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Pictorial representation of the learning categories. Here, "Q" and "C" denote quantum and classical computation respectively. The solid line represents the minimal computational requirements of the protocol during the learning process. The dashed lines in L 2 represent the possibility of having data that does not need to be represented classically.
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Here we discuss advances in the field of quantum machine learning. The
following document offers a hybrid discussion; both reviewing the field as it
is currently, and suggesting directions for further research. We include both
algorithms and experimental implementations in the discussion. The field's
outlook is generally positive, showing significa...
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... will group the scenarios into categories of learning, which are loosely based on 1 INTRODUCTION definitions made by A¨ımeurA¨ımeur, Brassard, and Gambs [5,6]. Figure 1 is a pictorial representation of the categories, which the reader should consult as they are defined. Here, "Q" and "C" denote quan- tum and classical computation respectively. ...
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... algorithms attempt to find lower dimensional manifolds, which contain all data points, in a high dimensional feature space. To "unfold" these manifolds, for example in the Isomap algorithm [70], it is again important to calculate a graph of near- est neighbours (Figure 10). Due to the immense complexity of these algorithms, especially for large datasets, using algorithms as described by Dürr et al. for dimensionality reduction appears promising. ...
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... to the immense complexity of these algorithms, especially for large datasets, using algorithms as described by Dürr et al. for dimensionality reduction appears promising. Figure 10: The "swiss roll" dataset. a) The euclidean distance (blue dashed line) of two points is shorter than on the manifold, hence they may seem to be more similar then they actually are. ...
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... actual experimental implementation of the quantum sub-process is performed on a small photonic quantum computer, the configuration of which is presented in Figure 11. Two bismuth borate crystals act as pair sources for entangled photons, using spontaneous parametric down- conversion to create a four-qubit entangled state encoded in the photon polarisations. ...
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... features of the character are then calculated and stored in a vector. In the case of Li et al., each number was split along the horizontal and vertical axes (Figure 12), such that the pixel number ratio across each division could be ascertained. These ratios (one for the horizontal split and one for the vertical) work well as features, since they are heavily dependent on whether the digit is a 6 or a 9. Finally, the features of the input characters are compared with those from a training set. ...
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... a result, it is possible to determine whether a hand-written digit is a 6 or a 9 simply by evaluating where its feature vector resides with respect to the hyperplane. The experimental results published by Li et al. are presented in Figure 13. We can see that their machine was able to recognise the hand-written characters across all instances. ...
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... specifically, it is a structure that learns given access to some finite set of training data and then uses that knowledge to infer classifications for unlabelled data. Geometrically, a perceptron can be thought of as a very simple neural network: W input nodes, labelled x i for 0 ≤ i ≤ W , are each connected to a single output node, y, by an edge (see Figure 14). These edges themselves have weights, w i . ...
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... approach is seemingly the most natural progression from Equation (14), but encounters particular problems when considering implementation of such an algorithm. Figure 15 displays how the method of Equation (15) would work in practice, which is summarised as follows: ...
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... method can be represented by the quantum circuit displayed in Figure 16. Here we forgo the issues with the previous method by not having to update the operatorˆOoperatorˆ operatorˆO once it has been initialised. ...
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... discussion of possible solutions for these operators is given in the sections below. Figure 16: A quantum circuit representation of the 'weights in states' strategy for a quantum perceptron. The operatorˆOoperatorˆ operatorˆO performs the training process of the algorithm and the dashed region represents classification of unlabelled data. ...
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... equation Aw = ˜ y is exactly the kind of linear system that is solved by the HHL algorithm. Therefore, the operatorˆOoperatorˆ operatorˆO in Figure 16 is given by the matrix A that must be inverted in order to solve the linear system. ...
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... goal of the perceptron once it is trained is merely to classify new instances correctly; the weights can remain hidden in a state indefinitely without impacting on its ability to classify new data. A schematic of a circuit suitable for classification is shown in Figure 17 and is denotedˆCdenotedˆ denotedˆC in Figure 16. Here, the trained weights are encoded in a register |w. ...
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... goal of the perceptron once it is trained is merely to classify new instances correctly; the weights can remain hidden in a state indefinitely without impacting on its ability to classify new data. A schematic of a circuit suitable for classification is shown in Figure 17 and is denotedˆCdenotedˆ denotedˆC in Figure 16. Here, the trained weights are encoded in a register |w. ...
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... ε is a measure of error in the weight vector [56]. Conversely, the best possible classical iterative algorithm for this problem is the conjugate gradient method, which has a runtime of Figure 17: A quantum circuit diagram representing the classification process for the 'weights in states' method. The circuit above corresponds to the dashed region in Figure 16. ...
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... the best possible classical iterative algorithm for this problem is the conjugate gradient method, which has a runtime of Figure 17: A quantum circuit diagram representing the classification process for the 'weights in states' method. The circuit above corresponds to the dashed region in Figure 16. ...
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Citations
... Without this, the parallel bucket-brigade circuit in 29 requires N − 2 compute-uncompute Toffoli pairs, 2N + log 2 N logical qubits and has Toffoli-depth log 2 N . From Eqs. (9), (13) and (15), this implies the following. ...
Quantum algorithms claim significant speedup over their classical counterparts for solving many problems. An important aspect of many of these algorithms is the existence of a quantum oracle, which needs to be implemented efficiently in order to realize the claimed advantages in practice. A quantum random access memory (QRAM) is a promising architecture for realizing these oracles. In this paper we develop a new design for QRAM and implement it with Clifford+T circuit. We focus on optimizing the T-count and T-depth since non-Clifford gates are the most expensive to implement fault-tolerantly in most error correction schemes. Integral to our design is a polynomial encoding of bit strings and so we refer to this design as . Compared to the previous state-of-the-art bucket brigade architecture for QRAM, we achieve an exponential improvement in T-depth, while reducing T-count and keeping the qubit-count same. Specifically, if N is the number of memory locations to be queried, then has T-depth , T-count and uses O(N) logical qubits, while the bucket brigade circuit has T-depth , T-count O(N) and uses O(N) qubits. Combining two we design a quantum look-up-table, , that has T-depth , T-count and qubit count . A quantum look-up table (qLUT) or quantum read-only memory (QROM) has restricted functionality than a QRAM. For example, it cannot write into a memory location and the circuit needs to be compiled each time the contents of the memory change. The previous state-of-the-art CSWAP architecture has T-depth , T-count and qubit count . Thus we achieve a double exponential improvement in T-depth while keeping the T-count and qubit-count asymptotically same. Additionally, with our polynomial encoding of bit strings, we develop a method to optimize the Toffoli-count of circuits, specially those consisting of multi-controlled-NOT gates.
... [17][18][19] In conjunction with ML, the parallel field of quantum machine learning (QML) is also rapidly developing, fueled by the idea that quantum-based computational paradigms could both speed up and improve the ability to find statistical patterns between sets of data, which is at the core of machine learning. [20][21][22] In this review, we specifically look at how developments in machine and quantum learning are advancing the field of diamond-based quantum applications. Color centers in diamond have quickly become archetypal systems for quantum technologies owing to their opticallyaddressable spins, long coherence times, room-temperature operation and the ability to create long-range entanglement through photons. ...
... Where the integral is replaced by summation in discrete parameter spaces (note that the number of parameters dim( ) does not need to be the same for each model). The different models can then be compared by comparing the respective probabilities given by (20). So, for instance, one can compare models and by simply calculating their relative probability, given the data : ...
... In this regard, however, we emphasize that the field of QML is still at its infancy and faces several unresolved challenges. 20 For instance, both state preparation and readout can still be exponentially costly in the number of qubits and simply replacing all the vectors in a classical ML algorithm with quantum states to realize QML algorithms usually fail to achieve any speedup, due to the restrictions of unitary evolution and projective measurement. 248,289 These challenges are not unique to diamond, but they will certainly have to be dealt with if diamond were to be used as hardware for quantum algorithm design and implementation. ...
In recent years, machine and quantum learning have gained considerable momentum sustained by growth in computational power and data availability and have shown exceptional aptness for solving recognition- and classification-type problems, as well as problems that require complex, strategic planning. In this work, we discuss and analyze the role machine and quantum learning are playing in the development of diamond-based quantum technologies. This matters as diamond and its optically-addressable spin defects are becoming prime hardware candidates for solid state-based applications in quantum information, computing and metrology. Through a selected number of demonstrations, we show that machine and quantum learning are leading to both practical and fundamental improvements in measurement speed and accuracy. This is crucial for quantum applications, especially for those where coherence time and signal-to-noise ratio are scarce resources. We summarize some of the most prominent machine and quantum learning approaches that have been conducive to the presented advances and discuss their potential for proposed and future quantum applications.
... J.C. Adcock et al.[23] presented a comparative comparison of standard machine learning (ML) and quantum machine learning (QML), highlighting the application of principal component analysis in QML. The authors discussed various quantum algorithms, including HHL, SVM, QSVM, k-Nearest Neighbour (KNN), among others. ...
Quantum machine learning (QML) provides a transformative approach to data analysis by integrating the principles of quantum computing with classical machine learning methods. With the exponential growth of data and the increasing complexity of computational tasks, quantum algorithms offer tremendous advantages in terms of processing speed, memory efficiency, and the ability to resolve issues intractable for classical systems. In this work, the use of QML techniques for both supervised and unsupervised learning problems is explored. Quantum-enhanced models such Quantum Support Vector Machines (QSVMs) and Quantum Neural Networks (QNNs) show outstanding performance in classification and regression tasks by using quantum kernels and entanglement in supervised learning. Moreover, hybrid quantum-classical solutions offer useful implementations on noisy intermediate-scale quantum (NISQ) devices, hence bridging the gap between present quantum technology and practical uses. By means of comparative analysis, this paper emphasizes the possible benefits and drawbacks of QML, thereby providing understanding of its future importance in sectors including material science, finance, and healthcare. In the end, QML opens the path for a new era of intelligent data processing and solves until unthinkable difficult challenges.
... [17][18][19] In conjunction with ML, the parallel field of quantum machine learning (QML) is also rapidly developing, fueled by the idea that quantum-based computational paradigms could both speed up and improve the ability to find statistical patterns between sets of data, which is at the core of machine learning. [20][21][22] In this review, we specifically look at how developments in machine and quantum learning are advancing the field of diamond-based quantum sensing and metrology. Color centers in diamond have quickly become archetypal systems for quantum technologies owing to their opticallyaddressable spins, long coherence times, room-temperature operation and the ability to create longrange entanglement through photons. ...
... Where the integral is replaced by summation in discrete parameter spaces (note that the number of parameters dim( ) does not need to be the same for each model). The different models can then be compared by comparing the respective probabilities given by (20). So, for instance, one can compare models and by simply calculating their relative probability, given the data : ...
In recent years, machine and quantum learning have gained considerable momentum sustained by growth in computational power and data availability and have shown exceptional aptness for solving recognition- and classification-type problems, as well as problems that require complex, strategic planning. In this work, we discuss and analyze the role machine and quantum learning are playing in the development of diamond-based quantum technologies. This matters as diamond and its optically-addressable spin defects are becoming prime hardware candidates for solid state-based applications in quantum information, computing and metrology. Through a selected number of demonstrations, we show that machine and quantum learning are leading to both practical and fundamental improvements in measurement speed and accuracy. This is crucial for quantum applications, especially for those where coherence time and signal-to-noise ratio are scarce resources. We summarize some of the most prominent machine and quantum learning approaches that have been conducive to the presented advances and discuss their potential for proposed and future quantum applications.
... Quantum machine learning combines ML and quantum computing to handle complex problems that are difficult to answer with classical ML [5,27]. In order to implement QML algorithms, supervised and unsupervised ML techniques are used. ...
Quantum machine learning (QML) is an evolving field which is capable of surpassing the classical machine learning in solving classification and clustering problems. The enormous growth in data size started creating barrier for classical machine learning techniques. QML stand out as a best solution to handle big and complex data. In this paper quantum support vector machine (QSVM) based models for the classification of three benchmarking datasets namely, Iris species, Pumpkin seed and Raisin has been constructed. These QSVM based classification models are implemented on real-time superconducting quantum computers/simulators. The performance of these classification models is evaluated in the context of execution time and accuracy and compared with the classical support vector machine (SVM) based models. The kernel based QSVM models for the classification of datasets when run on IBMQ_QASM_simulator appeared to be 232, 207 and 186 times faster than the SVM based classification model. The results indicate that quantum computers/algorithms deliver quantum speed-up.
... Instantaneous processing of huge datasets and solving the optimization task make the quantum computing technology one of the most promising tools in the ML area [13]. Processing a huge dataset input, the quantum computer offers quadratic and even exponential acceleration against the conventional ML as proposed in [14][15][16]. This advantage of the quantum computing has been already applied to various fields of information security. ...
Conventional machine learning approaches applied for the security intrusion detection degrades in case of big data input ( and more samples in a dataset). Model training and computing by traditional machine learning executed on big data at a common computing environment may produce accurate outputs but take a long time, or produce poor accuracy by quick training, both disparate to malicious activity. The paper observes the quantum machine learning (QML) methods overcoming the barriers of big data and the computing abilities of common hardware for the purpose of high performance intrusion detection. Quantum support vector machine (QSVM) and quantum convolution neural network (QCNN) as concurrent methods are discussed and evaluated comparing to the conventional intrusion detectors running on the traditional computer. The QML-based intrusion detection utilizes our own dataset that implements the grouping of the network packets into the input streams eatable for the QML. We have developed the software solution that encodes the network traffic streams ready to the quantum computing. Experimental results show the ability of the QML-based intrusion detection for processing big data inputs with high accuracy (98%) providing a twice faster speed comparing to the conventional machine learning algorithms utilized for the same task.
... After the idea of Feynman, Quantum Turing Machine, which proves the quantum computers are universal, is introduced by Deutsch [5]. Between 1992-1998 quantum algorithms such as Deutsch-Jotza, Shor, and Grover were developed [6]. But, first quantum computer is implemented in 1998. ...
... However, studies are carried out on this technology [14][15][16]. This technology, called qRAM, is expected to be created in the near future [6]. It is thought that there will be a leap forward in these computers with the reduction of noise, the development of structures such as qRAM, and the creation of circuits that can take parameters [17]. ...
... However, this structure requires O(Nd) physical resources. Its scale is exponential in the number of qubits, so whether it can provide real computational advantages in the actual experimental environment is still a big question [56,57]. ...
Quantum image processing (QIP) is a research branch of quantum information and quantum computing. It studies how to take advantage of quantum mechanics’ properties to represent images in a quantum computer and then, based on that image format, implement various image operations. Due to the quantum parallel computing derived from quantum state superposition and entanglement, QIP has natural advantages over classical image processing. But some related works misuse the notion of quantum superiority and mislead the research of QIP, which leads to a big controversy. In this paper, after describing this field’s research status, we list and analyze the doubts about QIP and argue “quantum image classification and recognition” would be the most significant opportunity to exhibit the real quantum superiority. We present the reasons for this judgment and dwell on the challenges for this opportunity in the era of NISQ (Noisy Intermediate-Scale Quantum).
... The optimization of hyperplane's position and alignment in SVM is possible using support vectors. The data in SVM is classified into two classes having values of '1' and '−1' [9]. ...
... The maximum distance between support vectors of two classes is 2 w . The linear SVM classifier [9] produces a decision output for a new data vector ...
... Quantum machine learning is the interaction between quantum computing and machine learning to solve complex problems that are very hard for classical machine learning [7][8][9]. The implementation of quantum machine algorithms basically involves supervised and unsupervised learning processes. ...
Quantum computing is proving to be very beneficial for solving complex machine learning problems. Quantum computers are inherently excellent in handling and manipulating vectors and matrix operations. The ever increasing size of data has started creating bottlenecks for classical machine learning systems. Quantum computers are emerging as potential solutions to tackle big data related problems. This paper presents a quantum machine learning model based on quantum support vector machine (QSVM) algorithm to solve a classification problem. The quantum machine learning model is practically implemented on quantum simulators and real-time superconducting quantum processors. The performance of quantum machine learning model is computed in terms of processing speed and accuracy and compared against its classical counterpart. The breast cancer dataset is used for the classification problem. The results are indicative that quantum computers offer quantum speed-up.
... It has been shown that application of quantum approaches to the field of classical machine learning may produce similar results. Such combination of quantum computing power and machine learning ideas would be a great boost to the quantum information science field and may evaluate new practical solutions for current machine learning problems [6][7][8][9]. Quantum computing has efficient advantage in multi-dimensional systems and multi-variable statistical analysis [10,11]. ...
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine learning algorithms. The quantum machine learning includes hybrid methods that involve both classical and quantum algorithms. Quantum approaches can be used to analyze quantum states instead of classical data. On other side, quantum algorithms can exponentially improve classical data science algorithm. Here, we show basic ideas of quantum machine learning. We present several new methods that combine classical machine learning algorithms and quantum computing methods. We demonstrate multiclass tree tensor network algorithm, and its approbation on IBM quantum processor. Also, we introduce neural networks approach to quantum tomography problem. Our tomography method allows us to predict quantum state excluding noise influence. Such classical-quantum approach can be applied in various experiments to reveal latent dependence between input data and output measurement results.
