The field of Quantum Machine Learning (QML) has emerged recently in the hopes of finding new machine learning protocols or exponential speedups for classical ones. Apart from problems with vanishing gradients and efficient encoding methods, these speedups are hard to find because the sampling nature of quantum computers promotes either simulating computations classically or running them many times on quantum computers in order to use approximate expectation values in gradient calculations. In this paper, we make a case for setting high single-sample accuracy as a primary goal. We discuss the statistical theory which enables highly accurate and precise sample inference, and propose a method of reversed training towards this end. We show the effectiveness of this training method by assessing several effective variational quantum circuits (VQCs), trained in both the standard and reversed directions, on random binary subsets of the MNIST and MNIST Fashion datasets, on which our method provides an increase of $10-15\%$ in single-sample inference accuracy.
Climate change and its impact on global sustainability are critical challenges, demanding innovative solutions that combine cutting-edge technologies and scientific insights. Quantum machine learning (QML) has emerged as a promising paradigm that harnesses the power of quantum computing to address complex problems in various domains including climate change and sustainability. In this work, we survey existing literature that applies quantum machine learning to solve climate change and sustainability-related problems. We review promising QML methodologies that have the potential to accelerate decarbonization including energy systems, climate data forecasting, climate monitoring, and hazardous events predictions. We discuss the challenges and current limitations of quantum machine learning approaches and provide an overview of potential opportunities and future work to leverage QML-based methods in the important area of climate change research.
The preservation of privacy is a critical concern in the implementation of artificial intelligence on sensitive training data. There are several techniques to preserve data privacy but quantum computations are inherently more secure due to the no-cloning theorem, resulting in a most desirable computational platform on top of the potential quantum advantages. There have been prior works in protecting data privacy by Quantum Federated Learning (QFL) and Quantum Differential Privacy (QDP) studied independently. However, to the best of our knowledge, no prior work has addressed both QFL and QDP together yet. Here, we propose to combine these privacy-preserving methods and implement them on the quantum platform, so that we can achieve comprehensive protection against data leakage (QFL) and model inversion attacks (QDP). This implementation promises more efficient and secure artificial intelligence. In this paper, we present a successful implementation of these privacy-preservation methods by performing the binary classification of the Cats vs Dogs dataset. Using our quantum-classical machine learning model, we obtained a test accuracy of over 0.98, while maintaining epsilon values less than 1.3. We show that federated differentially private training is a viable privacy preservation method for quantum machine learning on Noisy Intermediate-Scale Quantum (NISQ) devices.
Parameterized quantum circuits (PQCs) have emerged as a promising approach for quantum neural networks. However, understanding their expressive power in accomplishing machine learning tasks remains a crucial question. This paper investigates the expressivity of PQCs for approximating general multivariate function classes. Unlike previous Universal Approximation Theorems for PQCs, which are either nonconstructive or rely on parameterized classical data processing, we explicitly construct data re-uploading PQCs for approximating multivariate polynomials and smooth functions. We establish the first non-asymptotic approximation error bounds for these functions in terms of the number of qubits, quantum circuit depth, and number of trainable parameters. Notably, we demonstrate that for approximating functions that satisfy specific smoothness criteria, the quantum circuit size and number of trainable parameters of our proposed PQCs can be smaller than those of deep ReLU neural networks. We further validate the approximation capability of PQCs through numerical experiments. Our results provide a theoretical foundation for designing practical PQCs and quantum neural networks for machine learning tasks that can be implemented on near-term quantum devices, paving the way for the advancement of quantum machine learning.
Deep generative models are key-enabling technology to computer vision, text generation, and large language models. Denoising diffusion probabilistic models (DDPMs) have recently gained much attention due to their ability to generate diverse and high-quality samples in many computer vision tasks, as well as to incorporate flexible model architectures and a relatively simple training scheme. Quantum generative models, empowered by entanglement and superposition, have brought new insight to learning classical and quantum data. Inspired by the classical counterpart, we propose the quantum denoising diffusion probabilistic model (QuDDPM) to enable efficiently trainable generative learning of quantum data. QuDDPM adopts sufficient layers of circuits to guarantee expressivity, while it introduces multiple intermediate training tasks as interpolation between the target distribution and noise to avoid barren plateau and guarantee efficient training. We provide bounds on the learning error and demonstrate QuDDPM's capability in learning correlated quantum noise model, quantum many-body phases, and topological structure of quantum data. The results provide a paradigm for versatile and efficient quantum generative learning.
This work describes the selection approach and analysis of existing AutoML frameworks regarding their capability of a) incorporating Quantum Machine Learning (QML) algorithms into this automated solving approach of the AutoML framing and b) solving a set of industrial use-cases with different ML problem types by benchmarking their most important characteristics. For that, available open-source tools are condensed into a market overview and suitable frameworks are systematically selected on a multi-phase, multi-criteria approach. This is done by considering software selection approaches, as well as in terms of the technical perspective of AutoML. The requirements for the framework selection are divided into hard and soft criteria regarding their software and ML attributes. Additionally, a classification of AutoML frameworks is made into high- and low-level types, inspired by the findings of. Finally, we select Ray and AutoGluon as the suitable low- and high-level frameworks respectively, as they fulfil all requirements sufficiently and received the best evaluation feedback during the use-case study. Based on those findings, we build an extended Automated Quantum Machine Learning (AutoQML) framework with QC-specific pipeline steps and decision characteristics for hardware and software constraints.
Quantum Neural Networks (QNNs) are suggested as one of the quantum algorithms which can be efficiently simulated with a low depth on near-term quantum hardware in the presence of noises. However, their performance highly relies on choosing the most suitable architecture of Variational Quantum Algorithms (VQAs), and the problem-agnostic models often suffer issues regarding trainability and generalization power. As a solution, the most recent works explore Geometric Quantum Machine Learning (GQML) using QNNs equivariant with respect to the underlying symmetry of the dataset. GQML adds an inductive bias to the model by incorporating the prior knowledge on the given dataset and leads to enhancing the optimization performance while constraining the search space. This work proposes equivariant Quantum Convolutional Neural Networks (EquivQCNNs) for image classification under planar $p4m$ symmetry, including reflectional and $90^\circ$ rotational symmetry. We present the results tested in different use cases, such as phase detection of the 2D Ising model and classification of the extended MNIST dataset, and compare them with those obtained with the non-equivariant model, proving that the equivariance fosters better generalization of the model.
We propose several algorithms for learning unitary operators from quantum statistical queries (QSQs) with respect to their Choi-Jamiolkowski state. Quantum statistical queries capture the capabilities of a learner with limited quantum resources, which receives as input only noisy estimates of expected values of measurements. Our methods hinge on a novel technique for estimating the Fourier mass of a unitary on a subset of Pauli strings with a single quantum statistical query, generalizing a previous result for uniform quantum examples. Exploiting this insight, we show that the quantum Goldreich-Levin algorithm can be implemented with quantum statistical queries, whereas the prior version of the algorithm involves oracle access to the unitary and its inverse. Moreover, we prove that $\mathcal{O}(\log n)$-juntas and quantum Boolean functions with constant total influence are efficiently learnable in our model, and constant-depth circuits are learnable sample-efficiently with quantum statistical queries. On the other hand, all previous algorithms for these tasks require direct access to the Choi-Jamiolkowski state or oracle access to the unitary. In addition, our upper bounds imply that the actions of those classes of unitaries on locally scrambled ensembles can be efficiently learned. We also demonstrate that, despite these positive results, quantum statistical queries lead to an exponentially larger sample complexity for certain tasks, compared to separable measurements to the Choi-Jamiolkowski state. In particular, we show an exponential lower bound for learning a class of phase-oracle unitaries and a double exponential lower bound for testing the unitarity of channels, adapting to our setting previous arguments for quantum states. Finally, we propose a new definition of average-case surrogate models, showing a potential application of our results to hybrid quantum machine learning.
In this work, we initiate the study of learning quantum processes from quantum statistical queries. We focus on two fundamental learning tasks in this new access model: shadow tomography of quantum processes and process tomography with respect to diamond distance. For the former, we present an efficient average-case algorithm along with a nearly matching lower bound with respect to the number of observables to be predicted. For the latter, we present average-case query complexity lower bounds for learning classes of unitaries. We obtain an exponential lower bound for learning unitary 2-designs and a doubly exponential lower bound for Haar-random unitaries. Finally, we demonstrate the practical relevance of our access model by applying our learning algorithm to attack an authentication protocol using Classical-Readout Quantum Physically Unclonable Functions, partially addressing an important open question in quantum hardware security.
Quantum machine learning researchers often rely on incorporating Tensor Networks (TN) into Deep Neural Networks (DNN) and variational optimization. However, the standard optimization techniques used for training the contracted trainable weights of each model layer suffer from the correlations and entanglement structure between the model parameters on classical implementations. To address this issue, a multi-layer design of a Tensor Ring optimized variational Quantum learning classifier (Quan-TR) comprising cascading entangling gates replacing the fully connected (dense) layers of a TN is proposed, and it is referred to as Tensor Ring optimized Quantum-enhanced tensor neural Networks (TR-QNet). TR-QNet parameters are optimized through the stochastic gradient descent algorithm on qubit measurements. The proposed TR-QNet is assessed on three distinct datasets, namely Iris, MNIST, and CIFAR-10, to demonstrate the enhanced precision achieved for binary classification. On quantum simulations, the proposed TR-QNet achieves promising accuracy of $94.5\%$, $86.16\%$, and $83.54\%$ on the Iris, MNIST, and CIFAR-10 datasets, respectively. Benchmark studies have been conducted on state-of-the-art quantum and classical implementations of TN models to show the efficacy of the proposed TR-QNet. Moreover, the scalability of TR-QNet highlights its potential for exhibiting in deep learning applications on a large scale. The PyTorch implementation of TR-QNet is available on Github:https://github.com/konar1987/TR-QNet/
As an emerging field that aims to bridge the gap between human activities and computing systems, human-centered computing (HCC) in cloud, edge, fog has had a huge impact on the artificial intelligence algorithms. The quantum generative adversarial network (QGAN) is considered to be one of the quantum machine learning algorithms with great application prospects, which also should be improved to conform to the human-centered paradigm. The generation process of QGAN is relatively random and the generated model does not conform to the human-centered concept, so it is not quite suitable for real scenarios. In order to solve these problems, a hybrid quantum-classical conditional generative adversarial network (QCGAN) algorithm is proposed, which is a knowledge-driven human-computer interaction computing mode that can be implemented in cloud. The purposes of stabilizing the generation process and realizing the interaction between human and computing process are achieved by inputting artificial conditional information in the generator and discriminator. The generator uses the parameterized quantum circuit with an all-to-all connected topology, which facilitates the tuning of network parameters during the training process. The discriminator uses the classical neural network, which effectively avoids the "input bottleneck" of quantum machine learning. Finally, the BAS training set is selected to conduct experiment on the quantum cloud computing platform. The result shows that the QCGAN algorithm can effectively converge to the Nash equilibrium point after training and perform human-centered classification generation tasks.
Exploration into quantum machine learning has grown tremendously in recent years due to the ability of quantum computers to speed up classical programs. However, these efforts have yet to solve unsupervised similarity detection tasks due to the challenge of porting them to run on quantum computers. To overcome this challenge, we propose SLIQ, the first open-sourced work for resource-efficient quantum similarity detection networks, built with practical and effective quantum learning and variance-reducing algorithms.
Federated learning has emerged as a viable distributed solution to train machine learning models without the actual need to share data with the central aggregator. However, standard neural network-based federated learning models have been shown to be susceptible to data leakage from the gradients shared with the server. In this work, we introduce federated learning with variational quantum circuit model built using expressive encoding maps coupled with overparameterized ans\"atze. We show that expressive maps lead to inherent privacy against gradient inversion attacks, while overparameterization ensures model trainability. Our privacy framework centers on the complexity of solving the system of high-degree multivariate Chebyshev polynomials generated by the gradients of quantum circuit. We present compelling arguments highlighting the inherent difficulty in solving these equations, both in exact and approximate scenarios. Additionally, we delve into machine learning-based attack strategies and establish a direct connection between overparameterization in the original federated learning model and underparameterization in the attack model. Furthermore, we provide numerical scaling arguments showcasing that underparameterization of the expressive map in the attack model leads to the loss landscape being swamped with exponentially many spurious local minima points, thus making it extremely hard to realize a successful attack. This provides a strong claim, for the first time, that the nature of quantum machine learning models inherently helps prevent data leakage in federated learning.
Quantum machine learning is arguably one of the most explored applications of near-term quantum devices. Much focus has been put on notions of variational quantum machine learning where parameterized quantum circuits (PQCs) are used as learning models. These PQC models have a rich structure which suggests that they might be amenable to efficient dequantization via random Fourier features (RFF). In this work, we establish necessary and sufficient conditions under which RFF does indeed provide an efficient dequantization of variational quantum machine learning for regression. We build on these insights to make concrete suggestions for PQC architecture design, and to identify structures which are necessary for a regression problem to admit a potential quantum advantage via PQC based optimization.
Quantum neural networks (QNNs) and quantum kernels stand as prominent figures in the realm of quantum machine learning, poised to leverage the nascent capabilities of near-term quantum computers to surmount classical machine learning challenges. Nonetheless, the training efficiency challenge poses a limitation on both QNNs and quantum kernels, curbing their efficacy when applied to extensive datasets. To confront this concern, we present a unified approach: coreset selection, aimed at expediting the training of QNNs and quantum kernels by distilling a judicious subset from the original training dataset. Furthermore, we analyze the generalization error bounds of QNNs and quantum kernels when trained on such coresets, unveiling the comparable performance with those training on the complete original dataset. Through systematic numerical simulations, we illuminate the potential of coreset selection in expediting tasks encompassing synthetic data classification, identification of quantum correlations, and quantum compiling. Our work offers a useful way to improve diverse quantum machine learning models with a theoretical guarantee while reducing the training cost.
Differentiable quantum architecture search (DQAS) is a gradient-based framework to design quantum circuits automatically in the NISQ era. It was motivated by such as low fidelity of quantum hardware, low flexibility of circuit architecture, high circuit design cost, barren plateau (BP) problem, and periodicity of weights. People used it to address error mitigation, unitary decomposition, and quantum approximation optimization problems based on fixed datasets. Quantum reinforcement learning (QRL) is a part of quantum machine learning and often has various data. QRL usually uses a manually designed circuit. However, the pre-defined circuit needs more flexibility for different tasks, and the circuit design based on various datasets could become intractable in the case of a large circuit. The problem of whether DQAS can be applied to quantum deep Q-learning with various datasets is still open. The main target of this work is to discover the capability of DQAS to solve quantum deep Q-learning problems. We apply a gradient-based framework DQAS on reinforcement learning tasks and evaluate it in two different environments - cart pole and frozen lake. It contains input- and output weights, progressive search, and other new features. The experiments conclude that DQAS can design quantum circuits automatically and efficiently. The evaluation results show significant outperformance compared to the manually designed circuit. Furthermore, the performance of the automatically created circuit depends on whether the super-circuit learned well during the training process. This work is the first to show that gradient-based quantum architecture search is applicable to QRL tasks.
Variational algorithms require architectures that naturally constrain the optimisation space to run efficiently. In geometric quantum machine learning, one achieves this by encoding group structure into parameterised quantum circuits to include the symmetries of a problem as an inductive bias. However, constructing such circuits is challenging as a concrete guiding principle has yet to emerge. In this paper, we propose the use of spin networks, a form of directed tensor network invariant under a group transformation, to devise SU(2) equivariant quantum circuit ans\"atze -- circuits possessing spin rotation symmetry. By changing to the basis that block diagonalises SU(2) group action, these networks provide a natural building block for constructing parameterised equivariant quantum circuits. We prove that our construction is mathematically equivalent to other known constructions, such as those based on twirling and generalised permutations, but more direct to implement on quantum hardware. The efficacy of our constructed circuits is tested by solving the ground state problem of SU(2) symmetric Heisenberg models on the one-dimensional triangular lattice and on the Kagome lattice. Our results highlight that our equivariant circuits boost the performance of quantum variational algorithms, indicating broader applicability to other real-world problems.
We present an effective application of quantum machine learning in histopathological cancer detection. The study here emphasizes two primary applications of hybrid classical-quantum Deep Learning models. The first application is to build a classification model for histopathological cancer detection using the quantum transfer learning strategy. The second application is to test the performance of this model for various adversarial attacks. Rather than using a single transfer learning model, the hybrid classical-quantum models are tested using multiple transfer learning models, especially ResNet18, VGG-16, Inception-v3, and AlexNet as feature extractors and integrate it with several quantum circuit-based variational quantum circuits (VQC) with high expressibility. As a result, we provide a comparative analysis of classical models and hybrid classical-quantum transfer learning models for histopathological cancer detection under several adversarial attacks. We compared the performance accuracy of the classical model with the hybrid classical-quantum model using pennylane default quantum simulator. We also observed that for histopathological cancer detection under several adversarial attacks, Hybrid Classical-Quantum (HCQ) models provided better accuracy than classical image classification models.
One of the most promising applications in the era of NISQ (Noisy Intermediate-Scale Quantum) computing is quantum machine learning. Quantum machine learning offers significant quantum advantages over classical machine learning across various domains. Specifically, generative adversarial networks have been recognized for their potential utility in diverse fields such as image generation, finance, and probability distribution modeling. However, these networks necessitate solutions for inherent challenges like mode collapse. In this study, we capitalize on the concept that the estimation of mutual information between high-dimensional continuous random variables can be achieved through gradient descent using neural networks. We introduce a novel approach named InfoQGAN, which employs the Mutual Information Neural Estimator (MINE) within the framework of quantum generative adversarial networks to tackle the mode collapse issue. Furthermore, we elaborate on how this approach can be applied to a financial scenario, specifically addressing the problem of generating portfolio return distributions through dynamic asset allocation. This illustrates the potential practical applicability of InfoQGAN in real-world contexts.
We explore the interplay between symmetry and randomness in quantum information. Adopting a geometric approach, we consider states as $H$-equivalent if related by a symmetry transformation characterized by the group $H$. We then introduce the Haar measure on the homogeneous space $\mathbb{U}/H$, characterizing true randomness for $H$-equivalent systems. While this mathematical machinery is well-studied by mathematicians, it has seen limited application in quantum information: we believe our work to be the first instance of utilizing homogeneous spaces to characterize symmetry in quantum information. This is followed by a discussion of approximations of true randomness, commencing with $t$-wise independent approximations and defining $t$-designs on $\mathbb{U}/H$ and $H$-equivalent states. Transitioning further, we explore pseudorandomness, defining pseudorandom unitaries and states within homogeneous spaces. Finally, as a practical demonstration of our findings, we study the expressibility of quantum machine learning ansatze in homogeneous spaces. Our work provides a fresh perspective on the relationship between randomness and symmetry in the quantum world.