Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

LWDA

Adiabatic Quantum Computing for Kernel k=2 Means Clustering.

Christian Bauckhage, César Ojeda, Rafet Sifa, Stefan Wrobel

Published Jan 1, 2018• 8 citations
OpenAlex

Abstract

Adiabatic quantum computers are tailored towards finding minimum energy states of Ising models. The quest for implementations of machine learning algorithms on such devices thus is the quest for Ising model (re-)formulations of their underlying objective functions. In this paper, we discuss how to accomplish this for the problem of kernel binary clustering. We then discuss how our models can be solved on an adiabatic quantum computing device. Finally, in simulation experiments, we numerically solve the respective Schrödinger equations and observe our approaches to yield convincing results.

Related papers

Quantum Vision Clustering

Xuan-Bac Nguyen, Hugh Churchill, Khoa Luu +1 more

Abstract Unsupervised visual clustering has garnered significant attention recently, aiming to characterize distributions of unlabeled visual images through clustering based on a parameterized appearance approach. Alternatively, clustering algorithms can be viewed as assignment problems where an unlabelled sample needs to be assigned into a specific cluster. This problem can be formulated as Quadratic Unconstrained Binary Optimization that is characterized as NP-hard, yet precisely solvable for small instances on contemporary hardware. Adiabatic quantum computing (AQC) emerges as a promising solution to offer a good speed in solving the NP-hard optimization problems. However, existing clustering approaches face challenges in designing the problems to be solved by the quantum computer. In this study, we present the first clustering formulation tailored for resolution using Adiabatic quantum computing. An Ising model is introduced to represent the quantum mechanical system implemented on AQC. The proposed approach demonstrates high competitiveness compared to state-of-the-art optimization-based methods, even when utilizing off-the-shelf integer programming solvers. Lastly, this work showcases the solvability of the proposed clustering problem on current-generation real quantum computers for small examples and analyzes the properties of the obtained solutions.

arXiv:2309.09907•May 27, 2025•1 citation

Adiabatic Quantum Computing for Binary Clustering

Christian Bauckhage, Eduardo Barreto Brito, Kostadin Cvejoski +3 more

Quantum computing for machine learning attracts increasing attention and recent technological developments suggest that especially adiabatic quantum computing may soon be of practical interest. In this paper, we therefore consider this paradigm and discuss how to adopt it to the problem of binary clustering. Numerical simulations demonstrate the feasibility of our approach and illustrate how systems of qubits adiabatically evolve towards a solution.

arXiv:1706.05528•Jun 17, 2017•4 citations

Discrete optimisation problems on an adiabatic quantum computer

Tobias Stollenwerk, Elisabeth Lobe, Anke Tröltzsch

In the recent years the field of adiabatic quantum computing has gained importance due to the advances in the realisation of such machines, especially by the company D-Wave Systems. In contrast to a quantum computer in the conventional sense, an adiabatic quantum computer can solve a discrete optimisation problem by encoding the objective function into a quantum mechanical system. By carefully evolving the system in time from an initial state into the lowest energy state, the optimisation problem is solved. Due to the quantum nature of the device it is assumed that there is a substantial speedup compared to classical HPC facilities. The D-Wave machines are capable of finding the minimum of a subclass of the Ising model, a quadratic unconstrained binary optimisation problem. In this paper, we present a way of mapping more general problems to the subclass of Ising problems in order to make them solvable on an adiabatic quantum computer. As an example, we choose the maximum clique problem where one needs to find the maximal complete subgraph in an undirected graph. The corresponding decision problem is NP-complete. It has applications in social media or computational chemistry. Moreover, the solution of the maximum clique problem can be used to increase the number of logical variables which can be realised on a D-Wave machine. In addition, we investigate the applicability of adiabatic quantum computing to the scheduling optimisation of satellite missions performed by the German Aerospace Center.

•Jan 1, 2015•2 citations

Simulating adiabatic quantum computing with parameterized quantum circuits

Ioannis Kolotouros, Ioannis Petrongonas, Miloš Prokop +1 more

Abstract Adiabatic quantum computing is a universal model for quantum computing whose implementation using a gate-based quantum computer requires depths that are unreachable in the early fault-tolerant era. To mitigate the limitations of near-term devices, a number of hybrid approaches have been pursued in which a parameterized quantum circuit prepares and measures quantum states and a classical optimization algorithm minimizes an objective function that encompasses the solution to the problem of interest. In this work, we propose a different approach starting by analyzing how a small perturbation of a Hamiltonian affects the parameters that minimize the energy within a family of parameterized quantum states. We derive a set of equations that allow us to compute the new minimum by solving a constrained linear system of equations that is obtained from measuring a series of observables on the unperturbed system. We then propose a discrete version of adiabatic quantum computing that can be implemented in a near-term device while at the same time is insensitive to the initialization of the parameters and to other limitations hindered in the optimization part of variational quantum algorithms. We compare our proposed algorithm with the variational quantum eigensolver on two classical optimization problems, namely MaxCut and number partitioning, and on a quantum-spin configuration problem, the transverse-field ising chain model, and confirm that our approach demonstrates superior performance.

arXiv:2206.04373•Quantum Science and Technology•Sep 27, 2024•3 citations

QUBO formulations for training machine learning models

Prasanna Date, Davis Arthur, Lauren Pusey-Nazzaro

Training machine learning models on classical computers is usually a time and compute intensive process. With Moore's law nearing its inevitable end and an ever-increasing demand for large-scale data analysis using machine learning, we must leverage non-conventional computing paradigms like quantum computing to train machine learning models efficiently. Adiabatic quantum computers can approximately solve NP-hard problems, such as the quadratic unconstrained binary optimization (QUBO), faster than classical computers. Since many machine learning problems are also NP-hard, we believe adiabatic quantum computers might be instrumental in training machine learning models efficiently in the post Moore's law era. In order to solve problems on adiabatic quantum computers, they must be formulated as QUBO problems, which is very challenging. In this paper, we formulate the training problems of three machine learning models-linear regression, support vector machine (SVM) and balanced k-means clustering-as QUBO problems, making them conducive to be trained on adiabatic quantum computers. We also analyze the computational complexities of our formulations and compare them to corresponding state-of-the-art classical approaches. We show that the time and space complexities of our formulations are better (in case of SVM and balanced k-means clustering) or equivalent (in case of linear regression) to their classical counterparts.

arXiv:2008.02369•Scientific Reports•May 11, 2021•130 citations

Automatic and Effective Discovery of Quantum Kernels

Massimiliano Incudini, Daniele Lizzio Bosco, Francesco Martini +3 more

Quantum computing can empower machine learning models by enabling kernel machines to leverage quantum kernels for representing similarity measures between data. Quantum kernels are able to capture relationships in the data that are not efficiently computable on classical devices. However, there is no straightforward method to engineer the optimal quantum kernel for each specific use case. We present an approach to this problem, which employs optimization techniques, similar to those used in neural architecture search and AutoML, to automatically find an optimal kernel in a heuristic manner. To this purpose we define an algorithm for constructing a quantum circuit implementing the similarity measure as a combinatorial object, which is evaluated based on a cost function and then iteratively modified using a meta-heuristic optimization technique. The cost function can encode many criteria ensuring favorable statistical properties of the candidate solution, such as the rank of the Dynamical Lie Algebra. Importantly, our approach is independent of the optimization technique employed. The results obtained by testing our approach on a high-energy physics problem demonstrate that, in the best-case scenario, we can either match or improve testing accuracy with respect to the manual design approach, showing the potential of our technique to deliver superior results with reduced effort.

arXiv:2209.11144•IEEE Transactions on Emerging Topics in Computational Intelligence•Dec 23, 2024•15 citations
Adiabatic quantum computers are tailored towards finding minimum energy states of Ising models. The quest for implementations of machine learning algorithms on such devices thus is the quest for Ising model (re-)formulations of their underlying objective functions. In this paper, we discuss how to accomplish this for the problem of kernel binary clustering. We then discuss how our models can be solved on an adiabatic quantum computing device. Finally, in simulation experiments, we numerically solve the respective Schrödinger equations and observe our approaches to yield convincing results.
Abstract Unsupervised visual clustering has garnered significant attention recently, aiming to characterize distributions of unlabeled visual images through clustering based on a parameterized appearance approach. Alternatively, clustering algorithms can be viewed as assignment problems where an unlabelled sample needs to be assigned into a specific cluster. This problem can be formulated as Quadratic Unconstrained Binary Optimization that is characterized as NP-hard, yet precisely solvable for small instances on contemporary hardware. Adiabatic quantum computing (AQC) emerges as a promising solution to offer a good speed in solving the NP-hard optimization problems. However, existing clustering approaches face challenges in designing the problems to be solved by the quantum computer. In this study, we present the first clustering formulation tailored for resolution using Adiabatic quantum computing. An Ising model is introduced to represent the quantum mechanical system implemented on AQC. The proposed approach demonstrates high competitiveness compared to state-of-the-art optimization-based methods, even when utilizing off-the-shelf integer programming solvers. Lastly, this work showcases the solvability of the proposed clustering problem on current-generation real quantum computers for small examples and analyzes the properties of the obtained solutions.
In the recent years the field of adiabatic quantum computing has gained importance due to the advances in the realisation of such machines, especially by the company D-Wave Systems. In contrast to a quantum computer in the conventional sense, an adiabatic quantum computer can solve a discrete optimisation problem by encoding the objective function into a quantum mechanical system. By carefully evolving the system in time from an initial state into the lowest energy state, the optimisation problem is solved. Due to the quantum nature of the device it is assumed that there is a substantial speedup compared to classical HPC facilities. The D-Wave machines are capable of finding the minimum of a subclass of the Ising model, a quadratic unconstrained binary optimisation problem. In this paper, we present a way of mapping more general problems to the subclass of Ising problems in order to make them solvable on an adiabatic quantum computer. As an example, we choose the maximum clique problem where one needs to find the maximal complete subgraph in an undirected graph. The corresponding decision problem is NP-complete. It has applications in social media or computational chemistry. Moreover, the solution of the maximum clique problem can be used to increase the number of logical variables which can be realised on a D-Wave machine. In addition, we investigate the applicability of adiabatic quantum computing to the scheduling optimisation of satellite missions performed by the German Aerospace Center.
Abstract Adiabatic quantum computing is a universal model for quantum computing whose implementation using a gate-based quantum computer requires depths that are unreachable in the early fault-tolerant era. To mitigate the limitations of near-term devices, a number of hybrid approaches have been pursued in which a parameterized quantum circuit prepares and measures quantum states and a classical optimization algorithm minimizes an objective function that encompasses the solution to the problem of interest. In this work, we propose a different approach starting by analyzing how a small perturbation of a Hamiltonian affects the parameters that minimize the energy within a family of parameterized quantum states. We derive a set of equations that allow us to compute the new minimum by solving a constrained linear system of equations that is obtained from measuring a series of observables on the unperturbed system. We then propose a discrete version of adiabatic quantum computing that can be implemented in a near-term device while at the same time is insensitive to the initialization of the parameters and to other limitations hindered in the optimization part of variational quantum algorithms. We compare our proposed algorithm with the variational quantum eigensolver on two classical optimization problems, namely MaxCut and number partitioning, and on a quantum-spin configuration problem, the transverse-field ising chain model, and confirm that our approach demonstrates superior performance.
Training machine learning models on classical computers is usually a time and compute intensive process. With Moore's law nearing its inevitable end and an ever-increasing demand for large-scale data analysis using machine learning, we must leverage non-conventional computing paradigms like quantum computing to train machine learning models efficiently. Adiabatic quantum computers can approximately solve NP-hard problems, such as the quadratic unconstrained binary optimization (QUBO), faster than classical computers. Since many machine learning problems are also NP-hard, we believe adiabatic quantum computers might be instrumental in training machine learning models efficiently in the post Moore's law era. In order to solve problems on adiabatic quantum computers, they must be formulated as QUBO problems, which is very challenging. In this paper, we formulate the training problems of three machine learning models-linear regression, support vector machine (SVM) and balanced k-means clustering-as QUBO problems, making them conducive to be trained on adiabatic quantum computers. We also analyze the computational complexities of our formulations and compare them to corresponding state-of-the-art classical approaches. We show that the time and space complexities of our formulations are better (in case of SVM and balanced k-means clustering) or equivalent (in case of linear regression) to their classical counterparts.
Quantum computing can empower machine learning models by enabling kernel machines to leverage quantum kernels for representing similarity measures between data. Quantum kernels are able to capture relationships in the data that are not efficiently computable on classical devices. However, there is no straightforward method to engineer the optimal quantum kernel for each specific use case. We present an approach to this problem, which employs optimization techniques, similar to those used in neural architecture search and AutoML, to automatically find an optimal kernel in a heuristic manner. To this purpose we define an algorithm for constructing a quantum circuit implementing the similarity measure as a combinatorial object, which is evaluated based on a cost function and then iteratively modified using a meta-heuristic optimization technique. The cost function can encode many criteria ensuring favorable statistical properties of the candidate solution, such as the rank of the Dynamical Lie Algebra. Importantly, our approach is independent of the optimization technique employed. The results obtained by testing our approach on a high-energy physics problem demonstrate that, in the best-case scenario, we can either match or improve testing accuracy with respect to the manual design approach, showing the potential of our technique to deliver superior results with reduced effort.