The machine learning model can infer desired information on processing data sets without being explicitly programmed. It needs refined data to train the perfect model, hence preprocessing is mandatory. The principal component analysis is desired classical existing methods for preprocessing and it requires polynomial time. Now, the research field of computer science is getting influenced by existence of quantum computations, as it supports exponential operations to be performed in parallel over single step of execution. An intrinsic realization of quantum machine provides simultaneous access to either classical or quantum memory. The objective of paper is to understand the importance of data preprocessing and to suggest quantum based solution that takes the advantage of quantum parallelism and thus can obtain computational speedups. So, we contribute to the emergence of quantum computations, processing aspects using quantum accessible memory models and then classical equivalent quantum principal component analysis algorithm. At last we conclude with the mathematical justification over complexity analysis, computational speedups, and prove that quantum algorithms are efficient along with the suggestions of further directions.
The machine learning model can infer desired information on processing data sets without being explicitly programmed. It needs refined data to train the perfect model, hence preprocessing is mandatory. The principal component analysis is desired classical existing methods for preprocessing and it requires polynomial time. Now, the research field of computer science is getting influenced by existence of quantum computations, as it supports exponential operations to be performed in parallel over single step of execution. An intrinsic realization of quantum machine provides simultaneous access to either classical or quantum memory. The objective of paper is to understand the importance of data preprocessing and to suggest quantum based solution that takes the advantage of quantum parallelism and thus can obtain computational speedups. So, we contribute to the emergence of quantum computations, processing aspects using quantum accessible memory models and then classical equivalent quantum principal component analysis algorithm. At last we conclude with the mathematical justification over complexity analysis, computational speedups, and prove that quantum algorithms are efficient along with the suggestions of further directions.
Quantum principal component analysis (QPCA) is analogous to the classical method with additive speedup. This is based on the unsupervised dimensionality reduction mechanism that transforms exponentially high dimensional data points into low dimensional space by retaining significant features with the largest variance. To our knowledge, quantum computations are highly exponential and supports implicit parallelism. Therefore, quantum method for finding principal components are proved to achieve exponential speedup over existing classical solution. An advantage of quantum superposition is utilized for the Eigen decomposition of density matrix which is identical to covariance, however, a way through which its computation happen, is truly an interesting factor. This paper presents basic methodological framework to design QPCA algorithm. Our framework includes the methods for quantum data encoding, quantum memory processing, and the requisite quantum circuit implementations to realize QPCA algorithms. In addition, we categorized existing QPCA methods in view of recent advances. We then proposed the possible advancements that can benefit to design quantum based efficient algorithms for principal component analysis. At the last, suggested concepts are compared with existing methods based on complexities and other factors to justify our proposal as significant in perspective to future directions.
The paper presents necessity of data pre-processing to process the data set through machine learning algorithms, and it filters the raw data to make the data as in compatible format for analysis purpose. The methods such as mean normalization, feature scaling and dimensionality reduction are used for data smoothing and therefore formatted data set gets processed by learning algorithms to predict best possible outcome as per the analysis. Machine learning became famous for such processing purpose and through unsupervised learning we are capable of processing over various data formats. Such algorithms performance is up-to the mark, but as per the availability of inherent parallel processing through quantum machines, computational speedup can be achieved by designing classical equivalent quantum machine learning algorithms. In this paper, we discussed some of the classical unsupervised learning algorithms, and then we propose the equivalent quantum version of algorithms along with the mathematical justification over the complexity analysis and achieved computational speedup and show the betterment by processing such problems over quantum machines.
The paper presents an influence of machine learning techniques that can be efficiently solved using quantum computer. Machine learning is considered as a core concept of modeling and mining large dimensionality data and visualizes data instances as a vector. Support vector is one of the trending methods that use supervised learning for classifying the data efficiently irrespective of linearity or non-linearity in data. As the quantum computations already proved to be inherently parallel and can become one of the key factors in order to reduce the complexities while dealing with the classical machine learning model. The quantum machine learning takes advantage of parallelism and can explore the number of vectors and their dimensions in logarithmic time, and hence it can achieve the computational speedup. Now, the main contribution of the paper is to discuss quantum fundamental, quantum algorithm and then to review over classical equivalent quantum support vector machine along with their training algorithm and the comparative analysis between algorithmic growths. At last, the paper justifies the quantum support vector as a highly efficient model that gains the computational speedup and also shows the possibility of further improvement.
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint on the implementability of these quantum algorithms. It has even been shown that without such an access, the quantum computer cannot be stronger than the classical counterparts. Thus, whether a quantum computer can be useful for practical applications is still open. In this work, we develop several variants of quantum algorithms. Our key framework employs a classical preprocessing step and a quantum procedure to perform gradient descent. We then translate such algorithm into an algorithm for solving linear systems, performing least-square fitting, building a support vector machine, performing supervised cluster assignment, training neural network, and solving for ground-state/excited-state energy, performing principle component analysis, with end-to-end applications of quantum algorithms. The classical preprocessing and the quantum procedure of our framework are shown to have logarithmic complexity in the dimension of input data, and quantum coherent access to input data is not required. Thus, our framework suggests an alternatively efficient route for quantum computers to handle real-world problems.
Machine Learning (ML) is arguably the most ad-vanced sub-field of Artificial Intelligence (AI). It concerns the study of computer algorithms that can improve automatically by learning from data (experience) without being explicitly pre-programmed. On the other hand, the quantum version of ML, Quantum Machine Learning (QML), forms one of the most crucial and recent quantum computing applications. It uses quantum mechanical principles such as superposition, interference, and tunneling to enable quantum computers to learn from data. Some examples of QML algorithms include Quantum Principal Component Analysis (QPCA) and Quantum Support Vector Machine (QSVM). The QSVM is a robust supervised machine learning algorithm used for classification and regression. Therefore, this paper discusses the design and implementation of an efficient QSVM model. The model's efficiency is achieved using Principal Component Analysis (PCA) on the classical data, then loading the classical data into a quantum computer. Experimental results demonstrate the significance and application of the QSVM model reported in this paper.
A central roadblock to analyzing quantum algorithms on quantum states is the lack of a comparable input model for classical algorithms. Inspired by recent work of the author [E. Tang, STOC 2019.], we introduce such a model, where we assume we can efficiently perform ℓ^{2}-norm samples of input data, a natural analog to quantum algorithms that assume efficient state preparation of classical data. Though this model produces less practical algorithms than the (stronger) standard model of classical computation, it captures versions of many of the features and nuances of quantum linear algebra algorithms. With this model, we describe classical analogs to Lloyd, Mohseni, and Rebentrost's quantum algorithms for principal component analysis [S. Lloyd, M. Mohseni, and P. Rebentrost, Nat. Phys. 10, 631 (2014).NPAHAX1745-247310.1038/nphys3029] and nearest-centroid clustering [S. Lloyd, M. Mohseni, and P. Rebentrost, Quantum algorithms for supervised and unsupervised machine learning]. Since they are only polynomially slower, these algorithms suggest that the exponential speedups of their quantum counterparts are simply an artifact of state preparation assumptions.