Related papers: Classical Computer, Quantum Computer, and the G\"o…
$P$-divisibility is a central concept in both classical and quantum non-Markovian processes; in particular, it is strictly related to the notion of information backflow. When restricted to a fixed commutative algebra generated by a complete…
Universal quantum computers are the only general purpose quantum computers known that can be implemented as of today. These computers consist of a classical memory component which controls the quantum memory. In this paper, the space…
These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms. So far, we have only discovered a few techniques which can produce speed up versus classical…
We consider quantum learning machines -- quantum computers that modify themselves in order to improve their performance in some way -- that are trained to perform certain classical task, i.e. to execute a function which takes classical bits…
Quantum computers leverage the principles of quantum mechanics to do computation with a potential advantage over classical computers. While a single classical computer transforms one particular binary input into an output after applying one…
An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is…
The laptops, cell phones, and internet applications commonplace in our daily lives are all rooted in the idea of zeros and ones - in bits. This foundational element originated from the combination of mathematics and Claude Shannon's Theory…
We show that the main difference between classical and quantum systems can be understood in terms of information entropy. Classical systems can be considered the ones where the internal dynamics can be known with arbitrary precision while…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…
Two models of computer, a quantum and a classical "chemical machine" designed to compute the relevant part of Shor's factoring algorithm are discussed. The comparison shows that the basic quantum features believed to be responsible for the…
Quantum kernels are reproducing kernel functions built using quantum-mechanical principles and are studied with the aim of outperforming their classical counterparts. The enthusiasm for quantum kernel machines has been tempered by recent…
A new paradigm of quantum computing, namely, soft quantum computing, is proposed for nonclassical computation using real world quantum systems with naturally occurring environment-induced decoherence and dissipation. As a specific example…
Quantum computers are believed to surpass the classical ones. Moreover, it is claimed that this belief reaches the level of a mathematically proven fact within the oracle model of computation. Here we impair the whole class of the so-called…
A common way of stating the non-cloning theorem -- one of distinguishing characteristics of quantum theory -- is that one cannot make a copy of an arbitrary unknown quantum state. Even though this theorem is an important part of the ongoing…
The field of quantum algorithms aims to find ways to speed up the solution of computational problems by using a quantum computer. A key milestone in this field will be when a universal quantum computer performs a computational task that is…
Quantum machine learning (QML) sits at the intersection of quantum computing and classical machine learning, offering the prospect of new computational paradigms and advantages for processing complex data. This chapter introduces the…
The no-cloning theorem asserts that, unlike classical information, quantum information cannot be copied. This seemingly undesirable phenomenon is harnessed in quantum cryptography. Uncloneable cryptography studies settings in which the…
Noise is often regarded as anathema to quantum computation, but in some settings it can be an unlikely ally. We consider the problem of learning the class of $n$-bit parity functions by making queries to a quantum example oracle. In the…
Despite significant effort, the quantum machine learning community has only demonstrated quantum learning advantages for artificial cryptography-inspired datasets when dealing with classical data. In this paper we address the challenge of…
Cryptography plays a pivotal role in safeguarding sensitive information and facilitating secure communication. Classical cryptography relies on mathematical computations, whereas quantum cryptography operates on the principles of quantum…