Related papers: Quantum marginals, faces, and coatoms

We introduce the quantum mechanical formalism for treating surface plasmon polariton scattering at an interface. Our developed theory - which is fundamentally different from the analogous photonic scenario - is used to investigate the…

We study the properties of the set of marginal distributions of infinite translation-invariant systems in the 2D square lattice. In cases where the local variables can only take a small number $d$ of possible values, we completely solve the…

We consider the notions of (i) critical points, (ii) second-order points, (iii) local minima, and (iv) strict local minima for multivariate polynomials. For each type of point, and as a function of the degree of the polynomial, we study the…

The problem of sampling outputs of quantum circuits has been proposed as a candidate for demonstrating a quantum computational advantage (sometimes referred to as quantum "supremacy"). In this work, we investigate whether quantum advantage…

Quantum families of maps between quantum spaces are defined and studied. We prove that quantum semigroup (and sometimes quantum group) structures arise naturally on such objects out of more fundamental properties. As particular cases we…

Finding a Hadamard matrix (H-matrix) among the set of all binary matrices of corresponding order is a hard problem, which potentially can be solved by quantum computing. We propose a method to formulate the Hamiltonian of finding H-matrix…

The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for…

This paper initiates the explicit study of face numbers of matroid polytopes and their computation. We prove that, for the large class of split matroid polytopes, their face numbers depend solely on the number of cyclic flats of each rank…

A quantum walk model which reflects the $2$-cell embedding on the orientable closed surface of a graph in the dynamics is introduced. We show that the scattering matrix is obtained by finding the faces on the underlying surface which have…

In this paper, we explore the relationship between the width of a qubit lattice constrained in one dimension and physical thresholds for scalable, fault-tolerant quantum computation. To circumvent the traditionally low thresholds of small…

Finding ground states of quantum many-body systems is known to be hard for both classical and quantum computers. As a result, when Nature cools a quantum system in a low-temperature thermal bath, the ground state cannot always be found…

In this work, we consider a fundamental task in quantum many-body physics - finding and learning ground states of quantum Hamiltonians and their properties. Recent works have studied the task of predicting the ground state expectation value…

After intensive research, heterogenous face recognition is still a challenging problem. The main difficulties are owing to the complex relationship between heterogenous face image spaces. The heterogeneity is always tightly coupled with…

The quantum theory of atoms in molecules, QTAIM, is employed to identify AIM and quantify their interactions through the partitioning of molecule into atomic basins in the real space and it is confined only to the purely electronic systems…

Variational quantum algorithms involve training parameterized quantum circuits using a classical co-processor. An important variational algorithm, designed for combinatorial optimization, is the quantum approximate optimization algorithm.…

We examine qubit states under symmetric informationally-complete measurements, representing state vectors as probability 4-vectors within a 3-simplex in $bb(R)^4$. Using geometric transformations, this 3-simplex is mapped to a tetrahedron…

We construct a new family, indexed by the odd integers $N\geq 1$, of $(2+1)$-dimensional quantum field theories called {\it quantum hyperbolic field theories} (QHFT), and we study its main structural properties. The QHFT are defined for…

Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…

The establishment of a scalable scheme for quantum computing with addressable and long-lived qubits would be a scientific watershed, harnessing the laws of quantum physics to solve classically intractable problems. The design of many…

In quantum mechanics, geometry has been demonstrated as a useful tool for inferring non-classical behaviors and exotic properties of quantum systems. One standard approach to illustrate the geometry of quantum systems is to project the…