Related papers: Resolving Correlated States of Benzyne on a Quantu…
The electronic Schr\"odinger equation describes the motion of $N$ electrons under Coulomb interaction forces in a field of clamped nuclei. It is proved that its solutions for eigenvalues below the essential spectrum lie in the spectral…
Restricted Boltzmann machines (RBMs) have demonstrated considerable success as variational quantum states; however, their representational power remains incompletely understood. In this work, we present an analytical proof that RBMs can…
Many equations have been introduced and derived by the author indicated in the title in relation to multi-electron densities between the Hohenberg-Kohn theorems and variational principle, conversion of the non-relativistic electronic…
We study numerically the Coulomb interacting two-particle stationary states of the Schr\"odinger equation, where the particles are confined in a two-dimensional infinite square well. Inside the domain the particles are subjected to a…
This paper proposes a very simple perturbative technique to calculate the low-lying eigenvalues and eigenstates of a parity-symmetric quantum-mechanical potential. The technique is to solve the time-independent Schroedinger eigenvalue…
Calculations of the ground state of inhomogeneous many-electron systems involve a solving of the Poisson equation for Coulomb potential and the Schroedinger equation for single-particle orbitals. Due to nonlinearity and complexity this set…
Solving the electronic Schrodinger equation for strongly correlated ground states is a long-standing challenge. We present quantum algorithms for the variational optimization of wavefunctions correlated by products of unitary operators,…
This article explains and illustrates the use of a set of coupled dynamical equations, second order in a fictitious time, which converges to solutions of stationary Schr\"{o}dinger equations with additional constraints. We include three…
We propose a qubit efficient scheme to study ground state properties of quantum many-body systems on near-term noisy intermediate scale quantum computers. One can obtain a tensor network representation of the ground state using a number of…
We study the many-body problem of charged particles interacting with their self-generated electromagnetic field. We model the dynamics of the particles by the many-body Maxwell-Schr\"odinger system, where the particles are treated quantum…
Representability determines when a two-particle reduced density matrix (2-RDM) corresponds to a physical quantum state, enabling many-particle quantum calculations with 2-RDMs rather than the wave function. In this Letter, we present a…
Variational quantum eigensolvers offer a small-scale testbed to demonstrate the performance of error mitigation techniques with low experimental overhead. We present successful error mitigation by applying the recently proposed symmetry…
The non-relativistic electronic Hamiltonian, H(a)= Hkin + Hne + aHee, extended with coupling strength parameter (a), allows to switch the electron-electron repulsion energy off and on. First, the easier a=0 case is solved and the solution…
In this paper, we have provided exact two-body solutions to the 2D and 3D Schr\"odinger equations with isotropic van der Waals potentials of the form \(\pm 1/r^6\). Based on these solutions, we developed an analytical quantum defect theory…
Assuming Coulomb-like as well as confining scalar potential, we have solved Shr\"odinger equation perturbatively in $1/m_Q$ with a heavy quark mass $m_Q$. The lowest order equation is examined carefully. Mass levels are fitted with…
During recent years, quantum computers have received increasing attention, primarily due to their ability to significantly increase computational performance for specific problems. Computational performance could be improved for…
Understanding quantum many-body states of correlated electrons is one main theme in modern condensed matter physics. Given that the Fermi-Hubbard model, the prototype of correlated electrons, has been recently realized in ultracold optical…
The time-dependent Schrodinger equation of a many particle spin system consisting of an electron in a quantum dot interacting with the spins of the nuclei (N) in the dot due to hyperfine interaction is solved exactly for a given arbitrary…
An efficient way of solving 2D stability problems in fluid mechanics is to use, after discretization of the equations that cast the problem in the form of a generalized eigenvalue problem, the incomplete Arnoldi-Chebyshev method. This…
By design, the variational quantum eigensolver (VQE) strives to recover the lowest-energy eigenvalue of a given Hamiltonian by preparing quantum states guided by the variational principle. In practice, the prepared quantum state is…