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Quantum Machine Learning
Quantum machine learning is the integration of quantum algorithms within machine learning programs. The most common use of the term refers to machine learning algorithms for the analysis of classical data executed on a quantum computer, i.e. quantum-enhanced machine learning. While machine learning algorithms are used to compute immense quantities of data, quantum machine learning utilizes qubits and quantum operations or specialized quantum systems to improve computational speed and data storage done by algorithms in a program. This includes hybrid methods that involve both classical and quantum processing, where computationally difficult subroutines are outsourced to a quantum device. These routines can be more complex in nature and executed faster on a quantum computer. Furthermore, quantum algorithms can be used to analyze quantum states instead of classical data. Beyond quantum computing, the term "quantum machine learning" is also associated with classical machine learning ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Algorithm
In quantum computing, a quantum algorithm is an algorithm that runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation. A classical (or non-quantum) algorithm is a finite sequence of instructions, or a step-by-step procedure for solving a problem, where each step or instruction can be performed on a classical computer. Similarly, a quantum algorithm is a step-by-step procedure, where each of the steps can be performed on a quantum computer. Although all classical algorithms can also be performed on a quantum computer, the term quantum algorithm is generally reserved for algorithms that seem inherently quantum, or use some essential feature of quantum computation such as quantum superposition or quantum entanglement. Problems that are undecidable using classical computers remain undecidable using quantum computers. What makes quantum algorithms interesting is that they might be able to solve some problems fa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Inversion
In linear algebra, an invertible matrix (''non-singular'', ''non-degenarate'' or ''regular'') is a square matrix that has an inverse. In other words, if some other matrix is multiplied by the invertible matrix, the result can be multiplied by an inverse to undo the operation. An invertible matrix multiplied by its inverse yields the identity matrix. Invertible matrices are the same size as their inverse. Definition An -by- square matrix is called invertible if there exists an -by- square matrix such that\mathbf = \mathbf = \mathbf_n ,where denotes the -by- identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix is uniquely determined by , and is called the (multiplicative) ''inverse'' of , denoted by . Matrix inversion is the process of finding the matrix which when multiplied by the original matrix gives the identity matrix. Over a field, a square matrix that is ''not'' invertible is called singular or degenerat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Walk
Quantum walks are quantum analogs of classical random walks. In contrast to the classical random walk, where the walker occupies definite states and the randomness arises due to stochastic transitions between states, in quantum walks randomness arises through (1) quantum superposition of states, (2) non-random, reversible unitary evolution and (3) collapse of the wave function due to state measurements. Quantum walks are a technique for building quantum algorithms. As with classical random walks, quantum walks admit formulations in both discrete time and continuous time. Motivation Quantum walks are motivated by the widespread use of classical random walks in the design of randomized algorithms and are part of several quantum algorithms. For some oracular problems, quantum walks provide an exponential speedup over any classical algorithm. Quantum walks also give polynomial speedups over classical algorithms for many practical problems, such as the element distinctness prob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perceptron
In machine learning, the perceptron is an algorithm for supervised classification, supervised learning of binary classification, binary classifiers. A binary classifier is a function that can decide whether or not an input, represented by a vector of numbers, belongs to some specific class. It is a type of linear classifier, i.e. a classification algorithm that makes its predictions based on a linear predictor function combining a set of Weighting, weights with the feature vector. History The artificial neuron network was invented in 1943 by Warren McCulloch and Walter Pitts in ''A Logical Calculus of the Ideas Immanent in Nervous Activity, A logical calculus of the ideas immanent in nervous activity''. In 1957, Frank Rosenblatt was at the Cornell Aeronautical Laboratory. He simulated the perceptron on an IBM 704. Later, he obtained funding by the Information Systems Branch of the United States Office of Naval Research and the Rome Air Development Center, to build a custom- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-nearest Neighbour
In statistics, the ''k''-nearest neighbors algorithm (''k''-NN) is a non-parametric supervised learning method. It was first developed by Evelyn Fix and Joseph Hodges in 1951, and later expanded by Thomas Cover. Most often, it is used for classification, as a ''k''-NN classifier, the output of which is a class membership. An object is classified by a plurality vote of its neighbors, with the object being assigned to the class most common among its ''k'' nearest neighbors (''k'' is a positive integer, typically small). If ''k'' = 1, then the object is simply assigned to the class of that single nearest neighbor. The ''k''-NN algorithm can also be generalized for regression. In ''-NN regression'', also known as ''nearest neighbor smoothing'', the output is the property value for the object. This value is the average of the values of ''k'' nearest neighbors. If ''k'' = 1, then the output is simply assigned to the value of that single nearest neighbor, also known as '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-medians Clustering
K-medians clustering is a partitioning technique used in cluster analysis. It groups data into ''k'' clusters by minimizing the sum of distances—typically using the Manhattan (L1) distance—between data points and the median of their assigned clusters. This method is especially robust to outliers and is well-suited for discrete or categorical data. It is a generalization of the geometric median or 1-median algorithm, defined for a single cluster. ''k''-medians is a variation of ''k''-means clustering where instead of calculating the mean for each cluster to determine its centroid, one instead calculates the median. This has the effect of minimizing error over all clusters with respect to the 2- norm distance metric, as opposed to the squared 2-norm distance metric (which ''k''-means does). This relates directly to the ''k''-median problem which is the problem of finding ''k'' centers such that the clusters formed by them are the most compact with respect to the 2-norm. Formally ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grover's Algorithm
In quantum computing, Grover's algorithm, also known as the quantum search algorithm, is a quantum algorithm for unstructured search that finds with high probability the unique input to a black box function that produces a particular output value, using just O(\sqrt) evaluations of the function, where N is the size of the function's domain of a function, domain. It was devised by Lov Grover in 1996. The analogous problem in classical computation would have a query complexity O(N) (i.e., the function would have to be evaluated O(N) times: there is no better approach than trying out all input values one after the other, which, on average, takes N/2 steps). Charles H. Bennett (physicist), Charles H. Bennett, Ethan Bernstein, Gilles Brassard, and Umesh Vazirani proved that any quantum solution to the problem needs to evaluate the function \Omega(\sqrt) times, so Grover's algorithm is Asymptotically optimal algorithm, asymptotically optimal. Since classical algorithms for NP-completenes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amplitude Amplification
Amplitude amplification is a technique in quantum computing that generalizes the idea behind Grover's search algorithm, and gives rise to a family of quantum algorithms. It was discovered by Gilles Brassard and Peter Høyer in 1997, and independently rediscovered by Lov Grover in 1998. In a quantum computer, amplitude amplification can be used to obtain a quadratic speedup over several classical algorithms. Algorithm The derivation presented here roughly follows the one given by Brassard et al. in 2000. Assume we have an N-dimensional Hilbert space \mathcal representing the state space of a quantum system, spanned by the orthonormal computational basis states B := \_^. Furthermore assume we have a Hermitian projection operator P\colon \mathcal \to \mathcal. Alternatively, P may be given in terms of a Boolean oracle function \chi\colon\mathbb \to \ and an orthonormal operational basis B_ := \_^, in which case :P := \sum_ , \omega_k \rangle \langle \omega_k, . P can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unsupervised Learning
Unsupervised learning is a framework in machine learning where, in contrast to supervised learning, algorithms learn patterns exclusively from unlabeled data. Other frameworks in the spectrum of supervisions include weak- or semi-supervision, where a small portion of the data is tagged, and self-supervision. Some researchers consider self-supervised learning a form of unsupervised learning. Conceptually, unsupervised learning divides into the aspects of data, training, algorithm, and downstream applications. Typically, the dataset is harvested cheaply "in the wild", such as massive text corpus obtained by web crawling, with only minor filtering (such as Common Crawl). This compares favorably to supervised learning, where the dataset (such as the ImageNet1000) is typically constructed manually, which is much more expensive. There were algorithms designed specifically for unsupervised learning, such as clustering algorithms like k-means, dimensionality reduction techniques l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supervised Learning
In machine learning, supervised learning (SL) is a paradigm where a Statistical model, model is trained using input objects (e.g. a vector of predictor variables) and desired output values (also known as a ''supervisory signal''), which are often human-made labels. The training process builds a function that maps new data to expected output values. An optimal scenario will allow for the algorithm to accurately determine output values for unseen instances. This requires the learning algorithm to Generalization (learning), generalize from the training data to unseen situations in a reasonable way (see inductive bias). This statistical quality of an algorithm is measured via a ''generalization error''. Steps to follow To solve a given problem of supervised learning, the following steps must be performed: # Determine the type of training samples. Before doing anything else, the user should decide what kind of data is to be used as a Training, validation, and test data sets, trainin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Classification
Binary classification is the task of classifying the elements of a set into one of two groups (each called ''class''). Typical binary classification problems include: * Medical testing to determine if a patient has a certain disease or not; * Quality control in industry, deciding whether a specification has been met; * In information retrieval, deciding whether a page should be in the result set of a search or not * In administration, deciding whether someone should be issued with a driving licence or not * In cognition, deciding whether an object is food or not food. When measuring the accuracy of a binary classifier, the simplest way is to count the errors. But in the real world often one of the two classes is more important, so that the number of both of the different types of errors is of interest. For example, in medical testing, detecting a disease when it is not present (a '' false positive'') is considered differently from not detecting a disease when it is present (a '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noisy Intermediate-scale Quantum Era
The current state of quantum computing is referred to as the noisy intermediate-scale quantum (NISQ) era, characterized by quantum processors containing up to 1,000 qubits which are not advanced enough yet for fault-tolerance or large enough to achieve quantum advantage. These processors, which are sensitive to their environment (noisy) and prone to quantum decoherence, are not yet capable of continuous quantum error correction. This intermediate-scale is defined by the quantum volume, which is based on the moderate number of qubits and gate fidelity. The term NISQ was coined by John Preskill in 2018. According to Microsoft Azure Quantum's scheme, NISQ computation is considered level 1, the lowest of the quantum computing implementation levels. In October 2023, the 1,000 qubit mark was passed for the first time by Atom Computing's 1,180 qubit quantum processor. However, as of 2024, only two quantum processors have over 1,000 qubits, with sub-1,000 quantum processors still rem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
