Related papers: A variational method from the variance of energy
Quantum embedding theories are powerful tools for approximately solving large-scale strongly correlated quantum many-body problems. The main idea of quantum embedding is to glue together a highly accurate quantum theory at the local scale…
The dynamics of quantum droplets in 1D is analyzed on the basis of the variational approach (VA). It is shown that the VA based on the super-Gaussian function gives a good approximation of stationary states. The period of small oscillations…
We consider the dominant equations for the motion of the non-Newtonian fluid in a domain from an energetic point of view. We apply our energetic variational approaches and the first law of thermodynamics to derive the generalized…
The variational quantum power method (VQPM), which adapts the classical power iteration algorithm for quantum settings, has shown promise for eigenvector estimation and optimization on quantum hardware. In this work, we provide a…
The association of the variational method with supersymmetric quantum mechanics through an ansatz for the superpotential is reviewed and the approximate energy spectra of non-exactly solvable potentials, such like the Hulthen, the Morse and…
Effective low-energy theories represent powerful theoretical tools to reduce the complexity in modeling interacting quantum many-particle systems. However, common theoretical methods rely on perturbation theory, which limits their…
We consider the problem of estimating the energy of a quantum state preparation for a given Hamiltonian in Pauli decomposition. For various quantum algorithms, in particular in the context of quantum chemistry, it is crucial to have energy…
Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where the…
This work studies the variational quantum eigensolver algorithm, designed to determine the ground state of a quantum mechanical system by combining classical and quantum hardware. Methods of reducing the number of required qubit…
It is shown that gauge theories are most naturally studied via a polar decomposition of the field variable. Gauge transformations may be viewed as those that leave the density invariant but change the phase variable by additive amounts. The…
A variational calculus method is applied for hydrogen-like impurities states and exciton states in AlGaAs/GaAs quantum wells within the effective masses approach. The hamiltonian is separated into radial and transversal parts to be…
Continuous-variable Gaussian entanglement is an attractive notion, both as a fundamental concept in quantum information theory, based on the well-established Gaussian formalism for phase-space variables, and as a practical resource in…
Convergence results are stated for the variational iteration method applied to solve an initial value problem for a system of ordinary differential equations.
We propose a new quantum approach for describing a system of $n$ interacting particles with variable mass connected by an unknown field with variable form ($n$-VMVF systems). Instead of assuming any particular nature for variation of the…
Ordinary differential equations are widely-used in the field of systems biology and chemical engineering to model chemical reaction networks. Numerous techniques have been developed to estimate parameters like rate constants, initial…
An intrinsic measure of the quality of a variational wave function is given by its overlap with the ground state of the system. We derive a general formula to compute this overlap when quantum dynamics in imaginary time is accessible. The…
Variational quantum algorithms (VQAs) are prominent candidates for near-term quantum advantage but lack rigorous guarantees of convergence and generalization. By contrast, quantum phase estimation (QPE) provides provable performance under…
This work introduces a novel approach to quantum simulation by leveraging continuous-variable systems within a photonic hardware-inspired framework. The primary focus is on simulating static properties of the ground state of Hamiltonians…
Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…
For renormalizable models a method is presented to unambiguously compute the energy that is carried by localized field configurations (solitons). A variational approach for the total energy is utilized to search for soliton configurations.…