相关论文: Exact solution for low energy quantum anharmonic v…

Advances in quantum algorithms suggest a tentative scaling advantage on certain combinatorial optimization problems. Recent work, however, has also reinforced the idea that barren plateaus render variational algorithms ineffective on large…

We propose the use of an orthogonal wave packet basis to analyze the low-energy physics of interacting electron systems with short range order. We give an introduction to wave packets and the related phase space representation of fermion…

We propose a quantum algorithm for finding eigenvalues of non-unitary matrices. We show how to construct, through interactions in a quantum system and projective measurements, a non-Hermitian or non-unitary matrix and obtain its eigenvalues…

The problem analysis results made the author to draw a conclusion that the nature of the resonance frequency long-term instability and drift at harmonic excitation is related to the phase dynamics of the "atom + field" system in the small…

We propose a novel quantum algorithm for solving nuclear resonances, which is based on the iterative Harrow-Hassidim-Lloyd algorithm and eigenvector continuation with complex scaling. To validate this approach, we compute the resonant…

In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…

We study the dynamics of the $(\alpha+\beta)$ Fermi-Pasta-Ulam-Tsingou lattice (FPUT lattice, for short) for an arbitrary number $N$ of interacting particles, in regimes of small enough nonlinearity so that a Birkhoff-Gustavson type of…

Alchemical transformations showed that perturbation theory can be applied also to changes in the atomic nuclear charges of a molecule. The alchemical path that connects two different chemical species involves the conceptualization of a…

The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are…

The problem of the harmonic oscillator with a centrally located delta function potential can be exactly solved in one dimension where the eigenfunctions are expressed as superpositions of the Hermite polynomials or as confluent…

Starting from the recently proposed energy-based deviational formulation for solving the Boltzmann equation [J.-P. Peraud and N. G. Hadjiconstantinou, Phys. Rev. B 84, 2011], which provides significant computational speedup compared to…

The convergence of the Rayleigh-Ritz method with nonlinear parameters optimized through minimization of the trace of the truncated matrix is demonstrated by a comparison with analytically known eigenstates of various quasi-solvable systems.…

The manner in which probability amplitudes of paths sum up to form wave functions of a harmonic oscillator, as well as other, simple 1-dimensional problems, is described. Using known, closed-form, path-based propagators for each problem, an…

A procedure for calculation of rotation-vibration states of medium sized molecules is presented. It combines the advantages of variational calculations and perturbation theory. The vibrational problem is solved by diagonalizing a…

The accurate computational study of wavepacket nuclear dynamics is considered to be a classically intractable problem, particularly with increasing dimensions. Here we present two algorithms that, in conjunction with other methods developed…

Solutions of the system of evolutionary equations in the short-wavelength approximation are found and studied. A connection is established between the problem of the evolution of short-wavelength gravitational-scalar perturbations and the…

A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…

A systematic study of small, time-dependent, perturbations to geometric wave-equation domains is hardly existent. Acoustic enclosures are typical examples featuring locally reacting surfaces that respond to a pressure gradient or a pressure…

Accurate simulations of vibrational molecular spectra are expensive on conventional computers. Compared to the electronic structure problem, the vibrational structure problem with quantum computers is less investigated. In this work we…

This article presents the first complete application of a quantum time-marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The…