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We discuss quantum information processing machines. We start with single purpose machines that either redistribute quantum information or identify quantum states. We then move on to machines that can perform a number of functions, with the…

Quantum simulators are devices that actively use quantum effects to answer questions about model systems and, through them, real systems. Here we expand on this definition by answering several fundamental questions about the nature and use…

Complex processes often arise from sequences of simpler interactions involving a few particles at a time. These interactions, however, may not be directly accessible to experiments. Here we develop the first efficient method for unravelling…

In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…

In resisting attempts to explain the unity of a whole in terms of a multiplicity of interacting parts, quantum mechanics calls for an explanatory concept that proceeds in the opposite direction: from unity to multiplicity. It concerns the…

Computer programs are often factored into pure components -- simple, total functions from inputs to outputs -- and components that may have side effects -- errors, changes to memory, parallel threads, abortion of the current loop, etc. We…

The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…

We present a framework for quantifying information flow within general quantum processes. For this purpose, we introduce the signaling power of quantum channels and discuss its relevant operational properties. This function supports…

We construct, using the quantum dilogarithm, a series of *-representations of quantized cluster varieties. This includes a construction of infinite dimensional unitary projective representations of their discrete symmetry groups - the…

We present a logical separability analysis for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably…

The quantum world is fascinating. It presents a description of nature that defies our most rooted concepts about what reality is. For example, quantum objects possess \lq\lq spooky\rq\rq\ properties that allow them to be in multiple places…

We show that a separation between the class of all problems that can efficiently be solved on a quantum computer and those solvable using probabilistic classical algorithms in polynomial time implies the generalized contextuality of quantum…

The extremely fascinating behaviors of the quantum walks of particles, which differ much from the classical counterparts, have attracted many physicists. Here we investigate another interesting part of the quantum walks, that is the quantum…

We develop elements of a general dilation theory for operator-valued measures and bounded linear maps between operator algebras that are not necessarily completely-bounded. We prove our main results by extending and generalizing some known…

Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box and the aim is to compute function value for arbitrary input using as few queries as possible. We concentrate on quantum…

People usually regard algorithms as more abstract than the programs that implement them. The natural way to formalize this idea is that algorithms are equivalence classes of programs with respect to a suitable equivalence relation. We argue…

Theories for reasoning about programs with effects initially focused on basic manipulation of lists and other mutable data. The next challenge was to consider higher-order programming, adding functions as first class objects to mutable…

We present a way to apply quantum logic to the study of quantum programs. This is made possible by using an extension of the usual propositional language in order to make transformations performed on the system appear explicitly. This way,…

The Dirac equation provides a description of spin 1/2 particles, consistent with both the principles of quantum mechanics and of special relativity. Often its presentation to students is based on mathematical propositions that may hide the…

To simulate the quantum systems at classical or quantum computers, it is necessary to reduce continuous observables (e.g. coordinate and momentum or energy and time) to discrete ones. In this work we consider the continuous observables…