arXiv subjects

Thore Gerlach

Publications and source records attributed to Thore Gerlach.

23 records · Page 2Linked to original sources

arXiv2023

Optimum-Preserving QUBO Parameter Compression

Quadratic unconstrained binary optimization (QUBO) problems are well-studied, not least because they can be approached using contemporary quantum annealing or classical hardware acceleration. However, due to limited precision and hardware noise, the effective set of feasible parameter values is severely restricted. As a result, otherwise solvable problems become harder or even intractable. In this work, we study the implications of solving QUBO problems under limited precision. Specifically, it is shown that the problem's dynamic range has a crucial impact on the problem's robustness against distortions. We show this by formalizing the notion of preserving optima between QUBO instances and explore to which extend parameters can be modified without changing the set of minimizing solutions. Based on these insights, we introduce techniques to reduce the dynamic range of a given QUBO instance based on theoretical bounds of the minimal energy value. An experimental evaluation on random QUBO instances as well as QUBO-encoded Binary Clustering and Subset Sum problems show that our theoretical findings manifest in practice. Results on quantum annealing hardware show that the performance can be improved drastically when following our methodology.

quant-ph↗

arXiv2023

Shapley Values with Uncertain Value Functions

We propose a novel definition of Shapley values with uncertain value functions based on first principles using probability theory. Such uncertain value functions can arise in the context of explainable machine learning as a result of non-deterministic algorithms. We show that random effects can in fact be absorbed into a Shapley value with a noiseless but shifted value function. Hence, Shapley values with uncertain value functions can be used in analogy to regular Shapley values. However, their reliable evaluation typically requires more computational effort.

cs.LG↗

arXiv2022

Solving Subset Sum Problems using Quantum Inspired Optimization Algorithms with Applications in Auditing and Financial Data Analysis

Many applications in automated auditing and the analysis and consistency check of financial documents can be formulated in part as the subset sum problem: Given a set of numbers and a target sum, find the subset of numbers that sums up to the target. The problem is NP-hard and classical solving algorithms are therefore not practical to use in many real applications. We tackle the problem as a QUBO (quadratic unconstrained binary optimization) problem and show how gradient descent on Hopfield Networks reliably finds solutions for both artificial and real data. We outline how this algorithm can be applied by adiabatic quantum computers (quantum annealers) and specialized hardware (field programmable gate arrays) for digital annealing and run experiments on quantum annealing hardware.

math.OC↗

arXiv2022

Towards Bundle Adjustment for Satellite Imaging via Quantum Machine Learning

Given is a set of images, where all images show views of the same area at different points in time and from different viewpoints. The task is the alignment of all images such that relevant information, e.g., poses, changes, and terrain, can be extracted from the fused image. In this work, we focus on quantum methods for keypoint extraction and feature matching, due to the demanding computational complexity of these sub-tasks. To this end, k-medoids clustering, kernel density clustering, nearest neighbor search, and kernel methods are investigated and it is explained how these methods can be re-formulated for quantum annealers and gate-based quantum computers. Experimental results obtained on digital quantum emulation hardware, quantum annealers, and quantum gate computers show that classical systems still deliver superior results. However, the proposed methods are ready for the current and upcoming generations of quantum computing devices which have the potential to outperform classical systems in the near future.

quant-ph↗

arXiv2022

QUBOs for Sorting Lists and Building Trees

We show that the fundamental tasks of sorting lists and building search trees or heaps can be modeled as quadratic unconstrained binary optimization problems (QUBOs). The idea is to understand these tasks as permutation problems and to devise QUBOs whose solutions represent appropriate permutation matrices. We discuss how to construct such QUBOs and how to solve them using Hopfield nets or adiabatic) quantum computing. In short, we show that neurocomputing methods or quantum computers can solve problems usually associated with abstract data structures.

cs.DS↗