Related papers: Applications of the Numerov method to simple quant…
We present twelve numerical methods for evaluation of objects and concepts from Poisson geometry. We describe how each method works with examples, and explain how it is executed in code. These include methods that evaluate Hamiltonian and…
In this paper, we explore accelerating Hamiltonian ground state energy calculation on NISQ devices. We suggest using search-based methods together with machine learning to accelerate quantum algorithms, exemplified in the Quantum…
Dipolar coupled homonuclear spins present challenging, yet useful systems for quantum information processing. In such systems, eigenbasis of the system Hamiltonian is the appropriate computational basis and coherent control can be achieved…
We report the first electronic structure calculation performed on a quantum computer without exponentially costly precompilation. We use a programmable array of superconducting qubits to compute the energy surface of molecular hydrogen…
A novel hybrid quantum-classical approach has been developed to efficiently address the multireference quantum chemistry problem. The Handover Iterative Variational Quantum Eigensolver (HiVQE) is designed to accurately estimate ground-state…
This paper describes open-source scientific contributions in python surrounding the numerical solutions to hyperbolic Hamilton-Jacobi (HJ) partial differential equations viz., their implicit representation on co-dimension one surfaces;…
The quantum mechanical expression relating two commuting operators is reformulated such that the power method (also called method of moments) for iteratively calculating eigenvalues and eigenvectors becomes applicable. The new iterative…
We study the Hydrogen atom as a quantum mechanical system with a Coulomb like potential, with a semiclassical approach based on an effective description of quantum mechanics. This treatment allows us to describe the quantum state of the…
In this paper, based on the homotopy continuation method and the interval Newton method, an efficient algorithm is introduced to isolate the real roots of semi-algebraic system. Tests on some random examples and a variety of problems…
In this article I will describe how NMR techniques may be used to build simple quantum information processing devices, such as small quantum computers, and show how these techniques are related to more conventional NMR experiments.
Supersymmetric solution of PT-/non-PT-symmetric and non-Hermitian Morse potential is studied to get real and complex-valued energy eigenvalues and corresponding wave functions. Hamiltonian Hierarchy method is used in the calculations
The approximate numerical method for a calculation of a quantum wave impedance in a case of a potential energy with a complicated spatial structure is considered. It was proved that the approximation of a real potential by a piesewise…
We propose a quantum algorithm for inferring the molecular nuclear spin Hamiltonian from time-resolved measurements of spin-spin correlators, which can be obtained via nuclear magnetic resonance (NMR). We focus on learning the anisotropic…
Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolic-numeric deflation algorithm to restore the quadratic convergence of Newton's method. Using first-order derivatives of…
The dynamics of open quantum systems is governed by the Lindblad master equation, which provides a consistent framework for incorporating environmental effects into the evolution of the system. Since exact solutions are rarely available,…
Estimating the eigenvalues of a unitary transformation U by standard phase estimation requires the implementation of controlled-U-gates which are not available if U is only given as a black box. We show that a simple trick allows to measure…
One of the most challenging and frequently arising problems in many areas of science is to find solutions of a system of multivariate nonlinear equations. There are several numerical methods that can find many (or all if the system is small…
TenCirChem is an open-source Python library for simulating variational quantum algorithms for quantum computational chemistry. TenCirChem shows high performance on the simulation of unitary coupled-cluster circuits, using compact…
The Variational Method is applied within the context of Supersymmetric Quantum Mechanics to provide information about the energy states of a hydrogenic donor in a quantum dot.
The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting…