Related papers: Transforming quantum operations: quantum supermaps
A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…
Despite significant advances in quantum algorithms, quantum programs in practice are often expressed at the circuit level, forgoing helpful structural abstractions common to their classical counterparts. Consequently, as many quantum…
In many a traditional physics textbook, a quantum measurement is defined as a projective measurement represented by a Hermitian operator. In quantum information theory, however, the concept of a measurement is dealt with in complete…
Quantum control refers to our ability to manipulate quantum systems. This tutorial-style chapter focuses on the use of classical electromagnetic fields to steer the system dynamics. In this approach, the quantum nature of the control stems…
{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum…
Quantum information processing protocols are efficiently implemented on spin-$\frac{1}{2}$ networks. A quantum communication protocol generally involves a certain number of parties having local access to a subset of a larger system, whose…
Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described…
A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…
Quantum mechanics, the fundamental theory that governs the behaviour of matter and energy at microscopic scales, forms the foundation of quantum computing and quantum information science. As quantum technologies progress, software engineers…
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum…
Quantum entanglement lies at the heart of quantum mechanics in both fundamental and practical aspects. The entanglement of quantum states has been studied widely, however, the entanglement of operators has not been studied much in spite of…
Quantum Computing is a new paradigm that enables several advances which are impossible using classical technology. With the rise of quantum computers, the software is also invited to change so that it can better fit this new computation…
Classification, the computational process of categorizing an input into pre-existing classes, is now a cornerstone in modern computation in the era of machine learning. Here we propose a new type of quantum classifier, based on quantum…
Contrary to the classical case, the relation between quantum programming languages and quantum Turing Machines (QTM) has not being fully investigated. In particular, there are features of QTMs that have not been exploited, a notable example…
The concept of intrinsic and operational observables in quantum mechanics is introduced. In any realistic description of a quantum measurement that includes a macroscopic detecting device, it is possible to construct from the statistics of…
We revisit the question of universality in quantum computing and propose a new paradigm. Instead of forcing a physical system to enact a predetermined set of universal gates (e.g., single-qubit operations and CNOT), we focus on the…
A quantum impulse is a brief but strong perturbation that produces a sudden change in a wavefunction $\psi(x)$. We develop a theory of quantum impulses, distinguishing between ordinary and super impulses. An ordinary impulse paints a phase…
We present a method for optimizing quantum circuits architecture. The method is based on the notion of "quantum comb", which describes a circuit board in which one can insert variable subcircuits. The method allows one to efficiently…
A reinterpretation of noncommutativity as a mapping of paths is proposed at the level of quantum mechanics.
Information processing with light is ubiquitous, from communication, metrology and imaging to computing. When we consider light as a quantum mechanical object, new ways of information processing become possible. In this review I give an…