Quantum Programming Made Easy

We present IQu, namely a quantum programming language that extends Reynold's Idealized Algol, the paradigmatic core of Algol-like languages. IQu combines imperative programming with high-order features, mediated by a simple type theory. IQu mildly merges its quantum features with the classical programming style that we can experiment through Idealized Algol, the aim being to ease a transition towards the quantum programming world. The proposed extension is done along two main directions. First, IQu makes the access to quantum co-processors by means of quantum stores. Second, IQu includes some support for the direct manipulation of quantum circuits, in accordance with recent trends in the development of quantum programming languages. Finally, we show that IQu is quite effective in expressing well-known quantum algorithms.Comment: In Proceedings Linearity-TLLA 2018, arXiv:1904.0615

The Quantum Frontier

The success of the abstract model of computation, in terms of bits, logical operations, programming language constructs, and the like, makes it easy to forget that computation is a physical process. Our cherished notions of computation and information are grounded in classical mechanics, but the physics underlying our world is quantum. In the early 80s researchers began to ask how computation would change if we adopted a quantum mechanical, instead of a classical mechanical, view of computation. Slowly, a new picture of computation arose, one that gave rise to a variety of faster algorithms, novel cryptographic mechanisms, and alternative methods of communication. Small quantum information processing devices have been built, and efforts are underway to build larger ones. Even apart from the existence of these devices, the quantum view on information processing has provided significant insight into the nature of computation and information, and a deeper understanding of the physics of our universe and its connections with computation. We start by describing aspects of quantum mechanics that are at the heart of a quantum view of information processing. We give our own idiosyncratic view of a number of these topics in the hopes of correcting common misconceptions and highlighting aspects that are often overlooked. A number of the phenomena described were initially viewed as oddities of quantum mechanics. It was quantum information processing, first quantum cryptography and then, more dramatically, quantum computing, that turned the tables and showed that these oddities could be put to practical effect. It is these application we describe next. We conclude with a section describing some of the many questions left for future work, especially the mysteries surrounding where the power of quantum information ultimately comes from.Comment: Invited book chapter for Computation for Humanity - Information Technology to Advance Society to be published by CRC Press. Concepts clarified and style made more uniform in version 2. Many thanks to the referees for their suggestions for improvement

QPCF: higher order languages and quantum circuits

qPCF is a paradigmatic quantum programming language that ex- tends 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 properties of the system, such as Preservation and Progress Theorems. Moreover, we provide some higher-order examples of circuit encoding

Toward an architecture for quantum programming

It is becoming increasingly clear that, if a useful device for quantum computation will ever be built, it will be embodied by a classical computing machine with control over a truly quantum subsystem, this apparatus performing a mixture of classical and quantum computation. This paper investigates a possible approach to the problem of programming such machines: a template high level quantum language is presented which complements a generic general purpose classical language with a set of quantum primitives. The underlying scheme involves a run-time environment which calculates the byte-code for the quantum operations and pipes it to a quantum device controller or to a simulator. This language can compactly express existing quantum algorithms and reduce them to sequences of elementary operations; it also easily lends itself to automatic, hardware independent, circuit simplification. A publicly available preliminary implementation of the proposed ideas has been realized using the C++ language.Comment: 23 pages, 5 figures, A4paper. Final version accepted by EJPD ("swap" replaced by "invert" for Qops). Preliminary implementation available at: http://sra.itc.it/people/serafini/quantum-computing/qlang.htm

Equivalence of Additivity Questions in Quantum Information Theory

We reduce the number of open additivity problems in quantum information theory by showing that four of them are equivalent. We show that the conjectures of additivity of the minimum output entropy of a quantum channel, additivity of the Holevo expression for the classical capacity of a quantum channel, additivity of the entanglement of formation, and strong superadditivity of the entanglement of formation, are either all true or all false.Comment: now 20 pages, replaced to add a reference, remove a reference to a claimed result about locally minimal output entropy states (my proof of this was incorrect), correct minor typos, and add more explanation for the background of these conjecture