High-quality, large-scale datasets have played a crucial role in the development and success of classical machine learning. Quantum Machine Learning (QML) is a new field that aims to use quantum computers for data analysis, with the hope of obtaining a quantum advantage of some sort. While most proposed QML architectures are benchmarked using classical datasets, there is still doubt whether QML on classical datasets will achieve such an advantage. In this work, we argue that one should instead employ quantum datasets composed of quantum states. For this purpose, we introduce the NTangled dataset composed of quantum states with different amounts and types of multipartite entanglement. We first show how a quantum neural network can be trained to generate the states in the NTangled dataset. Then, we use the NTangled dataset to benchmark QML models for supervised learning classification tasks. We also consider an alternative entanglement-based dataset, which is scalable and is composed of states prepared by quantum circuits with different depths. As a byproduct of our results, we introduce a novel method for generating multipartite entangled states, providing a use-case of quantum neural networks for quantum entanglement theory.
Image classification is a major application domain for conventional deep learning (DL). Quantum machine learning (QML) has the potential to revolutionize image classification. In any typical DL-based image classification, we use convolutional neural network (CNN) to extract features from the image and multi-layer perceptron network (MLP) to create the actual decision boundaries. On one hand, QML models can be useful in both of these tasks. Convolution with parameterized quantum circuits (Quanvolution) can extract rich features from the images. On the other hand, quantum neural network (QNN) models can create complex decision boundaries. Therefore, Quanvolution and QNN can be used to create an end-to-end QML model for image classification. Alternatively, we can extract image features separately using classical dimension reduction techniques such as, Principal Components Analysis (PCA) or Convolutional Autoencoder (CAE) and use the extracted features to train a QNN. We review two proposals on quantum-classical hybrid ML models for image classification namely, Quanvolutional Neural Network and dimension reduction using a classical algorithm followed by QNN. Particularly, we make a case for trainable filters in Quanvolution and CAE-based feature extraction for image datasets (instead of dimension reduction using linear transformations such as, PCA). We discuss various design choices, potential opportunities, and drawbacks of these models. We also release a Python-based framework to create and explore these hybrid models with a variety of design choices.
Quantum Machine Learning (QML) is considered to be one of the most promising applications of near term quantum devices. However, the optimization of quantum machine learning models presents numerous challenges arising from the imperfections of hardware and the fundamental obstacles in navigating an exponentially scaling Hilbert space. In this work, we evaluate the potential of contemporary methods in deep reinforcement learning to augment gradient based optimization routines in quantum variational circuits. We find that reinforcement learning augmented optimizers consistently outperform gradient descent in noisy environments. All code and pretrained weights are available to replicate the results or deploy the models at: https://github.com/lockwo/rl_qvc_opt.
Machine learning has achieved dramatic success in a broad spectrum of applications. Its interplay with quantum physics may lead to unprecedented perspectives for both fundamental research and commercial applications, giving rise to an emergent research frontier of quantum machine learning. Along this line, quantum classifiers, which are quantum devices that aim to solve classification problems in machine learning, have attracted tremendous attention recently. In this review, we give a relatively comprehensive overview for the studies of quantum classifiers, with a focus on recent advances. First, we will review a number of quantum classification algorithms, including quantum support vector machines, quantum kernel methods, quantum decision tree classifiers, quantum nearest neighbor algorithms, and quantum annealing based classifiers. Then, we move on to introduce the variational quantum classifiers, which are essentially variational quantum circuits for classifications. We will review different architectures for constructing variational quantum classifiers and introduce the barren plateau problem, where the training of quantum classifiers might be hindered by the exponentially vanishing gradient. In addition, the vulnerability aspect of quantum classifiers in the setting of adversarial learning and the recent experimental progress on different quantum classifiers will also be discussed.
In recent years, near-term noisy intermediate scale quantum (NISQ) computing devices have become available. One of the most promising application areas to leverage such NISQ quantum computer prototypes is quantum machine learning. While quantum neural networks are widely studied for supervised learning, quantum reinforcement learning is still just an emerging field of this area. To solve a classical continuous control problem, we use a continuous-variable quantum machine learning approach. We introduce proximal policy optimization for photonic variational quantum agents and also study the effect of the data re-uploading. We present performance assessment via empirical study using Strawberry Fields, a photonic simulator Fock backend and a hybrid training framework connected to an OpenAI Gym environment and TensorFlow. For the restricted CartPole problem, the two variations of the photonic policy learning achieve comparable performance levels and a faster convergence than the baseline classical neural network of same number of trainable parameters.
Quantum computing is a new field that has recently attracted researchers from a broad range of fields due to its representation power, flexibility and promising results in both speed and scalability. Since 2020, laboratories around the globe have started to experiment with models that lie in the juxtaposition between machine learning and quantum computing. The availability of quantum processing units (QPUs) to the general scientific community through open APIs (e.g., Qiskit from IBM) have kindled the interest in developing and testing new approaches to old problems. In this paper, we present a hybrid quantum machine learning framework for health state diagnostics and prognostics. The framework is exemplified using a problem involving ball bearings dataset. To the best of our knowledge, this is the first attempt to harvest and leverage quantum computing to develop and apply a hybrid quantum-classical machine learning approach to a prognostics and health management (PHM) problem. We hope that this paper initiates the exploration and application of quantum machine learning algorithms in areas of risk and reliability.
Here we will give a perspective on new possible interplays between Machine Learning and Quantum Physics, including also practical cases and applications. We will explore the ways in which machine learning could benefit from new quantum technologies and algorithms to find new ways to speed up their computations by breakthroughs in physical hardware, as well as to improve existing models or devise new learning schemes in the quantum domain. Moreover, there are lots of experiments in quantum physics that do generate incredible amounts of data and machine learning would be a great tool to analyze those and make predictions, or even control the experiment itself. On top of that, data visualization techniques and other schemes borrowed from machine learning can be of great use to theoreticians to have better intuition on the structure of complex manifolds or to make predictions on theoretical models. This new research field, named as Quantum Machine Learning, is very rapidly growing since it is expected to provide huge advantages over its classical counterpart and deeper investigations are timely needed since they can be already tested on the already commercially available quantum machines.
The emergence of quantum computing enables for researchers to apply quantum circuit on many existing studies. Utilizing quantum circuit and quantum differential programming, many research are conducted such as \textit{Quantum Machine Learning} (QML). In particular, quantum reinforcement learning is a good field to test the possibility of quantum machine learning, and a lot of research is being done. This work will introduce the concept of quantum reinforcement learning using a variational quantum circuit, and confirm its possibility through implementation and experimentation. We will first present the background knowledge and working principle of quantum reinforcement learning, and then guide the implementation method using the PennyLane library. We will also discuss the power and possibility of quantum reinforcement learning from the experimental results obtained through this work.
Quantum computing offers the potential of exponential speedups for certain classical computations. Over the last decade, many quantum machine learning (QML) algorithms have been proposed as candidates for such exponential improvements. However, two issues unravel the hope of exponential speedup for some of these QML algorithms: the data-loading problem and, more recently, the stunning dequantization results of Tang et al. A third issue, namely the fault-tolerance requirements of most QML algorithms, has further hindered their practical realization. The quantum topological data analysis (QTDA) algorithm of Lloyd, Garnerone and Zanardi was one of the first QML algorithms that convincingly offered an expected exponential speedup. From the outset, it did not suffer from the data-loading problem. A recent result has also shown that the generalized problem solved by this algorithm is likely classically intractable, and would therefore be immune to any dequantization efforts. However, the QTDA algorithm of Lloyd et~al. has a time complexity of $O(n^4/(\epsilon^2 \delta))$ (where $n$ is the number of data points, $\epsilon$ is the error tolerance, and $\delta$ is the smallest nonzero eigenvalue of the restricted Laplacian) and requires fault-tolerant quantum computing, which has not yet been achieved. In this paper, we completely overhaul the QTDA algorithm to achieve an improved exponential speedup and depth complexity of $O(n\log(1/(\delta\epsilon)))$. Our approach includes three key innovations: (a) an efficient realization of the combinatorial Laplacian as a sum of Pauli operators; (b) a quantum rejection sampling approach to restrict the superposition to the simplices in the complex; and (c) a stochastic rank estimation method to estimate the Betti numbers. We present a theoretical error analysis, and the circuit and computational time and depth complexities for Betti number estimation.
Catastrophic forgetting describes the fact that machine learning models will likely forget the knowledge of previously learned tasks after the learning process of a new one. It is a vital problem in the continual learning scenario and recently has attracted tremendous concern across different communities. In this paper, we explore the catastrophic forgetting phenomena in the context of quantum machine learning. We find that, similar to those classical learning models based on neural networks, quantum learning systems likewise suffer from such forgetting problem in classification tasks emerging from various application scenes. We show that based on the local geometrical information in the loss function landscape of the trained model, a uniform strategy can be adapted to overcome the forgetting problem in the incremental learning setting. Our results uncover the catastrophic forgetting phenomena in quantum machine learning and offer a practical method to overcome this problem, which opens a new avenue for exploring potential quantum advantages towards continual learning.
The efficiency and reliability of real-time incident detection models directly impact the affected corridors' traffic safety and operational conditions. The recent emergence of cloud-based quantum computing infrastructure and innovations in noisy intermediate-scale quantum devices have revealed a new era of quantum-enhanced algorithms that can be leveraged to improve real-time incident detection accuracy. In this research, a hybrid machine learning model, which includes classical and quantum machine learning (ML) models, is developed to identify incidents using the connected vehicle (CV) data. The incident detection performance of the hybrid model is evaluated against baseline classical ML models. The framework is evaluated using data from a microsimulation tool for different incident scenarios. The results indicate that a hybrid neural network containing a 4-qubit quantum layer outperforms all other baseline models when there is a lack of training data. We have created three datasets; DS-1 with sufficient training data, and DS-2 and DS-3 with insufficient training data. The hybrid model achieves a recall of 98.9%, 98.3%, and 96.6% for DS-1, DS-2, and DS-3, respectively. For DS-2 and DS-3, the average improvement in F2-score (measures model's performance to correctly identify incidents) achieved by the hybrid model is 1.9% and 7.8%, respectively, compared to the classical models. It shows that with insufficient data, which may be common for CVs, the hybrid ML model will perform better than the classical models. With the continuing improvements of quantum computing infrastructure, the quantum ML models could be a promising alternative for CV-related applications when the available data is insufficient.
Quantum computers promise to enhance machine learning for practical applications. Quantum machine learning for real-world data has to handle extensive amounts of high-dimensional data. However, conventional methods for measuring quantum kernels are impractical for large datasets as they scale with the square of the dataset size. Here, we measure quantum kernels using randomized measurements. The quantum computation time scales linearly with dataset size and quadratic for classical post-processing. While our method scales in general exponentially in qubit number, we gain a substantial speed-up when running on intermediate-sized quantum computers. Further, we efficiently encode high-dimensional data into quantum computers with the number of features scaling linearly with the circuit depth. The encoding is characterized by the quantum Fisher information metric and is related to the radial basis function kernel. Our approach is robust to noise via a cost-free error mitigation scheme. We demonstrate the advantages of our methods for noisy quantum computers by classifying images with the IBM quantum computer. To achieve further speedups we distribute the quantum computational tasks between different quantum computers. Our method enables benchmarking of quantum machine learning algorithms with large datasets on currently available quantum computers.
Given the success of deep learning in classical machine learning, quantum algorithms for traditional neural network architectures may provide one of the most promising settings for quantum machine learning. Considering a fully-connected feedforward neural network, we show that conditions amenable to classical trainability via gradient descent coincide with those necessary for efficiently solving quantum linear systems. We propose a quantum algorithm to approximately train a wide and deep neural network up to $O(1/n)$ error for a training set of size $n$ by performing sparse matrix inversion in $O(\log n)$ time. To achieve an end-to-end exponential speedup over gradient descent, the data distribution must permit efficient state preparation and readout. We numerically demonstrate that the MNIST image dataset satisfies such conditions; moreover, the quantum algorithm matches the accuracy of the fully-connected network. Beyond the proven architecture, we provide empirical evidence for $O(\log n)$ training of a convolutional neural network with pooling.
Quantum computers hold unprecedented potentials for machine learning applications. Here, we prove that physical quantum circuits are PAC (probably approximately correct) learnable on a quantum computer via empirical risk minimization: to learn a parametric quantum circuit with at most $n^c$ gates and each gate acting on a constant number of qubits, the sample complexity is bounded by $\tilde{O}(n^{c+1})$. In particular, we explicitly construct a family of variational quantum circuits with $O(n^{c+1})$ elementary gates arranged in a fixed pattern, which can represent all physical quantum circuits consisting of at most $n^c$ elementary gates. Our results provide a valuable guide for quantum machine learning in both theory and practice.
The data-embedding process is one of the bottlenecks of quantum machine learning, potentially negating any quantum speedups. In light of this, more effective data-encoding strategies are necessary. We propose a photonic-based bosonic data-encoding scheme that embeds classical data points using fewer encoding layers and circumventing the need for nonlinear optical components by mapping the data points into the high-dimensional Fock space. The expressive power of the circuit can be controlled via the number of input photons. Our work shed some light on the unique advantages offers by quantum photonics on the expressive power of quantum machine learning models. By leveraging the photon-number dependent expressive power, we propose three different noisy intermediate-scale quantum-compatible binary classification methods with different scaling of required resources suitable for different supervised classification tasks.
The emerging field of quantum machine learning has the potential of revolutionizing our perspectives of quantum computing and artificial intelligence. In the predominantly empirical realm of quantum machine learning, a theoretical void persists. This paper addresses the gap by highlighting the quantum cross entropy, a pivotal counterpart to the classical cross entropy. We establish quantum cross entropy's role in quantum data compression, a fundamental machine learning task, by demonstrating that it acts as the compression rate for sub-optimal quantum source coding. Our approach involves a novel, universal quantum data compression protocol based on the quantum generalization of variable-length coding and the principle of quantum strong typicality. This reveals that quantum cross entropy can effectively serve as a loss function in quantum machine learning algorithms. Furthermore, we illustrate that the minimum of quantum cross entropy aligns with the von Neumann entropy, reinforcing its role as the optimal compression rate and underscoring its significance in advancing our understanding of quantum machine learning's theoretical framework.
For the last few decades, classical machine learning has allowed us to improve the lives of many through automation, natural language processing, predictive analytics and much more. However, a major concern is the fact that we're fast approach the threshold of the maximum possible computational capacity available to us by the means of classical computing devices including CPUs, GPUs and Application Specific Integrated Circuits (ASICs). This is due to the exponential increase in model sizes which now have parameters in the magnitude of billions and trillions, requiring a significant amount of computing resources across a significant amount of time, just to converge one single model. To observe the efficacy of using quantum computing for certain machine learning tasks and explore the improved potential of convergence, error reduction and robustness to noisy data, this paper will look forth to test and verify the aspects in which quantum machine learning can help improve over classical machine learning approaches while also shedding light on the likely limitations that have prevented quantum approaches to become the mainstream. A major focus will be to recreate the work by Farhi et al and conduct experiments using their theory of performing machine learning in a quantum context, with assistance from the Tensorflow Quantum documentation.
Quantum classifiers provide sophisticated embeddings of input data in Hilbert space promising quantum advantage. The advantage stems from quantum feature maps encoding the inputs into quantum states with variational quantum circuits. A recent work shows how to map discrete features with fewer quantum bits using Quantum Random Access Coding (QRAC), an important primitive to encode binary strings into quantum states. We propose a new method to embed discrete features with trainable quantum circuits by combining QRAC and a recently proposed strategy for training quantum feature map called quantum metric learning. We show that the proposed trainable embedding requires not only as few qubits as QRAC but also overcomes the limitations of QRAC to classify inputs whose classes are based on hard Boolean functions. We numerically demonstrate its use in variational quantum classifiers to achieve better performances in classifying real-world datasets, and thus its possibility to leverage near-term quantum computers for quantum machine learning.
Classification is a common task in machine learning. Random features (RFs) stand as a central technique for scalable learning algorithms based on kernel methods, and more recently proposed optimized random features, sampled depending on the model and the data distribution, can significantly reduce and provably minimize the required number of features. However, existing research on classification using optimized RFs has suffered from computational hardness in sampling each optimized RF; moreover, it has failed to achieve the exponentially fast error-convergence speed that other state-of-the-art kernel methods can achieve under a low-noise condition. To overcome these slowdowns, we here construct a classification algorithm with optimized RFs accelerated by means of quantum machine learning (QML) and study its runtime to clarify overall advantage. We prove that our algorithm can achieve the exponential error convergence under the low-noise condition even with optimized RFs; at the same time, our algorithm can exploit the advantage of the significant reduction of the number of features without the computational hardness owing to QML. These results discover a promising application of QML to acceleration of the leading kernel-based classification algorithm without ruining its wide applicability and the exponential error-convergence speed.
Image classification is an important task in various machine learning applications. In recent years, a number of classification methods based on quantum machine learning and different quantum image encoding techniques have been proposed. In this paper, we study the effect of three different quantum image encoding approaches on the performance of a convolution-inspired hybrid quantum-classical image classification algorithm called quanvolutional neural network (QNN). We furthermore examine the effect of variational - i.e. trainable - quantum circuits on the classification results. Our experiments indicate that some image encodings are better suited for variational circuits. However, our experiments show as well that there is not one best image encoding, but that the choice of the encoding depends on the specific constraints of the application.