Paper

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Towards Transfer Learning for Large-Scale Image Classification Using Annealing-Based Quantum Boltzmann Machines

Towards Transfer Learning for Large-Scale Image Classification Using Annealing-Based Quantum Boltzmann Machines

Daniëlle Schuman, Leo Sünkel, Philipp Altmann, Jonas Stein, Christoph Roch, Thomas Gabor, Claudia Linnhoff-Popien

Abstract

 

Quantum Transfer Learning (QTL) recently gained popularity as a hybrid quantum-classical approach for image classification tasks by efficiently combining the feature extraction capabilities of large Convolutional Neural Networks with the potential benefits of Quantum Machine Learning (QML). Existing approaches, however, only utilize gate-based Variational Quantum Circuits for the quantum part of these procedures. In this work we present an approach to employ Quantum Annealing (QA) in QTL-based image classification. Specifically, we propose using annealing-based Quantum Boltzmann Machines as part of a hybrid quantum-classical pipeline to learn the classification of real-world, large-scale data such as medical images through supervised training. We demonstrate our approach by applying it to the three-class COVID-CT-MD dataset, a collection of lung Computed Tomography (CT) scan slices. Using Simulated Annealing as a stand-in for actual QA, we compare our method to classical transfer learning, using a neural network of the same order of magnitude, to display its improved classification performance. We find that our approach consistently outperforms its classical baseline in terms of test accuracy and AUC-ROC-Score and needs less training epochs to do this.

Published in: 2023 IEEE International Conference on Quantum Computing and Engineering (QCE)

Evidence that PUBO outperforms QUBO when solving continuous optimization problems with the QAOA

Evidence that PUBO outperforms QUBO when solving continuous optimization problems with the QAOA

Jonas Stein, Farbod Chamanian, Maximilian Zorn, Jonas Nüßlein, Sebastian Zielinski, Michael Kölle, Claudia Linnhoff-Popien

Abstract

 

Quantum computing provides powerful algorithmic tools that have been shown to outperform established classical solvers in specific optimization tasks. A core step in solving optimization problems with known quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) is the problem formulation. While quantum optimization has historically centered around Quadratic Unconstrained Optimization (QUBO) problems, recent studies show, that many combinatorial problems such as the TSP can be solved more efficiently in their native Polynomial Unconstrained Optimization (PUBO) forms. As many optimization problems in practice also contain continuous variables, our contribution investigates the performance of the QAOA in solving continuous optimization problems when using PUBO and QUBO formulations. Our extensive evaluation on suitable benchmark functions, shows that PUBO formulations generally yield better results, while requiring less qubits. As the multi-qubit interactions needed for the PUBO variant have to be decomposed using the hardware gates available, i.e., currently single- and two-qubit gates, the circuit depth of the PUBO approach outscales its QUBO alternative roughly linearly in the order of the objective function. However, incorporating the planned addition of native multi-qubit gates such as the global Mølmer-Sørenson gate, our experiments indicate that PUBO outperforms QUBO for higher order continuous optimization problems in general.
 
GECCO ’23 Companion: Proceedings of the Companion Conference on Genetic and Evolutionary Computation
Pages 2254 – 2262
https://doi.org/10.1145/3583133.3596358

Applying QNLP to Sentiment Analysis in Finance

Applying QNLP to Sentiment Analysis in Finance

Jonas Stein, Ivo Christ, Nicolas Kraus, Maximilian Balthasar Mansky, Robert Müller, Claudia Linnhoff-Popien

Abstract

 

As an application domain where the slightest qualitative improvements can yield immense value, finance is a promising candidate for early quantum advantage. Focusing on the rapidly advancing field of Quantum Natural Language Processing (QNLP), we explore the practical applicability of the two central approaches DisCoCat (Distributional Compositional Categorical) and Quantum-Enhanced Long Short-Term Memory (QLSTM) to the problem of sentiment analysis in finance. Utilizing a novel ChatGPT-based data generation approach, we conduct a case study with more than 1000 realistic sentences and find that QLSTMs can be trained substantially faster than DisCoCat while also achieving close to classical results for their available software implementations.

Published in: 2023 IEEE International Conference on Quantum Computing and Engineering (QCE)

NISQ-Ready Community Detection Based on Separation-Node Identification

NISQ-Ready Community Detection Based on Separation-Node Identification

Jonas Stein, Dominik Ott, Jonas Nüßlein, David Bucher, Mirco Schönfeld, and Sebastian Feld

Abstract


The analysis of network structure is essential to many scientific areas ranging from biology to sociology. As the computational task of clustering these networks into partitions, i.e., solving the community detection problem, is generally NP-hard, heuristic solutions are indispensable. The exploration of expedient heuristics has led to the development of particularly promising approaches in the emerging technology of quantum computing. Motivated by the substantial hardware demands for all established quantum community detection approaches, we introduce a novel QUBO-based approach that only needs number-of-nodes qubits and is represented by a QUBO matrix as sparse as the input graph’s adjacency matrix. The substantial improvement in the sparsity of the QUBO matrix, which is typically very dense in related work, is achieved through the novel concept of separation nodes. Instead of assigning every node to a community directly, this approach relies on the identification of a separation-node set, which, upon its removal from the graph, yields a set of connected components, representing the core components of the communities. Employing a greedy heuristic to assign the nodes from the separation-node sets to the identified community cores, subsequent experimental results yield a proof of concept by achieving an up to 95% optimal solution quality on three established real-world benchmark datasets. This work hence displays a promising approach to NISQ-ready quantum community detection, catalyzing the application of quantum computers for the network structure analysis of large-scale, real-world problem instances.

Mathematics 2023, 11(15), 3323; https://doi.org/10.3390/math11153323


Approximative Lookup-Tables and Arbitrary Function Rotations for Facilitating NISQ-Implementations of the HHL and Beyond

Approximative Lookup-Tables and Arbitrary Function Rotations for Facilitating NISQ-Implementations of the HHL and Beyond

Petros Stougiannidis, Jonas Stein, David Bucher, Sebastian Zielinski, Claudia Linnhoff-Popien, and Sebastian Feld

Abstract

Many promising applications of quantum computing with a provable speedup center around the HHL algorithm. Due to restrictions on the hardware and its significant demand on qubits and gates in known implementations, its execution is prohibitive on near-term quantum computers. Aiming to facilitate such NISQ-implementations, we propose a novel circuit approximation technique that enhances the arithmetic subrou-tines in the HHL, which resemble a particularly resource-demanding component in small-scale settings. For this, we provide a description of the algorithmic implementation of space-efficient rotations of polynomial functions that do not demand explicit arithmetic calculations inside the quantum circuit. We show how these types of circuits can be reduced in depth by providing a simple and powerful approximation technique. Moreover, we provide an algorithm that converts lookup-tables for arbitrary function rotations into a structure that allows an application of the approximation technique. This allows implementing approximate rotation circuits for many polynomial and non-polynomial functions. Experimental results obtained for realistic early-application dimensions show significant improve-ments compared to the state-of-the-art, yielding small circuits while achieving good approximations.

Published in: 2023 IEEE International Conference on Quantum Computing and Engineering (QCE)


Hybrid Quantum Machine Learning Assisted Classification of COVID-19 from Computed Tomography Scans

Hybrid Quantum Machine Learning Assisted Classification of COVID-19 from Computed Tomography Scans

Leo Sünkel, Darya Martyniuk, Julia J. Reichwald, Andrei Morariu, Raja Havish Seggoju, Philipp Altmann

Abstract

Practical quantum computing (QC) is still in its in-fancy and problems considered are usually fairly small, especially in quantum machine learning when compared to its classical counterpart. Image processing applications in particular require models that are able to handle a large amount of features, and while classical approaches can easily tackle this, it is a major challenge and a cause for harsh restrictions in contemporary QC. In this paper, we apply a hybrid quantum machine learning approach to a practically relevant problem with real world-data. That is, we apply hybrid quantum transfer learning to an image processing task in the field of medical image processing. More specifically, we classify large CT-scans of the lung into COVID-19, CAP, or Normal. We discuss quantum image embedding as well as hybrid quantum machine learning and evaluate several approaches to quantum transfer learning with various quantum circuits and embedding techniques.

In progress

Influence of Different 3SAT-to-QUBO Transformations on the Solution Quality of Quantum Annealing: A Benchmark Study

Influence of Different 3SAT-to-QUBO Transformations on the Solution Quality of Quantum Annealing: A Benchmark Study

Sebastian Zielinski, Jonas Nüßlein, Jonas Stein, Thomas Gabor, Claudia Linnhoff-Popien, Sebastian Feld

Abstract

To solve 3sat instances on quantum annealers they need to be transformed to an instance of Quadratic Unconstrained Binary Optimization (QUBO). When there are multiple transformations available, the question arises whether different transformations lead to differences in the obtained solution quality. Thus, in this paper we conduct an empirical benchmark study, in which we compare four structurally different QUBO transformations for the 3sat problem with regards to the solution quality on D-Wave’s Advantage_system4.1. We show that the choice of QUBO transformation can significantly impact the number of correct solutions the quantum annealer returns. Furthermore, we show that the size of a QUBO instance (i.e., the dimension of the QUBO matrix) is not a sufficient predictor for solution quality, as larger QUBO instances may produce better results than smaller QUBO instances for the same problem. We also empirically show that the number of different quadratic values of a QUBO instance, combined with their range, can significantly impact the solution quality.

In progress

Pattern QUBOs: Algorithmic Construction of 3SAT-to-QUBO Transformations

Pattern QUBOs: Algorithmic Construction of 3SAT-to-QUBO Transformations

Sebastian Zielinski, Jonas Nüßlein, Jonas Stein, Thomas Gabor, Claudia Linnhoff-Popien, Sebastian Feld

Abstract

One way of solving 3sat instances on a quantum computer is to transform the 3sat instances into instances of Quadratic Unconstrained Binary Optimizations (QUBOs), which can be used as an input for the QAOA algorithm on quantum gate systems or as an input for quantum annealers. This mapping is performed by a 3sat-to-QUBO transformation. Recently, it has been shown that the choice of the 3sat-to-QUBO transformation can significantly impact the solution quality of quantum annealing. It has been shown that the solution quality can vary up to an order of magnitude difference in the number of correct solutions received, depending solely on the 3sat-to-QUBO transformation. An open question is: what causes these differences in the solution quality when solving 3sat-instances with different 3sat-to-QUBO transformations? To be able to conduct meaningful studies that assess the reasons for the differences in the performance, a larger number of different 3sat-to-QUBO transformations would be needed. However, currently, there are only a few known 3sat-to-QUBO transformations, and all of them were created manually by experts, who used time and clever reasoning to create these transformations. In this paper, we will solve this problem by proposing an algorithmic method that is able to create thousands of new and different 3sat-to-QUBO transformations, and thus enables researchers to systematically study the reasons for the significant difference in the performance of different 3sat-to-QUBO transformations. Our algorithmic method is an exhaustive search procedure that exploits properties of 4×4
dimensional pattern QUBOs, a concept which has been used implicitly in the creation of 3sat-to-QUBO transformations before, but was never described explicitly. We will thus also formally and explicitly introduce the concept of pattern QUBOs in this paper.

In progress

Algorithmic QUBO formulations for k-SAT and hamiltonian cycles

Algorithmic QUBO formulations for k-SAT and hamiltonian cycles

Jonas Nüßlein, Thomas Gabor, Claudia Linnhoff-Popien, Sebastian Feld

Abstract

Quadratic Unconstrained Binary Optimization (QUBO) can be seen as a generic language for optimization problems. QUBOs attract particular attention since they can be solved with quantum hardware, like quantum annealers or quantum gate computers running QAOA. In this paper, we present two novel QUBO formulations for k-SAT and Hamiltonian Cycles that scale significantly better than existing approaches. For k-SAT we reduce the growth of the QUBO matrix from O(k) to O(log(k)). For Hamiltonian Cycles the matrix no longer grows quadratically in the number of nodes, as currently, but linearly in the number of edges and logarithmically in the number of nodes.
We present these two formulations not as mathematical expressions, as most QUBO formulations are, but as meta-algorithms that facilitate the design of more complex QUBO formulations and allow easy reuse in larger and more complex QUBO formulations.

In progress

Towards Multi-Agent Reinforcement Learning using Quantum Boltzmann Machines

Towards Multi-Agent Reinforcement Learning using Quantum Boltzmann Machines

Tobias Müller, Christoph Roch, Kyrill Schmid, Philipp Altmann

Abstract

Reinforcement learning has driven impressive advances in machine learning. Simultaneously, quantum-enhanced machine learning algorithms using quantum annealing underlie heavy developments. Recently, a multi-agent reinforcement learning (MARL) architecture combining both paradigms has been proposed. This novel algorithm, which utilizes Quantum Boltzmann Machines (QBMs) for Q-value approximation has outperformed regular deep reinforcement learning in terms of time-steps needed to converge. However, this algorithm was restricted to single-agent and small 2×2 multi-agent grid domains. In this work, we propose an extension to the original concept in order to solve more challenging problems. Similar to classic DQNs, we add an experience replay buffer and use different networks for approximating the target and policy values. The experimental results show that learning becomes more stable and enables agents to find optimal policies in grid-domains with higher complexity. Additionally, we assess how parameter sharing influences the agents behavior in multi-agent domains. Quantum sampling proves to be a promising method for reinforcement learning tasks, but is currently limited by the QPU size and therefore by the size of the input and Boltzmann machine.

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