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We present an algorithm for quantum-assisted cluster analysis that makes use of the topological properties of a D-Wave 2000Q quantum processing unit. Clustering is a form of unsupervised machine learning, where instances are organized into groups whose members share similarities. The assignments are, in contrast to classification, not known a prior...
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... Many problems have already been solved using quantum annealing, giving reasonable solutions in real time [24] or giving optimal or very good solutions faster than classical alternatives [25]. Applications of quantum annealing are diverse and include traffic optimisation [24], finance [26], cyber security problems [27] and machine learning [13,25,28]. In quantum annealing, qubits are brought in an initial superposition state, after which a problem-specific Hamiltonian is applied to the qubits. ...
In this paper, we present implementations of an annealing-based and a gate-based quantum computing approach for finding the optimal policy to traverse a grid and compare them to a classical deep reinforcement learning approach. We extended these three approaches by allowing for stochastic actions instead of deterministic actions and by introducing a new learning technique called curriculum learning. With curriculum learning, we gradually increase the complexity of the environment and we find that it has a positive effect on the expected reward of a traversal. We see that the number of training steps needed for the two quantum approaches is lower than that needed for the classical approach.
... Quantum machine learning refers to quantum algorithms that are used to solve machine learning tasks, for instance, the outcome of the measurement of a qubit can represent the result of a binary classification task. Here we discuss different machine learning problems that have been addressed by making use of QA: classification [127] and reinforcement learning problems [135], cluster analysis [104,134], and matrix factorization [67,142,145]. For an introduction on the general topic, see, for example, [124,132]. ...
... A quantum-assisted clustering algorithm (QACA) was introduced by Neukart et al [134]. The algorithm is described as showing similarities with the self-organizing feature map, in the sense that the topological properties of the D-Wave QPU are exploited for cluster assignments. ...
Quantum annealing is a heuristic quantum optimization algorithm that can be used to solve combinatorial optimization problems. In recent years, advances in quantum technologies have enabled the development of small- and intermediate-scale quantum processors that implement the quantum annealing algorithm for programmable use. Specifically, quantum annealing processors produced by D-Wave Systems have been studied and tested extensively in both research and industrial settings across different disciplines. In this paper we provide a literature review of the theoretical motivations for quantum annealing as a heuristic quantum optimization algorithm, the software and hardware that is required to use such quantum processors, and the state-of-the-art applications and proofs-of-concepts that have been demonstrated using them. The goal of our review is to provide a centralized and condensed source regarding applications of quantum annealing technology. We identify the advantages, limitations, and potential of quantum annealing for both researchers and practitioners from various fields.
... Although there are various types of clustering, this work focuses on non-hierarchical and distance-based clustering. Because clustering can be formulated as a combinatorial optimization problem, several algorithms using Ising machines have been developed [28][29][30][31][32][33][34][35][36] . Clustering methods using a quantum computer and a quantum annealer have also been proposed and investigated 37,38 . ...
... Several methods inspired by classical clustering have been proposed and developed recently. For example, quantum-assisted clustering based on similarities 28 , K-means [29][30][31] and K-Medoids 32 clustering on a quantum annealer, as well as K-means clustering on a gate-model quantum computer 38 , have been proposed. K-means-like clustering on a digital Ising machine has also been investigated 36 . ...
In computer science, clustering is a technique for grouping data. Ising machines can solve distance-based clustering problems described by quadratic unconstrained binary optimization (QUBO) formulations. A typical simple method using an Ising machine makes each cluster size equal and is not suitable for clustering unevenly distributed data. We propose a new clustering method that provides better performance than the simple method, especially for unevenly distributed data. The proposed method is a hybrid algorithm including an iterative process that comprises solving a discrete optimization problem with an Ising machine and calculating parameters with a general-purpose computer. To minimize the communication overhead between the Ising machine and the general-purpose computer, we employed a low-latency Ising machine implementing the simulated bifurcation algorithm with a field-programmable gate array attached to a local server. The proposed method results in clustering 200 unevenly distributed data points with a clustering score 18% higher than that of the simple method. The discrete optimization with 2000 variables is performed 100 times per iteration, and the overhead time is reduced to approximately 20% of the total execution time. These results suggest that hybrid algorithms using Ising machines can efficiently solve practical optimization problems.
... Reinforcement learning: [121], [38]. Cluster analysis: [120], [93]. Matrix factorization: [128], [132], [59]. ...
... For instance, the outcome of the measurement of a qubit can represent the result of a binary classification task. Here we discuss different machine learning problems that have been addressed by making use of QA: classification [114] and reinforcement learning problems [121], cluster analysis [93,120], and matrix factorization [59,128,132]. For an introduction on the general topic, see, for example, Refs. ...
... A quantum-assisted clustering algorithm (QACA) was introduced by Neukart et al. [120]. The algorithm is described as showing similarities with the self-organizing feature map, in the sense that the topological properties of the D-Wave QPU are exploited for cluster assignments. ...
Quantum annealing is a heuristic quantum optimization algorithm that can be used to solve combinatorial optimization problems. In recent years, advances in quantum technologies have enabled the development of small- and intermediate-scale quantum processors that implement the quantum annealing algorithm for programmable use. Specifically, quantum annealing processors produced by D-Wave Systems have been studied and tested extensively in both research and industrial settings across different disciplines. In this paper we provide a literature review of the theoretical motivations for quantum annealing as a heuristic quantum optimization algorithm, the software and hardware that is required to use such quantum processors, and the state-of-the-art applications and proofs-of-concepts that have been demonstrated using them. The goal of our review is to provide a centralized and condensed source regarding applications of quantum annealing technology. We identify the advantages, limitations, and potential of quantum annealing for both researchers and practitioners from various fields.
... The D-Wave system has been used by Lockheed Martin, Los Alamos National Laboratory, Volkswagen, the Quantum Artificial Intelligence Lab, DENSO, and other organizations around the world. More than 250 users have developed early applications on D-Wave, covering optimization [52] , Artificial Intelligence [53,54] , Election Modeling [55] , Material Science [56] , Biology [57] , Traffic Scheduling [58,59] , Preventive Health Care [60] , Cryptography [61] , etc. In the near future, D-Wave has the potential to solve more complex problems for more users in more fields. ...
The intelligent transportation system (ITS) integrates a variety of advanced science and technology to support and monitor road traffic systems and accelerate the urbanization process of various countries. This paper analyzes the shortcomings of ITS, introduces the principle of quantum computing and the performance of universal quantum computer and special-purpose quantum computer, and shows how to use quantum advantages to improve the existing ITS. The application of quantum computer in transportation field is reviewed from three application directions: path planning, transportation operation management, and transportation facility layout. Due to the slow development of the current universal quantum computer, the D-Wave quantum machine is used as a breakthrough in the practical application. This paper makes it clear that quantum computing is a powerful tool to promote the development of ITS, emphasizes the importance and necessity of introducing quantum computing into intelligent transportation, and discusses the possible development direction in the future.
... The quantum computers that realize quantum annealing can efficiently find a solution to the QUBO problem 1 . Therefore, researchers are investigating potential applications of QUBO (such as machine learning [13], traffic flow optimization [12], and automated guided vehicle control in a factory [14]). ...
In this paper, we study the computational complexity of the quadratic unconstrained binary optimization (QUBO) problem under the functional problem FP^NP categorization. We focus on three sub-classes: (1) When all coefficients are integers QUBO is FP^NP-complete. When every coefficient is an integer lower bounded by a constant k, QUBO is FP^NP[log]-complete. (3) When coefficients can only be in the set {1, 0, -1}, QUBO is again FP^NP[log]-complete. With recent results in quantum annealing able to solve QUBO problems efficiently, our results provide a clear connection between quantum annealing algorithms and the FP^NP complexity class categorization. We also study the computational complexity of the decision version of the QUBO problem with integer coefficients. We prove that this problem is DP-complete.
... Companies such as D-Wave Systems have adopted an alternative approach, pursuing instead the physical implementation of quantum annealing algorithms, an adaptation of Adiabatic Quantum Optimization. Originally proposed as a heuristic optimization algorithm [6], the field of quantum annealing has grown significantly over time, with many potential applications being showcased in fields such as quantum simulation [7], [8], [9], quantum machine learning [10], [11], [12], optimization [13], [14], [15], and more [16], [17]. The majority of both gate-model and quantum annealing applications currently involve solving an optimization problem, typically formulated as either an Ising Model using spin variables s ∈ {−1, 1}, or a Quadratic Unconstrained Binary Optimization (QUBO) problem with binary variables x ∈ {0, 1}. ...
We present a generalization of the binary paint shop problem (BPSP) to tackle an automotive industry application, the multi-car paint shop (MCPS) problem. The objective of the optimization is to minimize the number of color switches between cars in a paint shop queue during manufacturing, a known NP-hard problem. We distinguish between different sub-classes of paint shop problems, and show how to formulate the basic MCPS problem as an Ising model. The problem instances used in this study are generated using real-world data from a factory in Wolfsburg, Germany. We compare the performance of the D-Wave 2000Q and Advantage quantum processors to other classical solvers and a hybrid quantum-classical algorithm offered by D-Wave Systems. We observe that the quantum processors are well-suited for smaller problems, and the hybrid algorithm for intermediate sizes. However, we find that the performance of these algorithms quickly approaches that of a simple greedy algorithm in the large size limit.
... Ushijima-Mwesigwa et al. demonstrate partitioning a graph into k parts concurrently using quantum annealing on the D-Wave 2X machine [23]. Neukart et al. propose a quantum-classical hybrid approach to clustering [24]. Wereszczynski et al. demonstrate the performance of a novel quantum clustering algorithm on small data sets using the D-Wave 2000Q [25]. ...
Adiabatic quantum computers are a promising platform for efficiently solving challenging optimization problems. Therefore, many are interested in using these computers to train computationally expensive machine learning models. We present a quantum approach to solving the balanced k-means clustering training problem on the D-Wave 2000Q adiabatic quantum computer. In order to do this, we formulate the training problem as a quadratic unconstrained binary optimization (QUBO) problem. Unlike existing classical algorithms, our QUBO formulation targets the global solution to the balanced k-means model. We test our approach on a number of small problems and observe that despite the theoretical benefits of the QUBO formulation, the clustering solution obtained by a modern quantum computer is usually inferior to the solution obtained by the best classical clustering algorithms. Nevertheless, the solutions provided by the quantum computer do exhibit some promising characteristics. We also perform a scalability study to estimate the run time of our approach on large problems using future quantum hardware. As a final proof of concept, we used the quantum approach to cluster random subsets of the Iris benchmark data set.
... Other works have also shown how to reformulate parts of classical clustering algorithms as quantum subroutines that can be executed on error-corrected gate-model QPUs (Alexander et al. 2018;Aimeur et al. 2013;Wiebe et al. 2015;Horn and Gottlieb 2001). In quantum annealing, a similar approach has been shown in which the objective function of the clustering task (minimizing distance metrics between high-dimensional vectors) has been directly translated to a QUBO, with each vector's possible assignment represented via one-hot encoding to physical qubits (Kumar et al. 2018;Neukart et al. 2018). ...
In this paper we develop methods to solve two problems related to time series (TS) analysis using quantum computing: reconstruction and classification. We formulate the task of reconstructing a given TS from a training set of data as an unconstrained binary optimization (QUBO) problem, which can be solved by both quantum annealers and gate-model quantum processors. We accomplish this by discretizing the TS and converting the reconstruction to a set cover problem, allowing us to perform a one-versus-all method of reconstruction. Using the solution to the reconstruction problem, we show how to extend this method to perform semi-supervised classification of TS data. We present results indicating our method is competitive with current semi- and unsupervised classification techniques, but using less data than classical techniques.
... Other works have also shown how to reformulate parts of classical clustering algorithms as quantum subroutines that can be executed on error-corrected gate-model QPUs [6,4,57,25]. In quantum annealing, a similar approach has been shown in which the objective function of the clustering task (minimizing distance metrics between high-dimensional vectors) has been directly translated to a QUBO, with each vector's possible assignment represented via one-hot encoding to physical qubits [31,40]. ...
In this paper we develop methods to solve two problems related to time series (TS) analysis using quantum computing: reconstruction and classification. We formulate the task of reconstructing a given TS from a training set of data as an unconstrained binary optimization (QUBO) problem, which can be solved by both quantum annealers and gate-model quantum processors. We accomplish this by discretizing the TS and converting the reconstruction to a set cover problem, allowing us to perform a one-versus-all method of reconstruction. Using the solution to the reconstruction problem, we show how to extend this method to perform semi-supervised classification of TS data. We present results indicating our method is competitive with current semi- and unsupervised classification techniques, but using less data than classical techniques.
