Related papers: Expectation values of single-particle operators in…
Quantum Phase Estimation (QPE), the quantum algorithm for estimating eigenvalues of a given Hermitian matrix and preparing its eigenvectors, is considered the most promising approach to finding the ground states and their energies of…
In [Phys. Rev. Lett. 128, 013001 (2022)] a novel ground state method was proposed. It has been suggested that this $i$-DMFT would be a method within one-particle reduced density matrix functional theory (DMFT), capable of describing…
We consider two related tasks: (a) estimating a parameterisation of a given Gibbs state and expectation values of Lipschitz observables on this state; and (b) learning the expectation values of local observables within a thermal or quantum…
We present a real-space method for computing the random phase approximation (RPA) correlation energy within Kohn-Sham density functional theory, leveraging the low-rank nature of the frequency-dependent density response operator. In…
We introduce a phase field approach for diffusion inside and outside a closed cell with damping and with source terms at the interface. The method is compared to exact solutions (where possible) and the more traditional finite element…
We present an analytic proof demonstrating the equivalence between the Random Phase Approximation (RPA) to the ground state correlation energy and a ring-diagram simplification of the Coupled Cluster Doubles (CCD) equations. In the CCD…
We demonstrate the connection between an operator's matrix element distribution and entangling power via numerical simulations of random, pseudo-random, and quantum chaotic operators. Creating operators with a random distribution of matrix…
We investigate the rational approximation of fractional powers of unbounded positive operators attainable with a specific integral representation of the operator function. We provide accurate error bounds by exploiting classical results in…
In the framework of the study of helium-like atomic systems possessing the collinear configuration, we propose a simple method for computing compact but very accurate wave functions describing the relevant $S$ state. It is worth noting that…
We develop a new projected wave function approach which is based on projection operators in the form of matrix-product operators (MPOs). Our approach allows to variationally improve the short range entanglement of a given trial wave…
We develop a scheme to exactly evaluate the correlation energy in the random-phase approximation, based on linear response theory. It is demonstrated that our formula is completely equivalent to a contour integral representation recently…
Starting from the matrix elements of the nucleon-nucleon interaction in momentum space we present a method to derive an operator representation with a minimal set of operators that is required to provide an optimal description of the…
A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground state energy analytically using our method provided certain consistency relations are satisfied. Analytic…
In the nonrelativistic many-electron approximation of the theory of photoionization of the atom in the formalism of secondary quantization and the theory of irreducible tensor operators, analytical structures for the quadrupole transition…
Extracting the outcome of a quantum computation is a difficult task. In many cases, the quantum phase estimation algorithm is used to digitally encode a value in a quantum register whose amplitudes' magnitudes reflect the discrete sinc…
In this paper, we define the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We…
We use Pade approximants to systematically approximate scalar unparticle propagators and their associated phase factors by a finite number of ordinary particles. This is possible for conformal dimensions 1<d<2, and also for d>2 if we add…
We present a simple approach to the fixed phase method in Quantum Monte Carlo. This applies to electrons in molecules and electron gas and is straightforwardly extended to the Schr\"odinger equation with magnetic field.
We consider $N_a$ three-level atoms (or systems) interacting with a one-mode electromagnetic field in the dipolar and rotating wave approximations. The order of the quantum phase transitions is determined explicitly for each of the…
The implementation and reliability of a quadratic diffusion Monte Carlo method for the study of ground-state properties of atoms are discussed. We show in the simple yet non-trivial calculation of the binding energy of the Li atom that the…