugging techniques to programs whose states cannot be examined. We further argue that the existing mathematical models of quantum computation make this an easier task than one could reasonably expect. In light of these observations we introduce QWIRE, a tool for writing verifiable, large scale quantum programs. QWIRE is not merely a language for writing and verifying quantum circuits: it is a verified circuit description language. This means that the semantics of QWIRE circuits are verified in the Coq proof assistant. We also implement verified abstractions, like ancilla management and reversible circuit compilation. Finally, we turn QWIRE and Coq\u27s abilities outwards, towards verifying popular quantum algorithms like quantum teleportation. We argue that this tool provides a solid foundation for research into quantum programming languages and formal verification going forward

Understanding Quantum Technologies 2022

Understanding Quantum Technologies 2022 is a creative-commons ebook that provides a unique 360 degrees overview of quantum technologies from science and technology to geopolitical and societal issues. It covers quantum physics history, quantum physics 101, gate-based quantum computing, quantum computing engineering (including quantum error corrections and quantum computing energetics), quantum computing hardware (all qubit types, including quantum annealing and quantum simulation paradigms, history, science, research, implementation and vendors), quantum enabling technologies (cryogenics, control electronics, photonics, components fabs, raw materials), quantum computing algorithms, software development tools and use cases, unconventional computing (potential alternatives to quantum and classical computing), quantum telecommunications and cryptography, quantum sensing, quantum technologies around the world, quantum technologies societal impact and even quantum fake sciences. The main audience are computer science engineers, developers and IT specialists as well as quantum scientists and students who want to acquire a global view of how quantum technologies work, and particularly quantum computing. This version is an extensive update to the 2021 edition published in October 2021.Comment: 1132 pages, 920 figures, Letter forma