Quantum loop programs

Loop is a powerful program construct in classical computation, but its power is still not exploited fully in quantum computation. The exploitation of such power definitely requires a deep understanding of the mechanism of quantum loop programs. In this paper, we introduce a general scheme of quantum loops and describe its computational process. The function computed by a quantum loop is defined, and a denotational semantics and a weakest precondition semantics of a quantum loop are given. The notions of termination and almost termination are proposed for quantum loops. This paper only consider the case of finite-dimensional state spaces. Necessary and sufficient conditions for termination and almost termination of a general quantum loop on any mixed input state are presented. A quantum loop is said to be (almost) terminating if it (almost) terminates on any input state. We show that a quantum loop is almost terminating if and only if it is uniformly almost terminating. It is observed that a small disturbance either on the unitary transformation in the loop body or on the measurement in the loop guard can make any quantum loop (almost) terminating, provided that some dimension restriction is satisfied. Moreover, a representation of the function computed by a quantum loop is given in terms of finite summations of matrices. To illustrate the notions and results obtained in this paper, two simple classes of quantum loop programs, one qubit quantum loops, and two qubit quantum loops defined by controlled gates, are carefully examined, and to show their expressive power, quantum loops are applied in describing quantum walks. © 2010 Springer-Verlag

Probabilistic bisimulations for quantum processes

Modeling and reasoning about concurrent quantum systems is very important for both distributed quantum computing and quantum protocol verification. As a consequence, a general framework formally describing communication and concurrency in complex quantum systems is necessary. For this purpose, we propose a model named qCCS. It is a natural quantum extension of classical value-passing CCS which can deal with input and output of quantum states, and unitary transformations and measurements on quantum systems. The operational semantics of qCCS is given in terms of probabilistic labeled transition system. This semantics has many different features compared with the proposals in the available literature in order to describe the input and output of quantum systems which are possibly correlated with other components. Based on this operational semantics, the notions of strong probabilistic bisimulation and weak probabilistic bisimulation between quantum processes are introduced. Furthermore, some properties of these two probabilistic bisimulations, such as congruence under various combinators, are examined. © 2007 Elsevier Inc. All rights reserved

Llenguatges de Programació Quàntica

Aprofundir en els coneixements de computació quàntica, tant des del vessant de la física com des del vessant de la teoria de la computació, que em situïn en un punt de "pre-recerca". Tenir un mapa de les diferents aproximacions a llenguatges de programació quàntica que s'han fet en els últims anys. Distingir els pros/contres i limitacions d'aquestes aproximacions. Investigar els avenços recents relacionats amb complexitat de la CQ i els seus límits des del punt de vista de la teoria de la computació. Investigar les diferents propostes de simulació de CQ en ordinadors actuals

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

Lambda calculi and logics for quantum computing

In questa tesi proponiamo diversi risultati originali riguardo i lambda calcoli e le logiche per le computazioni quantistiche. Il lavoro `e diviso in tre parti. Nella prima parte richiamiamo alcune nozioni fondamentali di algebra lineare, logica e computazione quantistica. La seconda parte volge l\u2019attenzione ai lambda calcoli quantistici. Introdurremo dapprima Q, un lambda calcolo quantistico con controllo classico. Studieremo le sue proprie`a classiche, come la confluenza e la Subject Reduction, proseguendo poi con un\u2019importante propriet`a quantistica, chiamata standardizzazione. In seguito sar`a studiato il potere espressivo di Q, attraverso la provata equivalenza con il formalismo delle famiglie di circuiti quantistici. A partire da Q, sar`a poi definito e studiato il sottolinguaggio SQ, ispirato alla Soft Linear Logic ed intrinsecamente polytime. Sia Q sia SQ non hanno nella sintassi un operatore di misurazione, e quindi un\u2019implicita misurazione viene assunta alla fine delle computazioni. I problemi relativi alla misura sono studiati in un terzo lambda calcolo chiamato Q*, che estende Q con un operatore di misura. Partendo dall\u2019osservazione che un esplicito operatore di misura interrompe l\u2019evoluzione altrimenti deterministica del calcolo, importando un comportamento probabilistico, sono stati definiti dei nuovi strumenti tecnici quali le computazioni probabilistiche e gli stati misti. Proveremo un forte teorema di confluenza, valido anche nell\u2019importante caso delle computazioni infinite. Nella terza parte della tesi studieremo invece due sistemi modali etichettati, chiamati rispettivamente MSQS e MSpQS, che permettono di ragionare qualitativamente sulle computazioni quantistiche. I due sistemi rappresentano un possibile punto di partenza verso un nuovo modello per ragionare qualitativamente sulle trasformazioni computazionali degli stati quantistici, viste come modelli di Kripke. 1In this thesis we propose several original results about lambda calculi and logics for quantum computing. The work is divided into three parts. The first one is devoted to recall the main notions about linear algebra, logics and quantum computing. The second and main part focalizes on quantum lambda calculi. We start with Q, a quantum lambda calculus with classical control. We study its classical properties, such as confluence and Subject Reduction. We go on with an important quantum property of Q, called standardization, and successively, we study the expressive power of the proposed calculus, by proving the equivalence with the computational model of quantum circuit families. From the calculus Q, subsequently a sublanguage of Q called SQ is defined and studied: SQ is inspired to the Soft Linear Logic and it is a quantum lambda calculus intrinsically poly-time. Since Q and SQ have not an explicit measurement operator in the syntax, an implicit measurement at the end of the computations is assumed. Measurement problems are explicitly studied in a third quantum lambda calculus called Q*, an extension of Q with a measurement operator. Starting from the observation that an explicit measurement operator breaks the deterministic evolution of the computation by importing a probabilistic behavior, new technical instruments, such as the probabilistic computations and the mixed states are defined. We prove a confluence result for the calculus, also for the relevant case of infinite computations. In the last part of the thesis, we propose two labeled modal deduction systems able to describe quantum computations from a qualitative point of view. The two systems, called respectively MSQS and MSpQS, represent a starting point toward a new model to deal (in a qualitative way) with computational quantum structures, seen as Kripke models.

Quantum Programming With Mixed States

AbstractIn this paper we offer a programming approach to quantum computation using mixed states. Mixed-state quantum systems generalise standard (pure) quantum systems by allowing the state of the system to be a probabilistic distribution of pure states. We build on previous work by Aharonov et al. and generalise their results from quantum circuits to probabilistic (and quantum) programs