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Chapman & Hall/CRC eBooks

Quantum Algorithm for Sequence Clustering

Arit Kumar Bishwas, A.S. Radha Mani, Vasile Palade

Published Oct 30, 2017• 0 citations
Publisher

Abstract

In recent years we have seen that the world is increasingly driven by data or information. Data has always been important for business and research, but in the current era the concept of big data is changing the way people employ data for decision making. Big data is playing a big role in informed decision making processes. In recent years, the importance of clustering with big sequential data sets has grown substantially due to its wide applications in areas like DNA genome modeling and financial data analysis. Handling big data clustering activity is a complex task. This intrinsic difficulty worsens with huge sequential data (can be termed as “Big Sequences” ) where the structure of the underlying process is often difficult to deduce because of the difference in lengths of sequences. In this chapter, we have proposed an interesting approach for clustering sequencing data in a quantum paradigm which is based on Quantum K-Means clustering and the Hidden Markov Model. In this approach, a new representation space of input data objects (sequences) is established. The vector of each object's similarities with respect to a pre-determinate set of other objects describes the respective object. These similarities are identified using the Hidden Markov Model . A novel representation space of input sequences has been mapped to quantum states with the help of quantum RAM (QRAM) . Then clustering is performed using quantum K -means clustering over the new transformed input data set. We have observed an exponential speed up gain in run time complexity in our approach as compared to the classical approaches.

DOI
10.1201/9781315154152-14

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In recent years we have seen that the world is increasingly driven by data or information. Data has always been important for business and research, but in the current era the concept of big data is changing the way people employ data for decision making. Big data is playing a big role in informed decision making processes. In recent years, the importance of clustering with big sequential data sets has grown substantially due to its wide applications in areas like DNA genome modeling and financial data analysis. Handling big data clustering activity is a complex task. This intrinsic difficulty worsens with huge sequential data (can be termed as “Big Sequences” ) where the structure of the underlying process is often difficult to deduce because of the difference in lengths of sequences. In this chapter, we have proposed an interesting approach for clustering sequencing data in a quantum paradigm which is based on Quantum K-Means clustering and the Hidden Markov Model. In this approach, a new representation space of input data objects (sequences) is established. The vector of each object's similarities with respect to a pre-determinate set of other objects describes the respective object. These similarities are identified using the Hidden Markov Model . A novel representation space of input sequences has been mapped to quantum states with the help of quantum RAM (QRAM) . Then clustering is performed using quantum K -means clustering over the new transformed input data set. We have observed an exponential speed up gain in run time complexity in our approach as compared to the classical approaches.
Supervised clustering is the process of grouping unlabeled objects by using some specific objectives and any supervised learning technique. In traditional clustering algorithms, the similarity measure is based on some distance finding formulations. In supervised clustering, this similarity measure is trained with the help of asupervised learning method. In this paper, we have designed a quantum supervised clustering algorithm and analyzed the overall runtime complexity of the algorithm. In our approach, we have trained the similarity measure model with quantum support vector machine. This quantum mechanically trained similarity measure model is used in the quantum K-Means algorithm, instead of the traditional distance-based similarity measure functions, for clustering unlabeled objects. Our analysis demonstrates that the proposed approach exhibits exponential speed up when compared to the classical implementation.
The exponential growth of data and the increasing complexity of high-dimensional classification problems have pushed classical computing methods to their limits. Quantum computing emerges as a promising paradigm to address these challenges. This research article explores advanced quantum algorithms for big data clustering and high-dimensional classification. We investigate quantum versions of K-means, spectral clustering, and support vector machines, comparing their performance with classical counterparts. Our results demonstrate significant speedups in processing time and improvements in clustering quality for high-dimensional datasets. Additionally, we propose a novel quantum-inspired classical algorithm that bridges the gap between quantum and classical approaches. This comprehensive study provides insights into the potential of quantum computing in revolutionizing data analysis and machine learning, paving the way for future advancements in the field.
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).
Many classes of algorithms that suffer from large complexities when implemented on conventional computers may be reformulated resulting in greatly reduced complexity when implemented on quantum computers. The dramatic reductions in complexity for certain types of quantum algorithms coupled with the computationally challenging problems in some bioinformatics problems motivates researchers to devise efficient quantum algorithms for sequence (DNA, RNA, protein) analysis. This chapter shows that the important sequence classification problem in bioinformatics is suitable for formulation as a quantum algorithm. This chapter leverages earlier research for sequence classification based on Extensible Markov Model (EMM) and proposes a quantum computing alternative. The authors utilize sequence family profiles built using EMM methodology which is based on using pre-counted word data for each sequence. Then a new method termed quantum seeding is proposed for generating a key based on high frequency words. The key is applied in a quantum search based on Grover algorithm to determine a candidate set of models resulting in a significantly reduced search space. Given Z as a function of M models of size N, the quantum version of the seeding algorithm has a time complexity in the order of as opposed to O(Z) for the standard classic version for large values of Z.
Many classes of algorithms that suffer from large complexities when implemented on conventional computers may be reformulated resulting in greatly reduced complexity when implemented on quantum computers. The dramatic reductions in complexity for certain types of quantum algorithms coupled with the computationally challenging problems in some bioinformatics problems motivates researchers to devise efficient quantum algorithms for sequence (DNA, RNA, protein) analysis. This chapter shows that the important sequence classification problem in bioinformatics is suitable for formulation as a quantum algorithm. This chapter leverages earlier research for sequence classification based on Extensible Markov Model (EMM) and proposes a quantum computing alternative. The authors utilize sequence family profiles built using EMM methodology which is based on using pre-counted word data for each sequence. Then a new method termed quantum seeding is proposed for generating a key based on high frequency words. The key is applied in a quantum search based on Grover algorithm to determine a candidate set of models resulting in a significantly reduced search space. Given Z as a function of M models of size N, the quantum version of the seeding algorithm has a time complexity in the order of as opposed to O(Z) for the standard classic version for large values of Z.
Fast sequencing and analysis of (microorganism, plant or human) genomes will open up new vistas in fields like personalised medication, food yield and epigenetic research. Current state-of-the-art DNA pattern matching techniques use heuristic algorithms on computing clusters of CPUs, GPUs and FPGAs. With genomic data set to eclipse social and astronomical big data streams within a decade, the alternate computing paradigm of quantum computation is explored to accelerate genome-sequence reconstruction. The inherent parallelism of quantum superposition of states is harnessed to design a quantum kernel for accelerating the search process. The project explores the merger of these two domains and identifies ways to fit these together to design a genome-sequence analysis pipeline with quantum algorithmic speedup. The design of a genome-sequence analysis pipeline with a quantum kernel is tested with a proof-of-concept demonstration using a quantum simulator.