Related papers: A Lower Bound for the Sturm-Liouville Eigenvalue P…
We provide the details of an implementation of Fourier techniques for solving second-order linear partial differential equations (with constant coefficients) using a computer algebra system. The general Sturm-Liouville problem for the heat,…
A new discrete model for energy relaxation of a quantum particle is described via a projection operator, causing the wave function collapse. Power laws for the evolution of the particle coordinate and momentum dispersions are derived. A new…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
Finding the ground-state energy of molecules is an important and challenging computational problem for which quantum computing can potentially find efficient solutions. The variational quantum eigensolver (VQE) is a quantum algorithm that…
We construct quantum algorithms to compute the solution and/or physical observables of nonlinear ordinary differential equations (ODEs) and nonlinear Hamilton-Jacobi equations (HJE) via linear representations or exact mappings between…
ROM-based quantum computation (QC) is an alternative to oracle-based QC. It has the advantages of being less ``magical'', and being more suited to implementing space-efficient computation (i.e. computation using the minimum number of…
QAOA is a hybrid quantum-classical algorithm to solve optimization problems in gate-based quantum computers. It is based on a variational quantum circuit that can be interpreted as a discretization of the annealing process that quantum…
Near-term quantum computers are expected to facilitate material and chemical research through accurate molecular simulations. Several developments have already shown that accurate ground-state energies for small molecules can be evaluated…
The number of measurements demanded by hybrid quantum-classical algorithms such as the variational quantum eigensolver (VQE) is prohibitively high for many problems of practical value. For such problems, realizing quantum advantage will…
Since a pure quantum system is incapable of faithfully simulating the solutions of the Schroedinger equation that actually pertains to itself, it is proposed that quantum computing technology (as opposed to cryptographic technology) not be…
The standard setting of quantum computation for continuous problems uses deterministic queries and the only source of randomness for quantum algorithms is through measurement. This setting is related to the worst case setting on a classical…
We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's…
Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an $N\times{N}$…
The method reducing the solution of the Schroedinger equation for several types of power potentials to the solution of the eigenvalue problem for the infinite system of algebraic equations is developed. The finite truncation of this system…
The fractional Sturm-Liouville eigenvalue problem appears in many situations, e.g., while solving anomalous diffusion equations coming from physical and engineering applications. Therefore to obtain solutions or approximation of solutions…
Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…
Determining the properties of molecules and materials is one of the premier applications of quantum computing. A major question in the field is how to use imperfect near-term quantum computers to solve problems of practical value. Inspired…
The single well 1D harmonic oscillator is one of the most fundamental and commonly solved problems in quantum mechanics. Traditionally, in most introductory quantum mechanics textbooks, it is solved using either a power series method, which…
I study some possibilities of analytically solving a particular Sturm-Liouville problem with step-wise (piece-constant) coefficients with help of an iterative procedure mentioned in my previous paper (Green's function sum rules). I…
We give a lower bound for the energy of a quantum particle in the infinite square well. We show that the bound is exact and identify the well-known element that fulfils the equality. Our approach is not directly dependent on the…