Quantum Machine Learning continues to be a highly active area of interest within Quantum Computing. Many of these approaches have adapted classical approaches to the quantum settings, such as QuantumFlow, etc. We push forward this trend and demonstrate an adaption of the Classical Convolutional Neural Networks to quantum systems - namely QuCNN. QuCNN is a parameterised multi-quantum-state based neural network layer computing similarities between each quantum filter state and each quantum data state. With QuCNN, back propagation can be achieved through a single-ancilla qubit quantum routine. QuCNN is validated by applying a convolutional layer with a data state and a filter state over a small subset of MNIST images, comparing the back propagated gradients, and training a filter state against an ideal target state.
The emergence of Quantum Machine Learning (QML) to enhance traditional classical learning methods has seen various limitations to its realisation. There is therefore an imperative to develop quantum models with unique model hypotheses to attain expressional and computational advantage. In this work we extend the linear quantum support vector machine (QSVM) with kernel function computed through quantum kernel estimation (QKE), to form a decision tree classifier constructed from a decision directed acyclic graph of QSVM nodes - the ensemble of which we term the quantum random forest (QRF). To limit overfitting, we further extend the model to employ a low-rank Nystr\"{o}m approximation to the kernel matrix. We provide generalisation error bounds on the model and theoretical guarantees to limit errors due to finite sampling on the Nystr\"{o}m-QKE strategy. In doing so, we show that we can achieve lower sampling complexity when compared to QKE. We numerically illustrate the effect of varying model hyperparameters and finally demonstrate that the QRF is able obtain superior performance over QSVMs, while also requiring fewer kernel estimations.
In this paper, we introduce an emerging quantum machine learning (QML) framework to assist classical deep learning methods for biosignal processing applications. Specifically, we propose a hybrid quantum-classical neural network model that integrates a variational quantum circuit (VQC) into a deep neural network (DNN) for electroencephalogram (EEG), electromyogram (EMG), and electrocorticogram (ECoG) analysis. We demonstrate that the proposed quantum neural network (QNN) achieves state-of-the-art performance while the number of trainable parameters is kept small for VQC.
Quantum machine learning (QML) is the use of quantum computing for the computation of machine learning algorithms. With the prevalence and importance of classical data, a hybrid quantum-classical approach to QML is called for. Parameterized Quantum Circuits (PQCs), and particularly Quantum Kernel PQCs, are generally used in the hybrid approach to QML. In this paper we discuss some important aspects of PQCs with quantum kernels including PQCs, quantum kernels, quantum kernels with quantum advantage, and the trainability of quantum kernels. We conclude that quantum kernels with hybrid kernel methods, a.k.a. quantum kernel methods, offer distinct advantages as a hybrid approach to QML. Not only do they apply to Noisy Intermediate-Scale Quantum (NISQ) devices, but they also can be used to solve all types of machine learning problems including regression, classification, clustering, and dimension reduction. Furthermore, beyond quantum utility, quantum advantage can be attained if the quantum kernels, i.e., the quantum feature encodings, are classically intractable.
Topological data analysis (TDA) is a powerful technique for extracting complex and valuable shape-related summaries of high-dimensional data. However, the computational demands of classical algorithms for computing TDA are exorbitant, and quickly become impractical for high-order characteristics. Quantum computers offer the potential of achieving significant speedup for certain computational problems. Indeed, TDA has been purported to be one such problem, yet, quantum computing algorithms proposed for the problem, such as the original Quantum TDA (QTDA) formulation by Lloyd, Garnerone and Zanardi, require fault-tolerance qualifications that are currently unavailable. In this study, we present NISQ-TDA, a fully implemented end-to-end quantum machine learning algorithm needing only a short circuit-depth, that is applicable to high-dimensional classical data, and with provable asymptotic speedup for certain classes of problems. The algorithm neither suffers from the data-loading problem nor does it need to store the input data on the quantum computer explicitly. The algorithm was successfully executed on quantum computing devices, as well as on noisy quantum simulators, applied to small datasets. Preliminary empirical results suggest that the algorithm is robust to noise.
Quantum kernels are considered as potential resources to illustrate benefits of quantum computing in machine learning. Considering the impact of hyperparameters on the performance of a classical machine learning model, it is imperative to identify promising hyperparameters using quantum kernel methods in order to achieve quantum advantages. In this work, we analyse and classify sentiments of textual data using a new quantum kernel based on linear and full entangled circuits as hyperparameters for controlling the correlation among words. We also find that the use of linear and full entanglement further controls the expressivity of the Quantum Support Vector Machine (QSVM). In addition, we also compare the efficiency of the proposed circuit with other quantum circuits and classical machine learning algorithms. Our results show that the proposed fully entangled circuit outperforms all other fully or linearly entangled circuits in addition to classical algorithms for most of the features. In fact, as the feature increases the efficiency of our proposed fully entangled model also increases significantly.
Current technologies in quantum-based communications bring a new integration of quantum data with classical data for hybrid processing. However, the frameworks of these technologies are restricted to a single classical or quantum task, which limits their flexibility in near-term applications. We propose a quantum reservoir processor to harness quantum dynamics in computational tasks requiring both classical and quantum inputs. This analog processor comprises a network of quantum dots in which quantum data is incident to the network and classical data is encoded via a coherent field exciting the network. We perform a multitasking application of quantum tomography and nonlinear equalization of classical channels. Interestingly, the tomography can be performed in a closed-loop manner via the feedback control of classical data. Therefore, if the classical input comes from a dynamical system, embedding this system in a closed loop enables hybrid processing even if access to the external classical input is interrupted. Finally, we demonstrate preparing quantum depolarizing channels as a novel quantum machine learning technique for quantum data processing.
Quantum Machine Learning (QML) hasn't yet demonstrated extensively and clearly its advantages compared to the classical machine learning approach. So far, there are only specific cases where some quantum-inspired techniques have achieved small incremental advantages, and a few experimental cases in hybrid quantum computing are promising considering a mid-term future (not taking into account the achievements purely associated with optimization using quantum-classical algorithms). The current quantum computers are noisy and have few qubits to test, making it difficult to demonstrate the current and potential quantum advantage of QML methods. This study shows that we can achieve better classical encoding and performance of quantum classifiers by using Linear Discriminant Analysis (LDA) during the data preprocessing step. As a result, Variational Quantum Algorithm (VQA) shows a gain of performance in balanced accuracy with the LDA technique and outperforms baseline classical classifiers.
Although quantum supremacy is yet to come, there has recently been an increasing interest in identifying the potential of quantum machine learning (QML) in the looming era of practical quantum computing. Motivated by this, in this article we re-design multi-agent reinforcement learning (MARL) based on the unique characteristics of quantum neural networks (QNNs) having two separate dimensions of trainable parameters: angle parameters affecting the output qubit states, and pole parameters associated with the output measurement basis. Exploiting this dyadic trainability as meta-learning capability, we propose quantum meta MARL (QM2ARL) that first applies angle training for meta-QNN learning, followed by pole training for few-shot or local-QNN training. To avoid overfitting, we develop an angle-to-pole regularization technique injecting noise into the pole domain during angle training. Furthermore, by exploiting the pole as the memory address of each trained QNN, we introduce the concept of pole memory allowing one to save and load trained QNNs using only two-parameter pole values. We theoretically prove the convergence of angle training under the angle-to-pole regularization, and by simulation corroborate the effectiveness of QM2ARL in achieving high reward and fast convergence, as well as of the pole memory in fast adaptation to a time-varying environment.
Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model's parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from quantum hardware. In this work we study the performance of quantum kernel models from the perspective of the resources needed to accurately estimate kernel values. We show that, under certain conditions, values of quantum kernels over different input data can be exponentially concentrated (in the number of qubits) towards some fixed value. Thus on training with a polynomial number of measurements, one ends up with a trivial model where the predictions on unseen inputs are independent of the input data. We identify four sources that can lead to concentration including: expressivity of data embedding, global measurements, entanglement and noise. For each source, an associated concentration bound of quantum kernels is analytically derived. Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration. Our results are verified through numerical simulations for several QML tasks. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods.
Heart disease morbidity and mortality rates are increasing, which has a negative impact on public health and the global economy. Early detection of heart disease reduces the incidence of heart mortality and morbidity. Recent research has utilized quantum computing methods to predict heart disease with more than 5 qubits and are computationally intensive. Despite the higher number of qubits, earlier work reports a lower accuracy in predicting heart disease, have not considered the outlier effects, and requires more computation time and memory for heart disease prediction. To overcome these limitations, we propose hybrid random forest quantum neural network (HQRF) using a few qubits (two to four) and considered the effects of outlier in the dataset. Two open-source datasets, Cleveland and Statlog, are used in this study to apply quantum networks. The proposed algorithm has been applied on two open-source datasets and utilized two different types of testing strategies such as 10-fold cross validation and 70-30 train/test ratio. We compared the performance of our proposed methodology with our earlier algorithm called hybrid quantum neural network (HQNN) proposed in the literature for heart disease prediction. HQNN and HQRF outperform in 10-fold cross validation and 70/30 train/test split ratio, respectively. The results show that HQNN requires a large training dataset while HQRF is more appropriate for both large and small training dataset. According to the experimental results, the proposed HQRF is not sensitive to the outlier data compared to HQNN. Compared to earlier works, the proposed HQRF achieved a maximum area under the curve (AUC) of 96.43% and 97.78% in predicting heart diseases using Cleveland and Statlog datasets, respectively with HQNN. The proposed HQRF is highly efficient in detecting heart disease at an early stage and will speed up clinical diagnosis.
Using quantum computing, this paper addresses two scientifically pressing and day-to-day relevant problems, namely, chemical retrosynthesis which is an important step in drug/material discovery and security of the semiconductor supply chain. We show that Quantum Long Short-Term Memory (QLSTM) is a viable tool for retrosynthesis. We achieve 65% training accuracy with QLSTM, whereas classical LSTM can achieve 100%. However, in testing, we achieve 80% accuracy with the QLSTM while classical LSTM peaks at only 70% accuracy! We also demonstrate an application of Quantum Neural Network (QNN) in the hardware security domain, specifically in Hardware Trojan (HT) detection using a set of power and area Trojan features. The QNN model achieves detection accuracy as high as 97.27%.
Quantum Bayesian Computation (QBC) is an emerging field that levers the computational gains available from quantum computers to provide an exponential speed-up in Bayesian computation. Our paper adds to the literature in two ways. First, we show how von Neumann quantum measurement can be used to simulate machine learning algorithms such as Markov chain Monte Carlo (MCMC) and Deep Learning (DL) that are fundamental to Bayesian learning. Second, we describe data encoding methods needed to implement quantum machine learning including the counterparts to traditional feature extraction and kernel embeddings methods. Our goal then is to show how to apply quantum algorithms directly to statistical machine learning problems. On the theoretical side, we provide quantum versions of high dimensional regression, Gaussian processes (Q-GP) and stochastic gradient descent (Q-SGD). On the empirical side, we apply a Quantum FFT model to Chicago housing data. Finally, we conclude with directions for future research.
This paper presents a first end-to-end application of a Quantum Support Vector Machine (QSVM) algorithm for a classification problem in the financial payment industry using the IBM Safer Payments and IBM Quantum Computers via the Qiskit software stack. Based on real card payment data, a thorough comparison is performed to assess the complementary impact brought in by the current state-of-the-art Quantum Machine Learning algorithms with respect to the Classical Approach. A new method to search for best features is explored using the Quantum Support Vector Machine's feature map characteristics. The results are compared using fraud specific key performance indicators: Accuracy, Recall, and False Positive Rate, extracted from analyses based on human expertise (rule decisions), classical machine learning algorithms (Random Forest, XGBoost) and quantum based machine learning algorithms using QSVM. In addition, a hybrid classical-quantum approach is explored by using an ensemble model that combines classical and quantum algorithms to better improve the fraud prevention decision. We found, as expected, that the results highly depend on feature selections and algorithms that are used to select them. The QSVM provides a complementary exploration of the feature space which led to an improved accuracy of the mixed quantum-classical method for fraud detection, on a drastically reduced data set to fit current state of Quantum Hardware.
Many recent machine learning tasks resort to quantum computing to improve classification accuracy and training efficiency by taking advantage of quantum mechanics, known as quantum machine learning (QML). The variational quantum circuit (VQC) is frequently utilized to build a quantum neural network (QNN), which is a counterpart to the conventional neural network. Due to hardware limitations, however, current quantum devices only allow one to use few qubits to represent data and perform simple quantum computations. The limited quantum resource on a single quantum device degrades the data usage and limits the scale of the quantum circuits, preventing quantum advantage to some extent. To alleviate this constraint, we propose an approach to implementing a scalable quantum neural network (SQNN) by utilizing the quantum resource of multiple small-size quantum devices cooperatively. In an SQNN system, several quantum devices are used as quantum feature extractors, extracting local features from an input instance in parallel, and a quantum device works as a quantum predictor, performing prediction over the local features collected through classical communication channels. The quantum feature extractors in the SQNN system are independent of each other, so one can flexibly use quantum devices of varying sizes, with larger quantum devices extracting more local features. Especially, the SQNN can be performed on a single quantum device in a modular fashion. Our work is exploratory and carried out on a quantum system simulator using the TensorFlow Quantum library. The evaluation conducts a binary classification on the MNIST dataset. It shows that the SQNN model achieves a comparable classification accuracy to a regular QNN model of the same scale. Furthermore, it demonstrates that the SQNN model with more quantum resources can significantly improve classification accuracy.
Despite years of effort, the quantum machine learning community has only been able to show quantum learning advantages for certain contrived cryptography-inspired datasets in the case of classical data. In this note, we discuss the challenges of finding learning problems that quantum learning algorithms can learn much faster than any classical learning algorithm, and we study how to identify such learning problems. Specifically, we reflect on the main concepts in computational learning theory pertaining to this question, and we discuss how subtle changes in definitions can mean conceptually significantly different tasks, which can either lead to a separation or no separation at all. Moreover, we study existing learning problems with a provable quantum speedup to distill sets of more general and sufficient conditions (i.e., ``checklists'') for a learning problem to exhibit a separation between classical and quantum learners. These checklists are intended to streamline one's approach to proving quantum speedups for learning problems, or to elucidate bottlenecks. Finally, to illustrate its application, we analyze examples of potential separations (i.e., when the learning problem is build from computational separations, or when the data comes from a quantum experiment) through the lens of our approach.
The existence of incompatible observables is a cornerstone of quantum mechanics and a valuable resource in quantum technologies. Here we introduce a measure of incompatibility, called the mutual eigenspace disturbance (MED), which quantifies the amount of disturbance induced by the measurement of a sharp observable on the eigenspaces of another. The MED provides a metric on the space of von Neumann measurements, and can be efficiently estimated by letting the measurement processes act in an indefinite order, using a setup known as the quantum switch, which also allows one to quantify the noncommutativity of arbitrary quantum processes. Thanks to these features, the MED can be used in quantum machine learning tasks. We demonstrate this application by providing an unsupervised algorithm that clusters unknown von Neumann measurements. Our algorithm is robust to noise can be used to identify groups of observers that share approximately the same measurement context.
This paper introduces a deep learning system based on a quantum neural network for the binary classification of points of a specific geometric pattern (Two-Moons Classification problem) on a plane. We believe that the use of hybrid deep learning systems (classical + quantum) can reasonably bring benefits, not only in terms of computational acceleration but in understanding the underlying phenomena and mechanisms; that will lead to the creation of new forms of machine learning, as well as to a strong development in the world of quantum computation. The chosen dataset is based on a 2D binary classification generator, which helps test the effectiveness of specific algorithms; it is a set of 2D points forming two interspersed semicircles. It displays two disjointed data sets in a two-dimensional representation space: the features are, therefore, the individual points' two coordinates, $x_1$ and $x_2$. The intention was to produce a quantum deep neural network with the minimum number of trainable parameters capable of correctly recognising and classifying points.
Training a quantum machine learning model generally requires a large labeled dataset, which incurs high labeling and computational costs. To reduce such costs, a selective training strategy, called active learning (AL), chooses only a subset of the original dataset to learn while maintaining the trained model's performance. Here, we design and implement two AL-enpowered variational quantum classifiers, to investigate the potential applications and effectiveness of AL in quantum machine learning. Firstly, we build a programmable free-space photonic quantum processor, which enables the programmed implementation of various hybrid quantum-classical computing algorithms. Then, we code the designed variational quantum classifier with AL into the quantum processor, and execute comparative tests for the classifiers with and without the AL strategy. The results validate the great advantage of AL in quantum machine learning, as it saves at most $85\%$ labeling efforts and $91.6\%$ percent computational efforts compared to the training without AL on a data classification task. Our results inspire AL's further applications in large-scale quantum machine learning to drastically reduce training data and speed up training, underpinning the exploration of practical quantum advantages in quantum physics or real-world applications.
Distributed quantum information processing protocols such as quantum entanglement distillation and quantum state discrimination rely on local operations and classical communications (LOCC). Existing LOCC-based protocols typically assume the availability of ideal, noiseless, communication channels. In this paper, we study the case in which classical communication takes place over noisy channels, and we propose to address the design of LOCC protocols in this setting via the use of quantum machine learning tools. We specifically focus on the important tasks of quantum entanglement distillation and quantum state discrimination, and implement local processing through parameterized quantum circuits (PQCs) that are optimized to maximize the average fidelity and average success probability in the respective tasks, while accounting for communication errors. The introduced approach, Noise Aware-LOCCNet (NA-LOCCNet), is shown to have significant advantages over existing protocols designed for noiseless communications.