Related papers: Quantum linear algebra for disordered electrons
We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum…
A new approach to nonperturbative calculations in quantum electrodynamics is proposed. The approach is based on a regular iteration scheme for solution of Schwinger-Dyson equations for generating functional of Green functions. The approach…
Power system dynamics are generally modeled by high dimensional nonlinear differential-algebraic equations (DAEs) given a large number of components forming the network. These DAEs' complexity can grow exponentially due to the increasing…
Power system dynamics are generally modeled by high dimensional nonlinear differential-algebraic equations (DAEs) given a large number of components forming the network. These DAEs' complexity can grow exponentially due to the increasing…
Neural networks have achieved impressive breakthroughs in both industry and academia. How to effectively develop neural networks on quantum computing devices is a challenging open problem. Here, we propose a new quantum neural network model…
We extend our previous results on local asymptotic normality (LAN) for qubits, to quantum systems of arbitrary finite dimension $d$. LAN means that the quantum statistical model consisting of $n$ identically prepared $d$-dimensional systems…
Motivated by current interest in disordered systems of interacting electrons, the effectiveness of the geometrically averaged density of states, $\rho_g(\omega)$, as an order parameter for the Anderson transition is examined. In the context…
This manuscript explores a variational quantum formulation for nonlinear elasticity problems arising from hyperelastic material models, targeting near term noisy intermediate scale quantum (NISQ) devices. The approach leverages the…
We study some basic quantum confinement effects through investigation a deformed harmonic oscillator algebra. We show that spatial confinement effects on a quantum harmonic oscillator can be represented by a deformation function within the…
Learning from data has led to a paradigm shift in computational materials science. In particular, it has been shown that neural networks can learn the potential energy surface and interatomic forces through examples, thus bypassing the…
The spectral properties of up to four interacting electrons confined within a quasi one--dimensional system of finite length are determined by numerical diagonalization including the spin degree of freedom. The ground state energy is…
We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras…
Theory of Random Matrix Ensembles have proven to be a useful tool in the study of the statistical distribution of energy or transmission levels of a wide variety of physical systems. We give an overview of certain q-generalizations of the…
In this Letter we present a field-theoretic formulation for describing non-ideal quantum electrodynamic effects. It generalizes its ideal counterpart and is valid in the non-ideal domain. We compute some non-ideal elementary processes both…
We introduce a mapping between a variety of superconducting circuits and a family of Hamiltonians describing localized magnetic impurities interacting with conduction bands. This includes the Anderson model, the single impurity one- and…
In this paper, we consider the following nonlinear disordered Stark model: $${\bf i}\partial_tu_n+\delta(u_{n+1}+u_{n-1})+nu_n+v_nu_n+\epsilon |u_n|^{2}u_n=0,\quad n\in\mathbb{Z}.$$ By employing the diagonalization of the associated linear…
The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting…
Machine learning offers a largely unexplored avenue for improving noisy disordered devices in physics using automated algorithms. Through simulations that include disorder in physical devices, particularly quantum devices, there is…
Quantum and q-deformed algebras find their application not only in mathematical physics and field theoretical context, but also in phenomenology of particle properties. We describe (i) the use of quantum algebras U_q(su_n) corresponding to…
The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatment, especially in non-equilibrium setups. Therefore, it is vital to recognize states which are locally less…