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Quantum phases of naturally-occurring systems exhibit distinctive collective phenomena as manifestation of their many-body correlations, in contrast to our persistent technological challenge to engineer at will such strong correlations…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
Computation of the spherical harmonic rotation coefficients or elements of Wigner's d-matrix is important in a number of quantum mechanics and mathematical physics applications. Particularly, this is important for the Fast Multipole Methods…
Mathematical models of quantum computers such as a multidimensional quantum Turing machine and quantum circuits are described and its relations with lattice spin models are discussed. One of the main open problems one has to solve if one…
Matrix quantum mechanics plays various important roles in theoretical physics, such as a holographic description of quantum black holes. Understanding quantum black holes and the role of entanglement in a holographic setup is of paramount…
Coherence and entanglement are fundamental properties of quantum systems, promising to power the near future quantum computers, sensors and simulators. Yet, their experimental detection is challenging, usually requiring full reconstruction…
Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…
The central objects in a quantum field theory are its n-point correlation functions and matrix elements. Their structure is determined by Lorentz invariance and leads to tensor decompositions whose Lorentz-invariant coefficient functions…
We present a method to quantify quantum correlations in arbitrary systems of indistinguishable fermions using witness operators. The method associates the problem of finding the optimal entan- glement witness of a state with a class of…
Quantum algorithms for computational linear algebra promise up to exponential speedups for applications such as simulation and regression, making them prime candidates for hardware realization. But these algorithms execute in a model that…
We introduce a new information theoretic measure of quantum correlations for multiparticle systems. We use a form of multivariate mutual information -- the interaction information and generalize it to multiparticle quantum systems. There…
We analyse the correlation function of the quantum curvature in complex quantum systems, using a random matrix model to provide an exemplar of a universal correlation function. We show that the correlation function diverges as the inverse…
A formulation for evaluating the performance of quantum error correcting codes for a general error model is presented. In this formulation, the correlation between errors is quantified by a Hamiltonian description of the noise process. We…
Scalable modern-time fault-tolerant quantum computation and quantum communication in a network employ a large number of physical qubits. For example, IBM is reported to have made a 127-qubit quantum computer. Unlike classical computation,…
We investigate decoherence effects in the recently suggested quantum computation scheme using weak nonlinearities, strong probe coherent fields, detection and feedforward methods. It is shown that in the weak-nonlinearity-based quantum…
The programs described in this article and distributed with it aim (1) at integrating the optical Bloch equations governing the time evolution of the density matrix representing the quantum state of an atomic system driven by laser or…
Quantum computation of vibrational properties of molecules is a promising platform to obtain computational advantages for computational chemistry. However, fault-tolerant quantum computations of vibrational properties remain a relatively…
The production and manipulation of quantum correlation protocols will play a central role where the quantum nature of the correlation can be used as a resource to yield properties unachievable within a classical framework is a very active…
Coherence is a fundamental ingredient in quantum physics and a key resource in quantum information processing. The quantification of quantum coherence is of great importance. We present a family of coherence quantifiers based on the Tsallis…
We derive quantum kinetic equations for fermions in a homogeneous time-dependent background in presence of decohering collisions, by use of the Schwinger-Keldysh CTP-formalism. The quantum coherence (between particles and antiparticles) is…