Related papers: Random Quantum Maps and Their Associated Quantum M…
We introduce a Sinkhorn-type algorithm for producing quantum permutation matrices encoding symmetries of graphs. Our algorithm generates square matrices whose entries are orthogonal projections onto one-dimensional subspaces satisfying a…
Using a representation of multichannel quantum defect theory in terms of a quantum Poincar\'e map for bound Rydberg molecules, we apply Jung's scattering map to derive a generalized quantum map, that includes the continuum. We show, that…
Markov random fields (MRFs) appear in many problems in machine learning and statistics. From a computational learning theory point of view, a natural problem of learning MRFs arises: given samples from an MRF from a restricted class, learn…
Matrix geometric means between two positive definite matrices can be defined from distinct perspectives - as solutions to certain nonlinear systems of equations, as points along geodesics in Riemannian geometry, and as solutions to certain…
We introduce a class of linear maps irreducibly covariant with respect to the finite group generated by the Weyl operators. This group provides a direct generalization of the quaternion group. In particular, we analyze the irreducibly…
In this paper, we will discuss a formal link between neural networks and quantum computing. For that purpose we will present a simple model for the description of the neural network by forming sub-graphs of the whole network with the same…
Most scholars maintain that quantum mechanics (QM) is a contextual theory and that quantum probability does not allow an epistemic (ignorance) interpretation. By inquiring possible connections between contextuality and non-classical…
We introduce two new formulations for the notion of "quantum metric on noncommutative space". For a compact noncommutative space associated to a unital C*-algebra, our quantum metrics are elements of the spatial tensor product of the…
This paper initiates a systematic study of operators arising as integrals of operator-valued functions with respect to positive operator-valued measures and utilizes these tools to provide relativization maps (Yen) for quantum reference…
A generalization of the Choi-Jamiolkowski isomorphism for completely positive maps between operator algebras is introduced. Particular emphasis is placed on the case of normal unital completely positive maps defined between von Neumann…
Quantum computing is a relatively new field of computing, which utilises the fundamental concepts of quantum mechanics to process data. The seminal paper of Moore et al. [2000] introduced quantum grammars wherein a set of amplitudes was…
Consider a Hamiltonian action of a compact connected Lie group on a symplectic manifold $(M,\omega)$. Conjecturally, under suitable assumptions there exists a morphism of cohomological field theories from the equivariant Gromov-Witten…
A quantum circuit must be preprocessed before implementing on NISQ devices due to the connectivity constraint. Quantum circuit mapping (QCM) transforms the circuit into an equivalent one that is compliant with the NISQ device's architecture…
In these Notes, a comprehensive description of the universal fractal geometry of conformally-invariant scaling curves or interfaces, in the plane or half-plane, is given. The present approach focuses on deriving critical exponents…
Randomness is an indispensable resource in modern science and information technology. Fortunately, an experimentally simple procedure exists to generate randomness with well-characterized devices: measuring a quantum system in a basis…
We investigate the presence of memory in the sequential measurement statistics of an open quantum system, as witnessed by the departure from the quantum regression theorem (QRT), that is, the possibility to predict multitime probabilities…
An effective, accessible abstraction hierarchy has made using and programming computers possible for people across all disciplines. Establishing such a hierarchy for quantum programming is an outstanding challenge, especially due to a…
This paper presents a quantum generalization of the multinomial distribution for the transition probabilities of $m$ identical photons in a $k$-port linear optical interferometer: two multinomial coefficients (one for the input…
The model of quantum associative memories (QAM) we propose here consists in simplifying and generalizing that of Rigui Zhou \etal \cite{zhou2012} who uses the quantum matrix with binary decision diagram and nonlinear search algorithm in his…
Operating on the principles of quantum mechanics, quantum algorithms hold the promise for solving problems that are beyond the reach of the best-available classical algorithms. An integral part of realizing such speedup is the…