Related papers: Quantum Computing and Hidden Variables I: Mapping …
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
Dirac talked about q-numbers versus c-numbers. Quantum observables are q-number variables that generally do not commute among themselves. He was proposing to have a generalized form of numbers as elements of a noncommutative algebra. That…
Generative Modelling has become a promising use case for near term quantum computers. In particular, due to the fundamentally probabilistic nature of quantum mechanics, quantum computers naturally model and learn probability distributions,…
Quantum Mechanics (QM) is one of the pillars of modern physics: an impressive amount of experiments have confirmed this theory and many technological applications are based on it. Nevertheless, at one century since its development, various…
The consistent histories formulation of the quantum theory of a closed system with pure initial state defines an infinite number of incompatible consistent sets, each of which gives a possible description of the physics. We investigate the…
The goal of demonstrating a quantum advantage with currently available experimental systems is of utmost importance in quantum information science. While this remains elusive for quantum computation, the field of communication complexity…
The study of representations invariant to common transformations of the data is important to learning. Most techniques have focused on local approximate invariance implemented within expensive optimization frameworks lacking explicit…
Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT…
Quantum computation is a novel way of information processing which allows, for certain classes of problems, exponential speedups over classical computation. Various models of quantum computation exist, such as the adiabatic, circuit and…
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…
We derive the classical Hamilton-Jacobi equation from first principles as the natural description for smooth stochastic processes when one neglects stochastic velocity fluctuations. The Schr\"{o}dinger equation is shown to be the natural…
Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is…
In quantum experiments the acquisition and representation of basic experimental information is governed by the multinomial probability distribution. There exist unique random variables, whose standard deviation becomes asymptotically…
Tailoring many-body interactions among a proper quantum system endows it with computing ability by means of static quantum computation in the sense that some of the physical degrees of freedom can be used to store binary information and the…
Quantum trajectory theories have not fully reconciled discrete quantum jumps with continuous unitary evolution. We address this challenge by developing a hidden variable formulation that reveals hidden correlations in individual trials. We…
Quantum computing is a fascinating interdisciplinary research field that promises to revolutionize computing by efficiently solving previously intractable problems. Recent years have seen tremendous progress on both the experimental…
The first clue, in the theory of relativity, the 4-vector force acting on a particle is orthogonal to the 4-vector velocity of the particle, this orthogonality means that there is some difference between the orthogonality and the usual…
The agenda of quantum algorithmic information theory, ordered `top-down,' is the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation. The fundamental…
Quantum computing is a disruptive paradigm widely believed to be capable of solving classically intractable problems. However, the route toward full-scale quantum computers is obstructed by immense challenges associated with the scalability…
"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is…