Quantum Clustering Algorithm Research Articles

QCLUE: a quantum clustering algorithm for multi-dimensional datasets

Clustering algorithms are at the basis of several technological applications, and are fueling the development of rapidly evolving fields such as machine learning. In the recent past, however, it has become apparent that they face challenges stemming from datasets that span more spatial dimensions. In fact, the best-performing clustering algorithms scale linearly in the number of points, but quadratically with respect to the local density of points. In this work, we introduce qCLUE, a quantum clustering algorithm that scales linearly in both the number of points and their density. qCLUE is inspired by CLUE, an algorithm developed to address the challenging time and memory budgets of Event Reconstruction (ER) in future High-Energy Physics experiments. As such, qCLUE marries decades of development with the quadratic speedup provided by quantum computers. We numerically test qCLUE in several scenarios, demonstrating its effectiveness and proving it to be a promising route to handle complex data analysis tasks – especially in high-dimensional datasets with high densities of points.

Breast cancer: A fractal approach, scaling analysis and quantum cluster algorithm

Tumor growth in the breast is a complex process, understanding this type of phenomenon is important in order to establish adequate strategies at diagnostic and therapeutic levels, beginning with the evaluation morphology, through adequate descriptors. Scaling analysis is used to extract parameters such as exponents of local roughness and fractal dimension, which characterize tumor growth. The results show that invasive lobular and ductal tumors in situ behave as proposed by Family-Vicsek (Family and Vicsek, 1991), while benign tumors behave differently.

Novel Enhanced Unsupervised Quantum Clustering Algorithm

Every day, humans generate approximately 2.5 billion gigabytes of new data. While this data is crucial in applications such as drug development and cybersecurity, it is mostly unstructured and unlabeled which makes it difficult to process effectively. Businesses and governments alike solve this problem by using machine learning algorithms to characterize the data and make decisions with it. However, conventional machine learning processes consume excessive computational resources and time: one of the most prominent, K-means clustering, has an approximate time complexity of O(n^2), where n is the input data size. This quadratic time complexity causes scalability problems with large datasets. In this project, I have created an improved, more scalable clustering algorithm by leveraging quantum computation. The approach (new Q-means) involves an Angle Embedding Feature Map, an d-dimensional SWAP Test, and a dynamic, threshold distance-based termination criteria. After implementing this algorithm using the IBM Qiskit SDK, the new Q-means algorithm was run several times on different dimensional datasets. On an average, the new Q-means performed 18% better than the K-means algorithm based on the Adjusted Rand Index. In terms of the simulation execution time, the new Q-means was about six times faster than the existing Q-means due to a multi-threaded implementation and faster convergence. The time complexity of the new Q-means without a Quantum Random Access Memory (QRAM) is O(n^2). While the existing Q-means algorithm, which utilizes QRAM, has a time complexity of O(n(log n)^p), the time complexity of the new Q-means with QRAM is significantly better—O(n).

Intelligent recommender system based on quantum clustering and matrix completion

AbstractFaster than classical algorithms, quantum algorithms benefit from the superposition property of quantum information to offer significant speedup to complex algorithms. Therefore, quantum computing can be used to help machine learning algorithms by boosting their performance and accelerate the processing of time‐consuming ones. Clustering algorithms are very complex unsupervised learning algorithms. Indeed, the similarity calculation (distance) between input vectors is a resource‐consuming step, especially when working with large datasets. In this article, we propose a new better‐performing recommender system that operates as a combination of an adapted quantum K‐means algorithm and the singular value decomposition (SVT) algorithm. We integrate the developed quantum clustering algorithm to a prediction process of the proposed recommender system using matrix completion. To the best of our knowledge, no system with such details was proposed in the literature. The system was applied on the MovieLens dataset without a dimensionality reduction step and evaluated according to measures of information retrieval systems. The results of the quantum K‐means algorithm show that the quantum version leads to a logarithmic reduction of the time complexity compared to the classical algorithm. The proposed system has proved to be better than the previous tested ones in terms of precision and recall.

Quantum cluster algorithm for data classification

We present a quantum algorithm for data classification based on the nearest-neighbor learning algorithm. The classification algorithm is divided into two steps: Firstly, data in the same class is divided into smaller groups with sublabels assisting building boundaries between data with different labels. Secondly we construct a quantum circuit for classification that contains multi control gates. The algorithm is easy to implement and efficient in predicting the labels of test data. To illustrate the power and efficiency of this approach, we construct the phase transition diagram for the metal-insulator transition of VO2, using limited trained experimental data, where VO2 is a typical strongly correlated electron materials, and the metallic-insulating phase transition has drawn much attention in condensed matter physics. Moreover, we demonstrate our algorithm on the classification of randomly generated data and the classification of entanglement for various Werner states, where the training sets can not be divided by a single curve, instead, more than one curves are required to separate them apart perfectly. Our preliminary result shows considerable potential for various classification problems, particularly for constructing different phases in materials.

Use of the quantum cluster algorithm and scaling dynamics in magnetic resonance imaging for prostate cancer staging

Malignant tumors in the prostate generally have amorphous geometries and roughness is evident on their surface. These characteristics, together with the escalation dynamics of this type of lesion, provide information on their degree of malignancy or stage, therefore, their understanding leads to establishing an adequate diagnosis and a good radiotherapeutic implementation. The geometry present in prostate cancers leads to an analysis based on scales and a fractal study. In the present work, an in vivo diagnosis of prostate cancer will be made with magnetic resonance images, three-dimensional, using the cluster quantum algorithm and the calculation of the critical exponents of local roughness and the fractal dimension, which will allow staging said lesions. and whose results are consistent with those reported in the literature.

Emulation of high-performance correlation-based quantum clustering algorithm for two-dimensional data on FPGA

Clustering algorithms are used to classify the unlabeled data into a number of categories with polynomial time complexity. Quantum clustering algorithms are developed to improve the performance and to achieve higher gain. In this work, we implement the quantum k-means clustering algorithm on field-programmable gate array (FPGA) by exploiting the implicit parallelism of the FPGA technology to achieve high speed among the software-implemented recent proposals. To do that, we establish a new method to measure the inner product between two qubits which is based on the correlation between the Euclidean distance and the inner product. We also optimize the quantum gates in terms of speed and removing the discretization error. Experimental results show a reduction in the running time by 500× as compared to the classical k-means algorithm for the A1 standard dataset.

An improved quantum clustering algorithm with weighted distance based on PSO and research on the prediction of electrical power demand

An improved quantum clustering algorithm with weighted distance based on PSO and research on the prediction of electrical power demand

Application of Quantum-Clustering on Thermograms of WiFi Circuits in Different Operation Modes

The purpose of this work is to evaluate the efficacy of applying a model-based quantum clustering (QC) algorithm on thermograms of functional modes in WiFi circuits. As unsupervised clustering algorithm, it can work on clusters of any shape and does not require any prior information. QC proves its efficacy for many applications, it has been tested, in this work, and compared with other algorithms which suffer randomness according to initialization. The tests are conducted on thermograms of an electronic chip in different operation modes. The benefits of QC are confirmed through performance analysis of clustering algorithms. Robustness analysis is also conducted against white-Gaussian noise clustering and so on classification of actual WiFi circuit operation modes based on thermograms.

Study of cervical cancer through fractals and a method of clustering based on quantum mechanics

Tumor growth in the cervix is a complex process. Understanding this phenomena is quite relevant in order to establish proper diagnosis and therapy strategies and a possible startpoint is to evaluate its complexity through the scaling analysis, which define the tumor growth geometry. In this work, tumor interface from primary tumors of squamous cells and adenocarcinomas for cervical cancer were extracted. Fractal dimension and local roughness exponent (Barabási and Stanley (1996)), αloc, were calculated to characterize the in vivo 3-D tumor growth. Image acquisition was carried out according to the standard protocol used for cervical cancer radiotherapy, i.e., axial, magnetic resonance T1 - weighted contrast enhanced images comprising the cervix volume for image registration. Image processing was carried out by a classification scheme based on quantum clustering algorithm (Mussa et al. (2015)) combined with the application of the K-means procedure upon contrasted images (Demirkaya et al. (2008)). The results show significant variations of the parameters depending on the tumor stage and its histological origin.

DCA++: A software framework to solve correlated electron problems with modern quantum cluster methods

We present the first open release of the DCA++ project, a high-performance research software framework to solve quantum many-body problems with cutting edge quantum cluster algorithms. DCA++ implements the dynamical cluster approximation (DCA) and its DCA+ extension with a continuous self-energy. The algorithms capture nonlocal correlations in strongly correlated electron systems, thereby giving insight into high-Tc superconductivity. The code’s scalability allows efficient usage of systems at all scales, from workstations to leadership computers. With regard to the increasing heterogeneity of modern computing machines, DCA++ provides portable performance on conventional and emerging new architectures, such as hybrid CPU–GPU, sustaining multiple petaflops on ORNL’s Titan and CSCS’ Piz Daint supercomputers. Moreover, we show how sustainable and scalable development of the code base has been achieved by adopting standard techniques of the software industry. These include employing a distributed version control system, applying test-driven development and following continuous integration. Program summaryProgram Title: DCA++Program Files doi:http://dx.doi.org/10.17632/482jm5cv77.1Licensing provisions: BSD-3-ClauseProgramming language: C++14 and CUDANature of problem: Understanding the fascinating physics of strongly correlated electron systems requires the development of sophisticated algorithms and their implementation on leadership computing systems.Solution method: The DCA++ code provides a highly scalable and efficient implementation of the dynamical cluster approximation (DCA) and its DCA+ extension.

Singular ferromagnetic susceptibility of the transverse-field Ising antiferromagnet on the triangular lattice

A transverse magnetic field $\Gamma$ is known to induce antiferromagnetic three-sublattice order of the Ising spins $\sigma^z$ in the triangular lattice Ising antiferromagnet at low enough temperature. This low-temperature order is known to melt on heating in a two-step manner, with a power-law ordered intermediate temperature phase characterized by power-law correlations at the three-sublattice wavevector ${\bf Q}$: $\langle \sigma^z(\vec{R}) \sigma^z(0)\rangle \sim \cos({\mathbf Q}\cdot \vec{R}) /|\vec{R}|^{\eta(T)}$ with the temperature-dependent power-law exponent $\eta(T) \in (1/9,1/4)$. Here, we use a newly developed quantum cluster algorithm to study the {\em ferromagnetic} easy-axis susceptibility $\chi_{u}(L)$ of an $L \times L$ sample in this power-law ordered phase. Our numerical results are consistent with a recent prediction of a singular $L$ dependence $\chi_{u}(L)\sim L^{2- 9 \eta}$ when $\eta(T)$ is in the range $(1/9,2/9)$. This finite-size result implies, via standard scaling arguments, that the ferromagnetic susceptibility $\chi_{u}(B)$ to a uniform field $B$ along the easy axis is singular at intermediate temperatures in the small $B$ limit, $\chi_{u}(B) \sim |B|^{-\frac{4 - 18 \eta}{4-9\eta}}$ for $\eta(T) \in (1/9, 2/9)$, although there is no ferromagnetic long-range order in the low temperature state.

On the application of quantum clustering on speech data

In this work, Quantum clustering (QC) algorithm is applied to a labeled dataset of Arabic vowels. The accuracy and processing time are, then, compared with nonhierarchical kernel approaches for unsupervised clustering; namely, k-means, self-organizing map and fuzzy c-means. The choice of speech data is according to large database statistics which reveal that vowels class represents about 60–70% of Arabic speech whereas the remaining percentage is distributed among other sounds. The analysis features, in this work, are the mel-frequency cepstarl coefficients. The results show that all algorithms are competitive from accuracy point of view while QC still guarantees the solution stability.

Quantum cluster algorithm for frustrated Ising models in a transverse field

Working within the stochastic series expansion framework, we introduce and characterize a new quantum cluster algorithm for quantum Monte Carlo simulations of transverse field Ising models with frustrated Ising exchange interactions. As a demonstration of the capabilities of this new algorithm, we show that a relatively small, ferromagnetic next-nearest neighbour coupling drives the transverse field Ising antiferromagnet on the triangular lattice from an antiferromagnetic three-sublattice ordered state at low temperature to a ferrimagnetic three-sublattice ordered state.

On a New Interpretation of Fuzzy C Mean Using Quantum Theory

A quantum mechanics interpretation of Fuzzy C-Mean (FCM) is presented. Cluster aims to study the data distribution in scale space. Its characteristics are very similar to the particle world in quantum physics. By analyzing the essence of the quantum potential and the quantum trap, the paper discusses the core and the basis of Quantum Clustering in quantum mechanics. A couple of drawbacks about Quantum Clustering algorithm is also presented. In addition, known from the fuzzy mathematical computing, the important fuzzy similarity parameter u in FCM is expressed by the quantum wave function. After a series of analysis, the important six innovation conclusions about Iris, FCM, and Quantum Clustering are proposed, and one of the most important is that there is a cryptical wave function existing in FCM, as well as several important experimental results prove it.

Multi-elitist immune clonal quantum clustering algorithm

The quantum clustering (QC) algorithm suffers from the issues of getting stuck in local extremes and computational bottleneck when handling large-size image segmentation. By embedding a potential evolution formula into affinity function calculation of multi-elitist immune clonal optimization, and updating the cluster center based on the distance matrix, the multi-elitist immune clonal quantum clustering algorithm (ME-ICQC) is proposed in this paper. In the proposed framework, elitist population is composed of the individuals with high affinity, which is considered to play dominant roles in the evolutionary process. It can help to find the global optimal solution or near-optimal solution for most tested tasks. The diversity of population can be well maintained by general subgroup evolution of ME-ICQC. These different functions are implemented by the dissimilar mutation strategies or crossover operators. The bi-group exchanges the information of excellence antibodies using the hypercube co-evolution operation. Compared with existing algorithms, the ME-ICQC achieves an improved clustering accuracy with more stable convergence, but it is not significantly better than other optimization techniques combined with QC. Also, the experimental results also show that our algorithm performs well on multi-class, parameters-sensitive and large-size datasets.

Quantum Cluster Algorithm Monte Carlo Method and Its Application to Higher-Spin Heisenberg Antiferromagnets

The quantum Monte Carlo technique for quantum magnets has been greatly improved during the last decade. In this paper, we review the quantum cluster algorithm (loop algorithm) for higher-spin Heisenberg antiferromagnets, together with some technical aspects including parallelization technique and with its application to low-dimensional Heisenberg antiferromagnets.

Cluster algorithms for general-S quantum spin systems.

We present a general strategy to extend quantum cluster algorithms for S = 1 / 2 spin systems, such as the loop algorithm, to those with an arbitrary size of spins. The partition function of a high- S spin system is generally represented by the path integral of a S = 1 / 2 model with special boundary conditions in the imaginary-time direction. We introduce additional graphs for the boundary part and give the labeling probability explicitly, which completes the algorithm together with an existing S = 1 / 2 algorithm. As a demonstration, we simulate the integer-spin antiferromagnetic Heisenberg chains. The magnitude of the first excitation gap is estimated to be 0.41048(6), 0.08917(4), and 0.01002(3) for S = 1, 2, and 3, respectively.

Extended cluster algorithm in quantum simulations

We propose an extension of the quantum cluster algorithm by a combined use of the Fortuin-Kasteleyn mapping and the Hubbard-Stratonovich transformation. To describe the idea, we consider the $S=\frac{1}{2}$ $\mathrm{XXZ}$ chain model and express the partition function as the sum in an extended configuration space of spins, graphs, and fields. Then it is clarified that this algorithm possesses a computationally tractable continuous-time limit and maintains virtues of the quantum cluster algorithm. Numerical simulations are performed and its applicability is demonstrated. Further, we discuss potential gains in our algorithm.

Correlation functions from quantum cluster algorithms: application to U(1) quantum spin and quantum link models

We demonstrate how correlation functions for non-diagonal operators can be measured with the loop-cluster algorithm for quantum spin models. We introduce the U(1) quantum link model and present the construction of a cluster algorithm for the model. We further show how an improved estimator for Wilson loops can be realised with the flux-cluster algorithm.