Related papers: Computing vibrational energy levels by solving lin…
We propose a new algorithm for calculation of vibrational spectra of molecules using tensor train decomposition. Under the assumption that eigenfunctions lie on a low-parametric manifold of low-rank tensors we suggest using well-known…
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…
We calculate rovibrational energy levels of H$_2$O using a trapped-ion quantum computer. We first derive the qubit form of Watson's Hamiltonian, including the rovibrational coupling terms. In a second step, we employ a variant of the…
Vibrational spectra and wavefunctions of polyatomic molecules can be calculated at low memory cost using low-rank sum-of-product (SOP) decompositions to represent basis functions generated using an iterative eigensolver. Using a SOP tensor…
We propose a method that exploits sparse representation of potential energy surfaces (PES) on a polynomial basis set selected by compressed sensing. The method is useful for studies involving large numbers of PES evaluations, such as the…
Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient…
Accurate vibrational spectra are essential for understanding how molecules behave, yet their computation remains challenging and benchmark data to reliably compare different methods are sparse. Here, we present high-accuracy eigenstate…
Exact solutions for vibrational levels of diatomic molecules via the Morse potential are obtained by means of the asymptotic iteration method. It is shown that, the numerical results for the energy eigenvalues of $^{7}Li_{2}$ are all in…
Quantum computation of vibrational properties of molecules is a promising platform to obtain computational advantages for computational chemistry. However, fault-tolerant quantum computations of vibrational properties remain a relatively…
We present an iterative method for the search of extreme entries in low-rank tensors which is based on a power iteration combined with a binary search. In this work we use the HT-format for low-rank tensors but other low-rank formats can be…
We propose an iterative method for computing vibrational spectra that significantly reduces the memory cost of calculations. It uses a direct product primitive basis, but does not require storing vectors with as many components as there are…
It is considered that the effective interaction between any two quarks in a baryon can be approximately described by a simple harmonic potential. Also, it is made use of the nonrelativistic approximation. The problem is firstly solved in…
Quantum computers are ideal for solving chemistry problems due to their polynomial scaling with system size in contrast to classical computers which scale exponentially. Until now molecular energy calculations using quantum computing…
While linear molecules in their vibrational ground state cannot carry angular momentum around their symmetry axis, the presence of vibrational excitations can induce deformations away from linearity and therefore also allow angular momentum…
We introduce tensor numerical techniques for solving optimal control problems constrained by elliptic operators in $\mathbb{R}^d$, $d=2,3$, with variable coefficients, which can be represented in a low rank separable form. We construct a…
Tensors are a natural way to express correlations among many physical variables, but storing tensors in a computer naively requires memory which scales exponentially in the rank of the tensor. This is not optimal, as the required memory is…
A variational solution to the rovibrational problem in curvilinear vibrational coordinates has been implemented and used to investigate the nuclear motions in several linear triatomic molecules, like HCN, OCS, and HCP. The dependence of the…
We develop a systematic way to solve linear equations involving tensors of arbitrary rank. We start off with the case of a rank $3$ tensor, which appears in many applications, and after finding the condition for a unique solution we derive…
The behavior of polyatomic molecules around their equilibrium positions can be regarded as quantum coupled anharmonic oscillators. Solving the corresponding Schr\"odinger equations can interpret or predict experimental spectra of molecules.…
The development of energy selective, photon counting X-ray detectors allows for a wide range of new possibilities in the area of computed tomographic image formation. Under the assumption of perfect energy resolution, here we propose a…