Cluster analysis is a crucial stage in the analysis and interpretation of single-cell gene expression (scRNA-seq) data. It is an inherently ill-posed problem whose solutions depend heavily on hyper-parameter and algorithmic choice. The popular approach of K-means clustering, for example, depends heavily on the choice of K and the convergence of the expectation-maximization algorithm to local minima of the objective. Exhaustive search of the space for multiple good quality solutions is known to be a complex problem. Here, we show that quantum computing offers a solution to exploring the cost function of clustering by quantum annealing, implemented on a quantum computing facility offered by D-Wave [1]. Out formulation extracts minimum vertex cover of an affinity graph to sub-sample the cell population and quantum annealing to optimise the cost function. A distribution of low-energy solutions can thus be extracted, offering alternate hypotheses about how genes group together in their space of expressions.
Cluster analysis is a crucial stage in the analysis and interpretation of single-cell gene expression (scRNA-seq) data. It is an inherently ill-posed problem whose solutions depend heavily on hyper-parameter and algorithmic choice. The popular approach of K-means clustering, for example, depends heavily on the choice of K and the convergence of the expectation-maximization algorithm to local minima of the objective. Exhaustive search of the space for multiple good quality solutions is known to be a complex problem. Here, we show that quantum computing offers a solution to exploring the cost function of clustering by quantum annealing, implemented on a quantum computing facility offered by D-Wave [1]. Out formulation extracts minimum vertex cover of an affinity graph to sub-sample the cell population and quantum annealing to optimise the cost function. A distribution of low-energy solutions can thus be extracted, offering alternate hypotheses about how genes group together in their space of expressions.
Feature selection is a machine learning technique for identifying relevant variables in classification and regression models. In single-cell RNA sequencing (scRNA-seq) data analysis, feature selection is used to identify relevant genes that are crucial for understanding cellular processes. Traditional feature selection methods often struggle with the complexity of scRNA-seq data and suffer from interpretation difficulties. Quantum annealing presents a promising alternative approach. In this study, we implement quantum annealing-empowered quadratic unconstrained binary optimization (QUBO) for feature selection in scRNA-seq data. Using data from a human cell differentiation system and an anticancer drug resistance study, we demonstrate that QUBO feature selection effectively identifies genes whose expression patterns reflect critical cell state transitions associated with differentiation and drug resistance development. Our findings indicate that quantum annealing-powered QUBO reveals complex gene expression patterns potentially missed by traditional methods, thereby enhancing scRNA-seq data analysis and interpretation.
A quantified RNA transcriptome is of particular interest in biomedical research as it can be for cancer diagnosis. Quantum algorithms can give exponential performance gains over their classical counterparts. In this paper, we implement a quantum clustering technique to classify the cells into different cancer types. To verify our implementation, we test it using the standard ‘gene expression cancer RNA-Seq’ dataset. The experimental results show that our algorithm achieves high accuracy of 94.8% (on average) in classifying the different types of cancer.
Clustering is a fundamental task in data science that aims to group data based on their similarities. However, defining similarity is often ambiguous, making it challenging to determine the most appropriate objective function for a given dataset. Traditional clustering methods, such as the k -means algorithm and weighted maximum k -cut, focus on specific objectives—typically relying on average or pairwise characteristics of the data—leading to performance that is highly data-dependent. Moreover, incorporating practical constraints into clustering objectives is not straightforward, and these problems are known to be NP-hard. In this study, we formulate the clustering problem as a search for the ground state of a Hamiltonian, providing greater flexibility in defining clustering objectives and incorporating constraints. This approach enables the application of various quantum simulation techniques, including both circuit-based quantum computation and quantum annealing, thereby opening a path toward quantum advantage in solving clustering problems. We propose various Hamiltonians to accommodate different clustering objectives, including the ability to combine multiple objectives and incorporate constraints. We evaluate the clustering performance through numerical simulations and implementations on the D-Wave quantum annealer. The results demonstrate the broad applicability of our approach to a variety of clustering problems on current quantum devices. Furthermore, we find that Hamiltonians designed for specific clustering objectives and constraints impose different requirements for qubit connectivity, indicating that certain clustering tasks are better suited to specific quantum hardware. Our experimental results highlight this by identifying the Hamiltonian that optimally utilizes the physical qubits available in the D-Wave System.
We present an algorithm for quantum-assisted cluster analysis (QACA) that makes use of the topological properties of a D-Wave 2000Q quantum processing unit (QPU). 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 priori, but generated by the algorithm. We explain how the problem can be expressed as a quadratic unconstrained binary optimization (QUBO) problem, and show that the introduced quantum-assisted clustering algorithm is, regarding accuracy, equivalent to commonly used classical clustering algorithms. Quantum annealing algorithms belong to the class of metaheuristic tools, applicable for solving binary optimization problems. Hardware implementations of quantum annealing, such as the quantum annealing machines produced by D-Wave Systems [1], have been subject to multiple analyses in research, with the aim of characterizing the technology’s usefulness for optimization, sampling, and clustering [2–16, 38]. Our first and foremost aim is to explain how to represent and solve parts of these problems with the help of the QPU, and not to prove supremacy over every existing classical clustering algorithm.
We present an algorithm for quantum-assisted cluster analysis (QACA) that makes use of the topological properties of a D-Wave 2000Q quantum processing unit (QPU). 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 priori, but generated by the algorithm. We explain how the problem can be expressed as a quadratic unconstrained binary optimization (QUBO) problem, and show that the introduced quantum-assisted clustering algorithm is, regarding accuracy, equivalent to commonly used classical clustering algorithms. Quantum annealing algorithms belong to the class of metaheuristic tools, applicable for solving binary optimization problems. Hardware implementations of quantum annealing, such as the quantum annealing machines produced by D-Wave Systems, have been subject to multiple analyses in research, with the aim of characterizing the technology's usefulness for optimization, sampling, and clustering. Our first and foremost aim is to explain how to represent and solve parts of these problems with the help of the QPU, and not to prove supremacy over every existing classical clustering algorithm.
High-dimensional data presents significant challenges to traditional clustering algorithms due to the "curse of dimensionality," leading to sparsity issues, increased computational complexity, and reduced cluster quality. This research investigates the application of quantum-inspired algorithms to enhance clustering performance in these scenarios. We propose a novel clustering framework leveraging concepts from quantum annealing and quantum walks to efficiently explore the feature space and identify clusters. The core idea is to mimic the probabilistic and superposition properties of quantum systems within the clustering process, allowing for more nuanced exploration of potential cluster configurations. The algorithms are designed to mitigate the effects of dimensionality by introducing stochastic search strategies and exploiting correlations between features. We evaluate the effectiveness of these algorithms on benchmark datasets, demonstrating improved clustering accuracy and reduced computational cost compared to established classical methods. The research highlights the potential of quantum-inspired approaches as a viable solution for high-dimensional clustering problems.