Related papers: Quantum Margulis expanders
We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum…
An extended Wigner function formalism is introduced for describing the quantum dynamics of particles with internal degrees of freedom in the presence of spatially inhomogeneous fields. The approach is used for quantitative simulations of…
Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of…
We study the classical limit of quantum mechanics on graphs by introducing a Wigner function for graphs. The classical dynamics is compared to the quantum dynamics obtained from the propagator. In particular we consider extended open graphs…
We present an approach to simulating quantum computation based on a classical model that directly imitates discrete quantum systems. Qubits are represented as harmonic functions in a 2D vector space. Multiplication of qubit representations…
The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being…
Mathematical tools related to coherence theory and classical-quantum equivalence, due to Wigner and Glauber, are essential to modern, practical and empirical understanding of electromagnetics in areas like quantum optics and…
Expander graphs are fundamental in both computer science and mathematics, with a wide array of applications. With quantum technology reshaping our world, quantum expanders have emerged, finding numerous uses in quantum information theory,…
In quantum theory, observables with a continuous spectrum are known to be fundamentally different from those with a discrete and finite spectrum. While some fundamental tests and applications of quantum mechanics originally formulated for…
A complete solution to the problem of setting up Wigner distribution for N-level quantum systems is presented. The scheme makes use of some of the ideas introduced by Dirac in the course of defining functions of noncommuting observables and…
A direct comparison of quantum and classical dynamical systems can be accomplished through the use of distribution functions. This is useful for both fundamental investigations such as the nature of the quantum-classical transition as well…
We introduce a quasi-probability phase space distribution with two pairs of azimuthal-angular coordinates. This representation is well adapted to describe quantum systems with discrete symmetry. Quantum error correction of states encoded in…
We formulate continuous time quantum walks (CTQW) in a discrete quantum mechanical phase space. We define and calculate the Wigner function (WF) and its marginal distributions for CTQWs on circles of arbitrary length $N$. The WF of the CTQW…
Wigner functions help visualise quantum states and dynamics while supporting quantitative analysis in quantum information. In the discrete setting, many inequivalent constructions coexist for each Hilbert-space dimension. This fragmentation…
(Abridged.) Quantum computers promise to solve some problems exponentially faster than traditional computers, but we still do not fully understand why this is the case. While the most studied model of quantum computation uses qubits, which…
We study the Wigner function for a quantum system with a discrete, infinite dimensional Hilbert space, such as a spinless particle moving on a one dimensional infinite lattice. We discuss the peculiarities of this scenario and of the…
Smoothed Wigner transforms have been used in signal processing, as a regularized version of the Wigner transform, and have been proposed as an alternative to it in the homogenization and / or semiclassical limits of wave equations. We…
As a stochastic model for quantum mechanics we present a stationary quantum Markov process for the time evolution of the Wigner function on a lattice phase space Z_N x Z_N with N odd. By introducing a phase factor extension to the phase…
The Wigner function is a well-known phase space distribution function with many applications in quantum mechanics. In this article, we consider an open quantum system consisting of a non-relativistic single particle interacting with a…
A quantum phase space with Wannier basis is constructed: (i) classical phase space is divided into Planck cells; (ii) a complete set of Wannier functions are constructed with the combination of Kohn's method and L\"owdin method such that…