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Artificial neural networks and machine learning have now reached a new era after several decades of improvement where applications are to explode in many fields of science, industry, and technology. Here, we use artificial neural networks…
A general framework is described which associates geometrical structures to any set of $D$ finite-dimensional hermitian matrices $X^a, \ a=1,...,D$. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and…
In order to support students in the development of expertise in quantum mechanics, we asked which concepts and structures can act as organizing principles of the non-relativistic theory. The research question has been addressed in a…
In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also…
Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…
We investigate the tomography of unknown unitary quantum processes within the framework of a finite-dimensional Wigner-type representation. This representation provides a rich visualization of quantum operators by depicting them as shapes…
Quantum phase transitions between different topologically ordered phases exhibit rich structures and are generically challenging to study in microscopic lattice models. In this work, we propose a tensor-network solvable model that allows us…
The rise of quantum information science has opened up a new venue for applications of the geometric phase (GP), as well as triggered new insights into its physical, mathematical, and conceptual nature. Here, we review this development by…
Quantum technologies exploit entanglement to enhance various tasks beyond their classical limits including computation, communication and measurements. Quantum metrology aims to increase the precision of a measured quantity that is…
Permutation-symmetric quantum states appear in a variety of physical situations, and they have been proposed for quantum information tasks. This article builds upon the results of [New J. Phys. 12, 073025 (2010)], where the maximally…
We present an algebraic algorithm for quantum state tomography that leverages measurements of certain observables to estimate structured entries of the underlying density matrix. Under low-rank assumptions, the remaining entries can be…
Classical dimensional analysis is one of the cornerstones of qualitative physics and is also used in the analysis of engineering systems, for example in engineering design. The basic power product relationship in dimensional analysis is…
We describe all the localization observables of a quantum particle in a one-dimensional box in terms of sequences of unit vectors in a Hilbert space. An alternative representation in terms of positive semidefinite complex matrices is…
We study the construction of both universal quantum computation and multi-partite entangled states in the topological diagrammatical approach to quantum teleportation. Our results show that the teleportation-based quantum circuit model…
We present "Diagrams of States", a way to graphically represent and analyze how quantum information is elaborated during the execution of quantum circuits. This introductory tutorial illustrates the basics, providing useful examples of…
Algebro-geometric methods have proven to be very successful in the study of graphical models in statistics. In this paper we introduce the foundations to carry out a similar study of their quantum counterparts. These quantum graphical…
We introduce a general mapping for encoding quantum communication protocols involving pure states of multiple qubits, unitary transformations, and projective measurements into another set of protocols that employ coherent states of light in…
High-dimensional quantum information processing has become a mature field of research with several different approaches being adopted for the encoding of $D$-dimensional quantum systems. Such progress has fueled the search of reliable…
We study the robustness of 3D intrinsic topogical order under external perturbations by investigating the paradigmatic microscopic model, the 3D toric code in an external magnetic field. Exact dualities as well as variational calculations…
We apply the recently suggested strategy to lift state spaces and operators for (2+1)-dimensional topological quantum field theories to state spaces and operators for a (3+1)-dimensional TQFT with defects. We start from the…