Juliana Kaizer Vizzotto

Structuring quantum effects: superoperators as arrows

We show that the model of quantum computation based on density matrices and superoperators can be decomposed into a pure classical (functional) part and an effectful part modelling probabilities and measurement. The effectful part can be modelled using a generalisation of monads called arrows. We express the resulting executable model of quantum computing in the Haskell programming language using its special syntax for arrow computations. However, the embedding in Haskell is not perfect: a faithful model of quantum computing requires type capabilities that are not directly expressible in Haskell.

An Algebra of Pure Quantum Programming

We develop a sound and complete equational theory for the functional quantum programming language QML. The soundness and completeness of the theory are with respect to the previously developed denotational semantics of QML. The completeness proof also gives rise to a normalisation algorithm following the normalisation-by-evaluation approach. The current work focuses on the pure fragment of QML, omitting measurements.

Quantum Arrows in Haskell

We argue that a realistic model for quantum computations should be general with respect to measurements, and complete with respect to the information flow between the quantum and classical worlds. We discuss two alternative models for general and complete quantum computations based on probability distributions of quantum state vectors and on density matrices with classical outputs. We show that both models can be structured using a generalization of monads called arrows.

A Double Effect λ-calculus for Quantum Computation

In this paper we present a double effect version of the simply typed λ-calculus where we can represent both pure and impure quantum computations. The double effect calculus comprises a quantum arrow layer defined over a quantum monadic layer. In previous works we have developed the quantum arrow calculus, a calculus where we can consider just impure (or mixed) quantum computations. Technically, here we extend the quantum arrow calculus with a construct (and equations) that allows the communication of the monadic layer with the arrow layer of the calculus. That is, the quantum arrow is defined over a monadic instance enabling to consider pure and impure quantum computations in the same framework. As a practical contribution, the calculus allows to express quantum algorithms including reversible operations over pure states and measurements in the middle of the computation using a traditional style of functional programming and reasoning. We also define equations for algebraic reasoning of computations involving measurements.

Reasoning about General Quantum Programs over Mixed States

In this work we present a functional programming language for quantum computation over mixed states. More interestingly, we develop a set of equations for the resulting programming language, proposing the first framework for equational reasoning about quantum computations over mixed states.

Quantum Computing: State-of-Art and Challenges

In this article we review the concept of quantum computing and briefly discuss the state-of-art and some actual challenges in the field of software (i.e. programming languages and algorithms) for quantum computing.

From Symmetric Pattern-Matching to Quantum Control

One perspective on quantum algorithms is that they are classical algorithms having access to a special kind of memory with exotic properties. This perspective suggests that, even in the case of quantum algorithms, the control flow notions of sequencing, conditionals, loops, and recursion are entirely classical. There is however, another notion of control flow, that is itself quantum. The notion of quantum conditional expression is reasonably well-understood: the execution of the two expressions becomes itself a superposition of executions. The quantum counterpart of loops and recursion is however not believed to be meaningful in its most general form.

FJQuantum - A Quantum Object Oriented Language

Several languages and libraries has been proposed to work with quantum programs, usually considering the imperative and functional paradigms. In this paper, we discuss the application of the FJQuantum language, an object-oriented language based on Featherweight Java to develop programs that handle quantum data and operations.

Composable Memory Transactions for Java Using a Monadic Intermediate Language

Transactional memory is a new programming abstraction that simplifies concurrent programming. This paper describes the parallel implementation of a Java extension for writing composable memory transactions in Java. Transactions are composable i.e., they can be combined to generate new transactions, and are first-class values, i.e., transactions can be passed as arguments to methods and can be returned as the result of a method call. We describe how composable memory transactions can be implemented in Java as a state passing monad, in which transactional blocks are compiled into an intermediate monadic language. We show that this intermediated language can support different transactional algorithms, such as TL2i¾?[9] and SWissTMi¾?[10]. The implementation described here also provides the high level construct retry, which allows possibly-blocking transactions to be composed in sequence. Although our prototype implementation is in Java using BGGA Closures, it could be implemented in any language that supports objects and closures in some way, e.g. C#, C++, and Python.

Typed context awareness Ambient Calculus for pervasive applications

The idea of pervasive computing is that information processing will become part of everyday life, and will be available everywhere, making computing so natural to the point of being invisible in the ambient. An important concept that arises with pervasive computing is context awareness. Context is any information that can be used to characterize an entity. Based on contextual information, applications can dynamically adapt themselves to the environments in which they operate. The Calculus of Context-aware Ambients (CCA) is an untyped formal language used to describe mobile and context-aware pervasive applications. The CCA extends the Ambient Calculus by providing new features, such as context-guarded action and process abstraction, allowing to model contexts and context-aware computations. In this work, we define a type system for the CCA, called CCAT, with the focus in the communication between processes and in the correct use of process abstraction and contexts, extending previous works on the definition of type systems for mobile computing. Moreover, we prove that the proposed type system has the subject reduction property (or type preservation). We also model a hospital scenario using CCAT to demonstrate the use of the proposed type system.