Quantum convolutional neural networks (QCNNs) represent a promising approach in quantum machine learning, paving new directions for both quantum and classical data analysis. This approach is particularly attractive due to the absence of the barren plateau problem, a fundamental challenge in training quantum neural networks (QNNs), and its feasibility. However, a limitation arises when applying QCNNs to classical data. The network architecture is most natural when the number of input qubits is a power of two, as this number is reduced by a factor of two in each pooling layer. The number of input qubits determines the dimensions (i.e. the number of features) of the input data that can be processed, restricting the applicability of QCNN algorithms to real-world data. To address this issue, we propose a QCNN architecture capable of handling arbitrary input data dimensions while optimizing the allocation of quantum resources such as ancillary qubits and quantum gates. This optimization is not only important for minimizing computational resources, but also essential in noisy intermediate-scale quantum (NISQ) computing, as the size of the quantum circuits that can be executed reliably is limited. Through numerical simulations, we benchmarked the classification performance of various QCNN architectures when handling arbitrary input data dimensions on the MNIST and Breast Cancer datasets. The results validate that the proposed QCNN architecture achieves excellent classification performance while utilizing a minimal resource overhead, providing an optimal solution when reliable quantum computation is constrained by noise and imperfections.
Financial crimes fast proliferation and sophistication require novel approaches that provide robust and effective solutions. This paper explores the potential of quantum algorithms in combating financial crimes. It highlights the advantages of quantum computing by examining traditional and Machine Learning (ML) techniques alongside quantum approaches. The study showcases advanced methodologies such as Quantum Machine Learning (QML) and Quantum Artificial Intelligence (QAI) as powerful solutions for detecting and preventing financial crimes, including money laundering, financial crime detection, cryptocurrency attacks, and market manipulation. These quantum approaches leverage the inherent computational capabilities of quantum computers to overcome limitations faced by classical methods. Furthermore, the paper illustrates how quantum computing can support enhanced financial risk management analysis. Financial institutions can improve their ability to identify and mitigate risks, leading to more robust risk management strategies by exploiting the quantum advantage. This research underscores the transformative impact of quantum algorithms on financial risk management. By embracing quantum technologies, organisations can enhance their capabilities to combat evolving threats and ensure the integrity and stability of financial systems.
The increasing capabilities of Machine Learning (ML) models go hand in hand with an immense amount of data and computational power required for training. Therefore, training is usually outsourced into HPC facilities, where we have started to experience limits in scaling conventional HPC hardware, as theorized by Moore's law. Despite heavy parallelization and optimization efforts, current state-of-the-art ML models require weeks for training, which is associated with an enormous $CO_2$ footprint. Quantum Computing, and specifically Quantum Machine Learning (QML), can offer significant theoretical speed-ups and enhanced expressive power. However, training QML models requires tuning various hyperparameters, which is a nontrivial task and suboptimal choices can highly affect the trainability and performance of the models. In this study, we identify the most impactful hyperparameters and collect data about the performance of QML models. We compare different configurations and provide researchers with performance data and concrete suggestions for hyperparameter selection.
Variational quantum algorithms are gaining attention as an early application of Noisy Intermediate-Scale Quantum (NISQ) devices. One of the main problems of variational methods lies in the phenomenon of Barren Plateaus, present in the optimization of variational parameters. Adding geometric inductive bias to the quantum models has been proposed as a potential solution to mitigate this problem, leading to a new field called Geometric Quantum Machine Learning. In this work, an equivariant architecture for variational quantum classifiers is introduced to create a label-invariant model for image classification with $C_4$ rotational label symmetry. The equivariant circuit is benchmarked against two different architectures, and it is experimentally observed that the geometric approach boosts the model's performance. Finally, a classical equivariant convolution operation is proposed to extend the quantum model for the processing of larger images, employing the resources available in NISQ devices.
In this study, we explore the innovative domain of Quantum Federated Learning (QFL) as a framework for training Quantum Machine Learning (QML) models via distributed networks. Conventional machine learning models frequently grapple with issues about data privacy and the exposure of sensitive information. Our proposed Federated Quantum Neural Network (FedQNN) framework emerges as a cutting-edge solution, integrating the singular characteristics of QML with the principles of classical federated learning. This work thoroughly investigates QFL, underscoring its capability to secure data handling in a distributed environment and facilitate cooperative learning without direct data sharing. Our research corroborates the concept through experiments across varied datasets, including genomics and healthcare, thereby validating the versatility and efficacy of our FedQNN framework. The results consistently exceed 86% accuracy across three distinct datasets, proving its suitability for conducting various QML tasks. Our research not only identifies the limitations of classical paradigms but also presents a novel framework to propel the field of QML into a new era of secure and collaborative innovation.
Benchmarking models via classical simulations is one of the main ways to judge ideas in quantum machine learning before noise-free hardware is available. However, the huge impact of the experimental design on the results, the small scales within reach today, as well as narratives influenced by the commercialisation of quantum technologies make it difficult to gain robust insights. To facilitate better decision-making we develop an open-source package based on the PennyLane software framework and use it to conduct a large-scale study that systematically tests 12 popular quantum machine learning models on 6 binary classification tasks used to create 160 individual datasets. We find that overall, out-of-the-box classical machine learning models outperform the quantum classifiers. Moreover, removing entanglement from a quantum model often results in as good or better performance, suggesting that "quantumness" may not be the crucial ingredient for the small learning tasks considered here. Our benchmarks also unlock investigations beyond simplistic leaderboard comparisons, and we identify five important questions for quantum model design that follow from our results.
Machine learning, particularly deep neural networks, has been widely used in high-energy physics, demonstrating remarkable results in various applications. Furthermore, the extension of machine learning to quantum computers has given rise to the emerging field of quantum machine learning. In this paper, we propose the Quantum Complete Graph Neural Network (QCGNN), which is a variational quantum algorithm based model designed for learning on complete graphs. QCGNN with deep parametrized operators offers a polynomial speedup over its classical and quantum counterparts, leveraging the property of quantum parallelism. We investigate the application of QCGNN with the challenging task of jet discrimination, where the jets are represented as complete graphs. Additionally, we conduct a comparative analysis with classical models to establish a performance benchmark.
Considering the noise level limit, one crucial aspect for quantum machine learning is to design a high-performing variational quantum circuit architecture with small number of quantum gates. As the classical neural architecture search (NAS), quantum architecture search methods (QAS) employ methods like reinforcement learning, evolutionary algorithms and supernet optimiza-tion to improve the search efficiency. In this paper, we propose a novel qubit-wise architec-ture search (QWAS) method, which progres-sively search one-qubit configuration per stage, and combine with Monte Carlo Tree Search al-gorithm to find good quantum architectures by partitioning the search space into several good and bad subregions. The numerical experimental results indicate that our proposed method can balance the exploration and exploitation of cir-cuit performance and size in some real-world tasks, such as MNIST, Fashion and MOSI. As far as we know, QWAS achieves the state-of-art re-sults of all tasks in the terms of accuracy and circuit size.
Quantum combs play a vital role in characterizing and transforming quantum processes, with wide-ranging applications in quantum information processing. However, obtaining the explicit quantum circuit for the desired quantum comb remains a challenging problem. We propose PQComb, a novel framework that employs parameterized quantum circuits (PQCs) or quantum neural networks to harness the full potential of quantum combs for diverse quantum process transformation tasks. This method is well-suited for near-term quantum devices and can be applied to various tasks in quantum machine learning. As a notable application, we present two streamlined protocols for the time-reversal simulation of unknown qubit unitary evolutions, reducing the ancilla qubit overhead from six to three compared to the previous best-known method. We also extend PQComb to solve the problems of qutrit unitary transformation and channel discrimination. Furthermore, we demonstrate the hardware efficiency and robustness of our qubit unitary inversion protocol under realistic noise simulations of IBM-Q superconducting quantum hardware, yielding a significant improvement in average similarity over the previous protocol under practical regimes. PQComb's versatility and potential for broader applications in quantum machine learning pave the way for more efficient and practical solutions to complex quantum tasks.
Attention mechanisms have revolutionized natural language processing. Combining them with quantum computing aims to further advance this technology. This paper introduces a novel Quantum Mixed-State Self-Attention Network (QMSAN) for natural language processing tasks. Our model leverages quantum computing principles to enhance the effectiveness of self-attention mechanisms. QMSAN uses a quantum attention mechanism based on mixed state, allowing for direct similarity estimation between queries and keys in the quantum domain. This approach leads to more effective attention coefficient calculations. We also propose an innovative quantum positional encoding scheme, implemented through fixed quantum gates within the circuit, improving the model's ability to capture sequence information without additional qubit resources. In numerical experiments of text classification tasks on public datasets, QMSAN outperforms Quantum Self-Attention Neural Network (QSANN). Furthermore, we demonstrate QMSAN's robustness in different quantum noise environments, highlighting its potential for near-term quantum devices.
The potential impact of quantum machine learning algorithms on industrial applications remains an exciting open question. Conventional methods for encoding classical data into quantum computers are not only too costly for a potential quantum advantage in the algorithms but also severely limit the scale of feasible experiments on current hardware. Therefore, recent works, despite claiming the near-term suitability of their algorithms, do not provide experimental benchmarking on standard machine learning datasets. We attempt to solve the data encoding problem by improving a recently proposed variational algorithm [1] that approximately prepares the encoded data, using asymptotically shallow circuits that fit the native gate set and topology of currently available quantum computers. We apply the improved algorithm to encode the Fashion-MNIST dataset [2], which can be directly used in future empirical studies of quantum machine learning algorithms. We deploy simple quantum variational classifiers trained on the encoded dataset on a current quantum computer ibmq-kolkata [3] and achieve moderate accuracies, providing a proof of concept for the near-term usability of our data encoding method.
Quantum Machine Learning (QML) has surfaced as a pioneering framework addressing sequential control tasks and time-series modeling. It has demonstrated empirical quantum advantages notably within domains such as Reinforcement Learning (RL) and time-series prediction. A significant advancement lies in Quantum Recurrent Neural Networks (QRNNs), specifically tailored for memory-intensive tasks encompassing partially observable environments and non-linear time-series prediction. Nevertheless, QRNN-based models encounter challenges, notably prolonged training duration stemming from the necessity to compute quantum gradients using backpropagation-through-time (BPTT). This predicament exacerbates when executing the complete model on quantum devices, primarily due to the substantial demand for circuit evaluation arising from the parameter-shift rule. This paper introduces the Quantum Fast Weight Programmers (QFWP) as a solution to the temporal or sequential learning challenge. The QFWP leverages a classical neural network (referred to as the 'slow programmer') functioning as a quantum programmer to swiftly modify the parameters of a variational quantum circuit (termed the 'fast programmer'). Instead of completely overwriting the fast programmer at each time-step, the slow programmer generates parameter changes or updates for the quantum circuit parameters. This approach enables the fast programmer to incorporate past observations or information. Notably, the proposed QFWP model achieves learning of temporal dependencies without necessitating the use of quantum recurrent neural networks. Numerical simulations conducted in this study showcase the efficacy of the proposed QFWP model in both time-series prediction and RL tasks. The model exhibits performance levels either comparable to or surpassing those achieved by QLSTM-based models.
With the advent of the Post-Moore era, the scientific community is faced with the challenge of addressing the demands of current data-intensive machine learning applications, which are the cornerstone of urgent analytics in distributed computing. Quantum machine learning could be a solution for the increasing demand of urgent analytics, providing potential theoretical speedups and increased space efficiency. However, challenges such as (1) the encoding of data from the classical to the quantum domain, (2) hyperparameter tuning, and (3) the integration of quantum hardware into a distributed computing continuum limit the adoption of quantum machine learning for urgent analytics. In this work, we investigate the use of Edge computing for the integration of quantum machine learning into a distributed computing continuum, identifying the main challenges and possible solutions. Furthermore, exploring the data encoding and hyperparameter tuning challenges, we present preliminary results for quantum machine learning analytics on an IoT scenario.
This paper provides an introduction to quantum machine learning, exploring the potential benefits of using quantum computing principles and algorithms that may improve upon classical machine learning approaches. Quantum computing utilizes particles governed by quantum mechanics for computational purposes, leveraging properties like superposition and entanglement for information representation and manipulation. Quantum machine learning applies these principles to enhance classical machine learning models, potentially reducing network size and training time on quantum hardware. The paper covers basic quantum mechanics principles, including superposition, phase space, and entanglement, and introduces the concept of quantum gates that exploit these properties. It also reviews classical deep learning concepts, such as artificial neural networks, gradient descent, and backpropagation, before delving into trainable quantum circuits as neural networks. An example problem demonstrates the potential advantages of quantum neural networks, and the appendices provide detailed derivations. The paper aims to help researchers new to quantum mechanics and machine learning develop their expertise more efficiently.
Quantum Neural Networks (QNNs) are a popular approach in Quantum Machine Learning. We analyze this frequency spectrum using the Minkowski sum for sets and the set of differences, which makes it particularly easy to express and calculate the frequency spectrum algebraically, and prove different maximality results for a large class of models. Furthermore, we prove that under some mild conditions there exists a bijection between classes of models with the same area $A:=R\cdot L$ that preserves the frequency spectrum, where $R$ denotes the number of qubits and $L$ the number of layers, which we consequently call spectral invariance under area-preserving transformations. With this we explain the symmetry in $R$ and $L$ in the results often observed in the literature and show that the maximal frequency spectrum depends only on the area $A=RL$ and not on the individual values of $R$ and $L$. Moreover, we collect and extend existing results and specify the maximum possible frequency spectrum of a QNN with arbitrarily many layers as a function of the spectrum of its generators. In the case of arbitrary dimensional generators, where our two introduces notions of maximality differ, we extend existing results based on the so-called Golomb ruler and introduce a second novel approach based on a variation of the turnpike problem, which we call the relaxed turnpike problem.
Quantum embedding with transformers is a novel and promising architecture for quantum machine learning to deliver exceptional capability on near-term devices or simulators. The research incorporated a vision transformer (ViT) to advance quantum significantly embedding ability and results for a single qubit classifier with around 3 percent in the median F1 score on the BirdCLEF-2021, a challenging high-dimensional dataset. The study showcases and analyzes empirical evidence that our transformer-based architecture is a highly versatile and practical approach to modern quantum machine learning problems.
Cloud hosting of quantum machine learning (QML) models exposes them to a range of vulnerabilities, the most significant of which is the model stealing attack. In this study, we assess the efficacy of such attacks in the realm of quantum computing. We conducted comprehensive experiments on various datasets with multiple QML model architectures. Our findings revealed that model stealing attacks can produce clone models achieving up to $0.9\times$ and $0.99\times$ clone test accuracy when trained using Top-$1$ and Top-$k$ labels, respectively ($k:$ num\_classes). To defend against these attacks, we leverage the unique properties of current noisy hardware and perturb the victim model outputs and hinder the attacker's training process. In particular, we propose: 1) hardware variation-induced perturbation (HVIP) and 2) hardware and architecture variation-induced perturbation (HAVIP). Although noise and architectural variability can provide up to $\sim16\%$ output obfuscation, our comprehensive analysis revealed that models cloned under noisy conditions tend to be resilient, suffering little to no performance degradation due to such obfuscations. Despite limited success with our defense techniques, this outcome has led to an important discovery: QML models trained on noisy hardwares are naturally resistant to perturbation or obfuscation-based defenses or attacks.
Quantum machine learning provides a fundamentally different approach to analyzing data. However, many interesting datasets are too complex for currently available quantum computers. Present quantum machine learning applications usually diminish this complexity by reducing the dimensionality of the data, e.g., via auto-encoders, before passing it through the quantum models. Here, we design a classical-quantum paradigm that unifies the dimensionality reduction task with a quantum classification model into a single architecture: the guided quantum compression model. We exemplify how this architecture outperforms conventional quantum machine learning approaches on a challenging binary classification problem: identifying the Higgs boson in proton-proton collisions at the LHC. Furthermore, the guided quantum compression model shows better performance compared to the deep learning benchmark when using solely the kinematic variables in our dataset.
Recent theoretical results in quantum machine learning have demonstrated a general trade-off between the expressive power of quantum neural networks (QNNs) and their trainability; as a corollary of these results, practical exponential separations in expressive power over classical machine learning models are believed to be infeasible as such QNNs take a time to train that is exponential in the model size. We here circumvent these negative results by constructing a hierarchy of efficiently trainable QNNs that exhibit unconditionally provable, polynomial memory separations of arbitrary constant degree over classical neural networks -- including state-of-the-art models, such as Transformers -- in performing a classical sequence modeling task. This construction is also computationally efficient, as each unit cell of the introduced class of QNNs only has constant gate complexity. We show that contextuality -- informally, a quantitative notion of semantic ambiguity -- is the source of the expressivity separation, suggesting that other learning tasks with this property may be a natural setting for the use of quantum learning algorithms.
Quantum Machine Learning (QML) has emerged as a promising field of research, aiming to leverage the capabilities of quantum computing to enhance existing machine learning methodologies. Recent studies have revealed that, like their classical counterparts, QML models based on Parametrized Quantum Circuits (PQCs) are also vulnerable to adversarial attacks. Moreover, the existence of Universal Adversarial Perturbations (UAPs) in the quantum domain has been demonstrated theoretically in the context of quantum classifiers. In this work, we introduce QuGAP: a novel framework for generating UAPs for quantum classifiers. We conceptualize the notion of additive UAPs for PQC-based classifiers and theoretically demonstrate their existence. We then utilize generative models (QuGAP-A) to craft additive UAPs and experimentally show that quantum classifiers are susceptible to such attacks. Moreover, we formulate a new method for generating unitary UAPs (QuGAP-U) using quantum generative models and a novel loss function based on fidelity constraints. We evaluate the performance of the proposed framework and show that our method achieves state-of-the-art misclassification rates, while maintaining high fidelity between legitimate and adversarial samples.