Quantum machine learning has gained attention for its potential to address computational challenges. However, whether those algorithms can effectively solve practical problems and outperform their classical counterparts, especially on current quantum hardware, remains a critical question. In this work, we propose a novel quantum machine learning method, called Parameter-Efficient Quantum Anomaly Detection (PEQAD), for practical image anomaly detection, which aims to achieve both parameter efficiency and superior accuracy compared to classical models. Emulation results indicate that PEQAD demonstrates favourable recognition capabilities compared to classical baselines, achieving an average accuracy of over 90% on benchmarks with significantly fewer trainable parameters. Theoretical analysis confirms that PEQAD has a comparable expressivity to classical counterparts while requiring only a fraction of the parameters. Furthermore, we demonstrate the first implementation of a quantum anomaly detection method for general image datasets on a superconducting quantum processor. Specifically, we achieve an accuracy of over 80% with only 16 parameters on the device, providing initial evidence of PEQAD's practical viability in the noisy intermediate-scale quantum era and highlighting its significant reduction in parameter requirements.
Harnessing the potential computational advantage of quantum computers for machine learning tasks relies on the uploading of classical data onto quantum computers through what are commonly referred to as quantum encodings. The choice of such encodings may vary substantially from one task to another, and there exist only a few cases where structure has provided insight into their design and implementation, such as symmetry in geometric quantum learning. Here, we propose the perspective that category theory offers a natural mathematical framework for analyzing encodings that respect structure inherent in datasets and learning tasks. We illustrate this with pedagogical examples, which include geometric quantum machine learning, quantum metric learning, topological data analysis, and more. Moreover, our perspective provides a language in which to ask meaningful and mathematically precise questions for the design of quantum encodings and circuits for quantum machine learning tasks.
A common trait of many machine learning models is that it is often difficult to understand and explain what caused the model to produce the given output. While the explainability of neural networks has been an active field of research in the last years, comparably little is known for quantum machine learning models. Despite a few recent works analyzing some specific aspects of explainability, as of now there is no clear big picture perspective as to what can be expected from quantum learning models in terms of explainability. In this work, we address this issue by identifying promising research avenues in this direction and lining out the expected future results. We additionally propose two explanation methods designed specifically for quantum machine learning models, as first of their kind to the best of our knowledge. Next to our pre-view of the field, we compare both existing and novel methods to explain the predictions of quantum learning models. By studying explainability in quantum machine learning, we can contribute to the sustainable development of the field, preventing trust issues in the future.
Log-based anomaly detection (LogAD) is the main component of Artificial Intelligence for IT Operations (AIOps), which can detect anomalous that occur during the system on-the-fly. Existing methods commonly extract log sequence features using classical machine learning techniques to identify whether a new sequence is an anomaly or not. However, these classical approaches often require trade-offs between efficiency and accuracy. The advent of quantum machine learning (QML) offers a promising alternative. By transforming parts of classical machine learning computations into parameterized quantum circuits (PQCs), QML can significantly reduce the number of trainable parameters while maintaining accuracy comparable to classical counterparts. In this work, we introduce a unified framework, \ourframework{}, for evaluating QML models in the context of LogAD. This framework incorporates diverse log data, integrated QML models, and comprehensive evaluation metrics. State-of-the-art methods such as DeepLog, LogAnomaly, and LogRobust, along with their quantum-transformed counterparts, are included in our framework.Beyond standard metrics like F1 score, precision, and recall, our evaluation extends to factors critical to QML performance, such as specificity, the number of circuits, circuit design, and quantum state encoding. Using \ourframework{}, we conduct extensive experiments to assess the performance of these models and their quantum counterparts, uncovering valuable insights and paving the way for future research in QML model selection and design for LogAD.
Long-term time series forecasting (LTSF) involves predicting a large number of future values of a time series based on the past values. This is an essential task in a wide range of domains including weather forecasting, stock market analysis and disease outbreak prediction. Over the decades LTSF algorithms have transitioned from statistical models to deep learning models like transformer models. Despite the complex architecture of transformer based LTSF models `Are Transformers Effective for Time Series Forecasting? (Zeng et al., 2023)' showed that simple linear models can outperform the state-of-the-art transformer based LTSF models. Recently, quantum machine learning (QML) is evolving as a domain to enhance the capabilities of classical machine learning models. In this paper we initiate the application of QML to LTSF problems by proposing QuLTSF, a simple hybrid QML model for multivariate LTSF. Through extensive experiments on a widely used weather dataset we show the advantages of QuLTSF over the state-of-the-art classical linear models, in terms of reduced mean squared error and mean absolute error.
We present an application of a single-qubit Data Re-Uploading (QRU) quantum model for particle classification in calorimetric experiments. Optimized for Noisy Intermediate-Scale Quantum (NISQ) devices, this model requires minimal qubits while delivering strong classification performance. Evaluated on a novel simulated dataset specific to particle physics, the QRU model achieves high accuracy in classifying particle types. Through a systematic exploration of model hyperparameters -- such as circuit depth, rotation gates, input normalization and the number of trainable parameters per input -- and training parameters like batch size, optimizer, loss function and learning rate, we assess their individual impacts on model accuracy and efficiency. Additionally, we apply global optimization methods, uncovering hyperparameter correlations that further enhance performance. Our results indicate that the QRU model attains significant accuracy with efficient computational costs, underscoring its potential for practical quantum machine learning applications.
Recent advancements in quantum computing (QC) and machine learning (ML) have garnered significant attention, leading to substantial efforts toward the development of quantum machine learning (QML) algorithms to address a variety of complex challenges. The design of high-performance QML models, however, requires expert-level knowledge, posing a significant barrier to the widespread adoption of QML. Key challenges include the design of data encoding mechanisms and parameterized quantum circuits, both of which critically impact the generalization capabilities of QML models. We propose a novel method that encodes quantum circuit architecture information to enable the evolution of quantum circuit designs. In this approach, the fitness function is based on the effective dimension, allowing for the optimization of quantum circuits towards higher model capacity. Through numerical simulations, we demonstrate that the proposed method is capable of discovering variational quantum circuit architectures that offer improved learning capabilities, thereby enhancing the overall performance of QML models for complex tasks.
Quantum machine learning offers a transformative approach to solving complex problems, but the inherent noise hinders its practical implementation in near-term quantum devices. This obstacle makes it difficult to understand the generalizability of quantum circuit models. Designing robust quantum machine learning models under noise requires a principled understanding of complexity and generalization, extending beyond classical capacity measures. This study investigates the generalization properties of parameterized quantum machine learning models under the influence of noise. We present a data-dependent generalization bound grounded in the quantum Fisher information matrix. We leverage statistical learning theory to relate the parameter space volumes and training sizes to estimate the generalization capability of the trained model. We provide a structured characterization of complexity in quantum models by integrating local parameter neighborhoods and effective dimensions defined through quantum Fisher information matrix eigenvalues. We also analyze the tightness of the bound and discuss the tradeoff between model expressiveness and generalization performance.
Quantum machine learning is considered one of the flagship applications of quantum computers, where variational quantum circuits could be the leading paradigm both in the near-term quantum devices and the early fault-tolerant quantum computers. However, it is not clear how to identify the regime of quantum advantages from these circuits, and there is no explicit theory to guide the practical design of variational ansatze to achieve better performance. We address these challenges with the stabilizer bootstrap, a method that uses stabilizer-based techniques to optimize quantum neural networks before their quantum execution, together with theoretical proofs and high-performance computing with 10000 qubits or random datasets up to 1000 data. We find that, in a general setup of variational ansatze, the possibility of improvements from the stabilizer bootstrap depends on the structure of the observables and the size of the datasets. The results reveal that configurations exhibit two distinct behaviors: some maintain a constant probability of circuit improvement, while others show an exponential decay in improvement probability as qubit numbers increase. These patterns are termed strong stabilizer enhancement and weak stabilizer enhancement, respectively, with most situations falling in between. Our work seamlessly bridges techniques from fault-tolerant quantum computing with applications of variational quantum algorithms. Not only does it offer practical insights for designing variational circuits tailored to large-scale machine learning challenges, but it also maps out a clear trajectory for defining the boundaries of feasible and practical quantum advantages.
Kernel methods map data into high-dimensional spaces, enabling linear algorithms to learn nonlinear functions without explicitly storing the feature vectors. Quantum kernel methods promise efficient learning by encoding feature maps into exponentially large Hilbert spaces inherent in quantum systems. In this work, we implement quantum kernels on a 10-qubit star-topology register in a nuclear magnetic resonance (NMR) platform. We experimentally encode classical data in the evolution of multiple quantum coherence orders using data-dependent unitary transformations and then demonstrate one-dimensional regression and two-dimensional classification tasks. By extending the register to a double-layered star configuration, we propose an extended quantum kernel to handle non-parametrized operator inputs. Specifically, we set up a kernel for the classification of entangling and non-entangling operations and then validate this kernel first numerically by computing it on a double-layered star register and then experimentally by computing it on a three-qubit NMR register. Our results show that this kernel exhibits an ability to generalize well over unseen data. These results confirm that quantum kernels possess strong capabilities in classical as well as quantum machine learning tasks.
Understanding the properties of excited states of complex molecules is crucial for many chemical and physical processes. Calculating these properties is often significantly more resource-intensive than calculating their ground state counterparts. We present a quantum machine learning model that predicts excited-state properties from the molecular ground state for different geometric configurations. The model comprises a symmetry-invariant quantum neural network and a conventional neural network and is able to provide accurate predictions with only a few training data points. The proposed procedure is fully NISQ compatible. This is achieved by using a quantum circuit that requires a number of parameters linearly proportional to the number of molecular orbitals, along with a parameterized measurement observable, thereby reducing the number of necessary measurements. We benchmark the algorithm on three different molecules with three different system sizes: $H_2$ with four orbitals, LiH with five orbitals, and $H_4$ with six orbitals. For these molecules, we predict the excited state transition energies and transition dipole moments. We show that, in many cases, the procedure is able to outperform various classical models (support vector machines, Gaussian processes, and neural networks) that rely solely on classical features, by up to two orders of magnitude in the test mean squared error.
Since classical machine learning has become a powerful tool for developing data-driven algorithms, quantum machine learning is expected to similarly impact the development of quantum algorithms. The literature reflects a mutually beneficial relationship between machine learning and quantum computing, where progress in one field frequently drives improvements in the other. Motivated by the fertile connection between machine learning and quantum computing enabled by parameterized quantum circuits, we use a resource-efficient and scalable Single-Qubit Quantum Neural Network (SQQNN) for both regression and classification tasks. The SQQNN leverages parameterized single-qubit unitary operators and quantum measurements to achieve efficient learning. To train the model, we use gradient descent for regression tasks. For classification, we introduce a novel training method inspired by the Taylor series, which can efficiently find a global minimum in a single step. This approach significantly accelerates training compared to iterative methods. Evaluated across various applications, the SQQNN exhibits virtually error-free and strong performance in regression and classification tasks, including the MNIST dataset. These results demonstrate the versatility, scalability, and suitability of the SQQNN for deployment on near-term quantum devices.
Fidelity quantum kernels have shown promise in classification tasks, particularly when a group structure in the data can be identified and exploited through a covariant feature map. In fact, there exist classification problems on which covariant kernels provide a provable advantage, thus establishing a separation between quantum and classical learners. However, their practical application poses two challenges: on one side, the group structure may be unknown and approximate in real-world data, and on the other side, scaling to the `utility' regime (above 100 qubits) is affected by exponential concentration. In this work, we address said challenges by applying fidelity kernels to real-world data with unknown structure, related to the scheduling of a fleet of electric vehicles, and to synthetic data generated from the union of subspaces, which is then close to many relevant real-world datasets. Furthermore, we propose a novel error mitigation strategy specifically tailored for fidelity kernels, called Bit Flip Tolerance (BFT), to alleviate the exponential concentration in our utility-scale experiments. Our multiclass classification reaches accuracies comparable to classical SVCs up to 156 qubits, thus constituting the largest experimental demonstration of quantum machine learning on IBM devices to date. For the real-world data experiments, the effect of the proposed BFT becomes manifest on 40+ qubits, where mitigated accuracies reach 80%, in line with classical, compared to 33% without BFT. Through the union-of-subspace synthetic dataset with 156 qubits, we demonstrate a mitigated accuracy of 80%, compared to 83% of classical models, and 37% of unmitigated quantum, using a test set of limited size.
Software defect prediction is a critical aspect of software quality assurance, as it enables early identification and mitigation of defects, thereby reducing the cost and impact of software failures. Over the past few years, quantum computing has risen as an exciting technology capable of transforming multiple domains; Quantum Machine Learning (QML) is one of them. QML algorithms harness the power of quantum computing to solve complex problems with better efficiency and effectiveness than their classical counterparts. However, research into its application in software engineering to predict software defects still needs to be explored. In this study, we worked to fill the research gap by comparing the performance of three QML and five classical machine learning (CML) algorithms on the 20 software defect datasets. Our investigation reports the comparative scenarios of QML vs. CML algorithms and identifies the better-performing and consistent algorithms to predict software defects. We also highlight the challenges and future directions of employing QML algorithms in real software defect datasets based on the experience we faced while performing this investigation. The findings of this study can help practitioners and researchers further progress in this research domain by making software systems reliable and bug-free.
Predicting loan eligibility with high accuracy remains a significant challenge in the finance sector. Accurate predictions enable financial institutions to make informed decisions, mitigate risks, and effectively adapt services to meet customer needs. However, the complexity and the high-dimensional nature of financial data have always posed significant challenges to achieving this level of precision. To overcome these issues, we propose a novel approach that employs Quantum Machine Learning (QML) for Loan Eligibility Prediction using Quantum Neural Networks (LEP-QNN).Our innovative approach achieves an accuracy of 98% in predicting loan eligibility from a single, comprehensive dataset. This performance boost is attributed to the strategic implementation of a dropout mechanism within the quantum circuit, aimed at minimizing overfitting and thereby improving the model's predictive reliability. In addition, our exploration of various optimizers leads to identifying the most efficient setup for our LEP-QNN framework, optimizing its performance. We also rigorously evaluate the resilience of LEP-QNN under different quantum noise scenarios, ensuring its robustness and dependability for quantum computing environments. This research showcases the potential of QML in financial predictions and establishes a foundational guide for advancing QML technologies, marking a step towards developing advanced, quantum-driven financial decision-making tools.
In this study, we propose a novel architecture, the Quantum Pointwise Convolution, which incorporates pointwise convolution within a quantum neural network framework. Our approach leverages the strengths of pointwise convolution to efficiently integrate information across feature channels while adjusting channel outputs. By using quantum circuits, we map data to a higher-dimensional space, capturing more complex feature relationships. To address the current limitations of quantum machine learning in the Noisy Intermediate-Scale Quantum (NISQ) era, we implement several design optimizations. These include amplitude encoding for data embedding, allowing more information to be processed with fewer qubits, and a weight-sharing mechanism that accelerates quantum pointwise convolution operations, reducing the need to retrain for each input pixels. In our experiments, we applied the quantum pointwise convolution layer to classification tasks on the FashionMNIST and CIFAR10 datasets, where our model demonstrated competitive performance compared to its classical counterpart. Furthermore, these optimizations not only improve the efficiency of the quantum pointwise convolutional layer but also make it more readily deployable in various CNN-based or deep learning models, broadening its potential applications across different architectures.
The integration of algorithms from quantum information with neural networks has enabled unprecedented advancements in various domains. Nonetheless, the application of quantum machine learning algorithms for image classification predominantly relies on traditional architectures such as variational quantum circuits. The performance of these models is closely tied to the scale of their parameters, with the substantial demand for parameters potentially leading to limitations in computational resources and a significant increase in computation time. In this paper, we introduce a Lean Classical-Quantum Hybrid Neural Network (LCQHNN), which achieves efficient classification performance with only four layers of variational circuits, thereby substantially reducing computational costs. Our experiments demonstrate that LCQHNN achieves 100\%, 99.02\%, and 85.55\% classification accuracy on MNIST, FashionMNIST, and CIFAR-10 datasets. Under the same parameter conditions, the convergence speed of this method is also faster than that of traditional models. Furthermore, through visualization studies, it is found that the model effectively captures key data features during training and establishes a clear association between these features and their corresponding categories. This study confirms that the employment of quantum algorithms enhances the model's ability to handle complex classification problems.
Learning quantum states is a crucial task for realizing quantum information technology. Recently, neural approaches have emerged as promising methods for learning quantum states. We propose a meta-learning model that utilizes reinforcement learning (RL) to optimize the process of learning quantum states. To improve the data efficiency of the RL, we introduce an action repetition strategy inspired by curriculum learning. The RL agent significantly improves the sample efficiency of learning random quantum states, and achieves infidelity scaling close to the Heisenberg limit. We also show that the RL agent trained using 3-qubit states can generalize to learning up to 5-qubit states. These results highlight the utility of RL-driven meta-learning to enhance the efficiency and generalizability of learning quantum states. Our approach can be applied to improve quantum control, quantum optimization, and quantum machine learning.
Parkinsons disease, the fastest growing neurodegenerative disorder globally, has seen a 50 percent increase in cases within just two years. As speech, memory, and motor symptoms worsen over time, early diagnosis is crucial for preserving patients quality of life. While machine-learning-based detection has shown promise, relying on a single feature for classification can be error-prone due to the variability of symptoms between patients. To address this limitation we utilized the mPower database, which includes 150,000 samples across four key biomarkers: voice, gait, tapping, and demographic data. From these measurements, we extracted 64 features and trained a baseline Random Forest model to select the features above the 80th percentile. For classification, we designed a simulatable quantum support vector machine (qSVM) that detects high-dimensional patterns, leveraging recent advancements in quantum machine learning. With a novel, simulatable architecture that can be run on standard hardware rather than resource-intensive quantum computers, our model achieves an accuracy of 90 percent and an AUC of 0.98, surpassing benchmark models. By utilizing an innovative classification framework built on a diverse set of features, our model offers a pathway for accessible global Parkinsons screening.
Quantum machine learning (QML) has surged as a prominent area of research with the objective to go beyond the capabilities of classical machine learning models. A critical aspect of any learning task is the process of data embedding, which directly impacts model performance. Poorly designed data-embedding strategies can significantly impact the success of a learning task. Despite its importance, rigorous analyses of data-embedding effects are limited, leaving many cases without effective assessment methods. In this work, we introduce a metric for binary classification tasks, the class margin, by merging the concepts of average randomness and classification margin. This metric analytically connects data-induced randomness with classification accuracy for a given data-embedding map. We benchmark a range of data-embedding strategies through class margin, demonstrating that data-induced randomness imposes a limit on classification performance. We expect this work to provide a new approach to evaluate QML models by their data-embedding processes, addressing gaps left by existing analytical tools.