arXiv subjects

Peter Jaksch

Publications and source records attributed to Peter Jaksch.

5 recordsLinked to original sources

arXiv2025

Successive generation of nontrivial Riemann zeros from a Wu-Sprung type potential

A series of numerical experiments are performed, where a symmetric potential is generated for the 1D time-independent Schr\"odinger equation, with an eigenspectrum that matches the imaginary part of the first nontrivial zeros of the Riemann Zeta Function. The potential is generated as a series of correction functions, where the starting point is a potential that matches the smooth Riemann -- von Mangoldt approximation. It is found that the correction functions display a clear pattern that can be explained in simple terms, almost entirely dependent on the approximation error in the Riemann -- von Mangoldt formula. This also provides an explanation for the fractal pattern in the potential that was observed by Wu and Sprung.

quant-ph↗

arXiv2022

Implementation of a digitally encoded multigrid algorithm on a quantum computer

Multigrid has become a popular method for solving some of the most challenging real-world computational problems, such as computational fluid dynamics (CFD). The reason for this is the very good scaling properties of multigrid, which is often linear, or close to linear, with respect to problem size. In this paper a method is presented, which can be used to implement a quantum version of the multigrid algorithm. The method relies upon a quantum state that is maintained in a equal superposition throughout the calculation, and where information is encoded digitally in the qubits in a way more similar to a classical computer. This differs from many existing quantum algorithms where information is encoded in the amplitudes of the quantum states in the superposition. At the core of the method is an algorithm for sharing information between the states in the superposition. An exponential speedup is provided for classes of problems where the solution vector can be compressed efficiently, and where a quantum compiler can reduce the quantum circuit depth efficiently.

quant-ph↗

arXiv2020

GivEn -- Shape Optimization for Gas Turbines in Volatile Energy Networks

This paper describes the project GivEn that develops a novel multicriteria optimization process for gas turbine blades and vanes using modern "adjoint" shape optimization algorithms. Given the many start and shut-down processes of gas power plants in volatile energy grids, besides optimizing gas turbine geometries for efficiency, the durability understood as minimization of the probability of failure is a design objective of increasing importance. We also describe the underlying coupling structure of the multiphysical simulations and use modern, gradient based multicriteria optimization procedures to enhance the exploration of Pareto-optimal solutions.

math.OC↗

arXiv2005

Efficient Preparation of Quantum States With Exponential Precision

It has been shown that, starting from the state |0>, in the general case, an arbitrary quantum state |ψ> cannot be prepared with exponential precision in polynomial time. However, we show that for the important special case when |ψ> represents discrete values of some real, continuous function ψ(x), efficient preparation is possible by applying the eigenvalue estimation algorithm to a Hamiltonian which has ψ(x) as an eigenstate. We construct the required Hamiltonian explicitly and present an iterative algorithm for removing unwanted superpositions from the output state in order to reach |ψ> within exponential accuracy. The method works under very general conditions and can be used to provide the quantum simulation algorithm with very accurate and general starting states.

quant-ph↗

arXiv2003

Eigenvector Approximation Leading to Exponential Speedup of Quantum Eigenvalue Calculation

We present an efficient method for preparing the initial state required by the eigenvalue approximation quantum algorithm of Abrams and Lloyd. Our method can be applied when solving continuous Hermitian eigenproblems, e.g., the Schroedinger equation, on a discrete grid. We start with a classically obtained eigenvector for a problem discretized on a coarse grid, and we efficiently construct, quantum mechanically, an approximation of the same eigenvector on a fine grid. We use this approximation as the initial state for the eigenvalue estimation algorithm, and show the relationship between its success probability and the size of the coarse grid.

quant-ph↗