Quantum machine learning

Plastic particles and fluorescent brightener co-modify Chlorella pyrenoidosa photosynthesis and a machine learning approach predict algae growth

Global release of plastics exerts various impacts on the ecological cycle, particularly on primary photosynthesis, while the impacts of plastic additives are unknown. As a carrier of fluorescent brightener, plastic particles co-modify Chlorella pyrenoidosa (C. pyrenoidosa) growth and its photosynthetic parameters. In general, adding to the oxidative damage induced by polystyrene, fluorescent brightener-doped polystyrene produces stronger visible light and the amount of negative charge is more likely to cause photodamage in C. pyrenoidosa leading to higher energy dissipation through conditioning than in the control group with a date of ETR (II) inhibition rate of 33 %, Fv/Fm inhibition rate of 8.3 % and Pm inhibition rate of 48.8 %. To elucidate the ecological effect of fluorescent brightener doping in plastic particles, a machine learning method is performed to establish a Gradient Boosting Machine model for predicting the impact of environmental factors on algal growth. Upon validation, the model achieved an average fitting degree of 88 %. Relative concentration of plastic particles and algae claimed the most significant factor by interpretability analysis of the machine learning. Additionally, both Gradient Boosting Machine prediction and experimental results indicate a matching result that plastic additives have an inhibitive effect on algal growth.

Inferring Physical Properties of Symmetric States from the Fewest Copies

Learning physical properties of high-dimensional states is crucial for developing quantum technologies but usually consumes an exceedingly large number of samples which are difficult to afford in practice. In this Letter, we use the methodology of quantum metrology to tackle this difficulty, proposing a strategy built upon entangled measurements for dramatically reducing sample complexity. The strategy, whose characteristic feature is symmetrization of observables, is powered by the exploration of symmetric structures of states which are ubiquitous in physics. It is provably optimal under some natural assumption, efficiently implementable in a variety of contexts, and capable of being incorporated into existing methods as a basic building block. We apply the strategy to different scenarios motivated by experiments, demonstrating exponential reductions in sample complexity.

Benchmarking quantum versions of the kNN algorithm with a metric based on amplitude-encoded features

This work introduces a quantum subroutine for computing the distance between two patterns and integrates it into two quantum versions of the kNN classifier algorithm: one proposed by Schuld et al. and the other proposed by Quezada et al. Notably, our proposed subroutine is tailored to be memory-efficient, requiring fewer qubits for data encoding, while maintaining the overall complexity for both QkNN versions. This research focuses on comparing the performance of the two quantum kNN algorithms using the original Hamming distance with qubit-encoded features and our proposed subroutine, which computes the distance using amplitude-encoded features. Results obtained from analyzing thirteen different datasets (Iris, Seeds, Raisin, Mine, Cryotherapy, Data Bank Authentication, Caesarian, Wine, Haberman, Transfusion, Immunotherapy, Balance Scale, and Glass) show that both algorithms benefit from the proposed subroutine, achieving at least a 50% reduction in the number of required qubits, while maintaining a similar overall performance. For Shuld's algorithm, the performance improved in Cryotherapy (68.89% accuracy compared to 64.44%) and Balance Scale (85.33% F1 score compared to 78.89%), was worse in Iris (86.0% accuracy compared to 95.33%) and Raisin (77.67% accuracy compared to 81.56%), and remained similar in the remaining nine datasets. While for Quezada's algorithm, the performance improved in Caesarian (68.89% F1 score compared to 58.22%), Haberman (69.94% F1 score compared to 62.31%) and Immunotherapy (76.88% F1 score compared to 69.67%), was worse in Iris (82.67% accuracy compared to 95.33%), Balance Scale (77.97% F1 score compared to 69.21%) and Glass (40.04% F1 score compared to 28.79%), and remained similar in the remaining seven datasets.

Shadows of quantum machine learning

Quantum machine learning is often highlighted as one of the most promising practical applications for which quantum computers could provide a computational advantage. However, a major obstacle to the widespread use of quantum machine learning models in practice is that these models, even once trained, still require access to a quantum computer in order to be evaluated on new data. To solve this issue, we introduce a class of quantum models where quantum resources are only required during training, while the deployment of the trained model is classical. Specifically, the training phase of our models ends with the generation of a 'shadow model' from which the classical deployment becomes possible. We prove that: (i) this class of models is universal for classically-deployed quantum machine learning; (ii) it does have restricted learning capacities compared to 'fully quantum' models, but nonetheless (iii) it achieves a provable learning advantage over fully classical learners, contingent on widely believed assumptions in complexity theory. These results provide compelling evidence that quantum machine learning can confer learning advantages across a substantially broader range of scenarios, where quantum computers are exclusively employed during the training phase. By enabling classical deployment, our approach facilitates the implementation of quantum machine learning models in various practical contexts.

Visualising quantum innovation: A regional case study

At the beginning of this century, the advent of a second generation of 'quantum technologies' was announced together with its revolutionary potential to change existing information technologies. Despite the rapidly increasing paid to quantum technological development, there has been little attention paid to the specific characteristics or relationships within emerging quantum ecosystems. The aim of this study is to visualize the innovation structures and relationships that are emerging to shape these technological developments. As these structures typically depend on specific regional features, we have specifically focused on the Spanish case, as it is potentially indicative of the differences between European innovation models and other regional patterns. This objective was achieved by researching the funding network of the ecosystem, collected from a systematic review of various official sources and relevant previous literature. The resulting dataset was framed using the Innovation Ecosystem model and broken down through network analysis theory, as well as characterized through descriptive statistics. This framework identified the significant role that projects play in European scientific and technological innovation, which work as hubs to concentrate resources and incentive cooperation between actors. This is relevant because current work on quantum technologies neglects their importance, as their analysis focuses on the quantity of institutions rather than their relations. Moreover, this paper points out the prominence of public funding to drive quantum innovation, largely stemming from the European Commission. This is another key mechanism that is missed by the existing literature. Finally, it also sheds light on the recipients of this funding, who are mostly research centres. These results allow us to conceptualize the Spanish quantum ecosystem and offer the opportunity for comparative studies with other quantum technologies ecosystems.

On the quantum circuit implementation of modus ponens

The process of inference reflects the structure of propositions with assigned truth values, either true or false. Modus ponens is a fundamental form of inference that involves affirming the antecedent to affirm the consequent. Inspired by the quantum computer, the superposition of true and false is used for the parallel processing. In this work, we propose a quantum version of modus ponens. Additionally, we introduce two generations of quantum modus ponens: quantum modus ponens inference chain and multidimensional quantum modus ponens. Finally, a simple implementation of quantum modus ponens on the OriginQ quantum computing cloud platform is demonstrated.

Exponential concentration in quantum kernel methods

Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model's parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from quantum hardware. In this work we study the performance of quantum kernel models from the perspective of the resources needed to accurately estimate kernel values. We show that, under certain conditions, values of quantum kernels over different input data can be exponentially concentrated (in the number of qubits) towards some fixed value. Thus on training with a polynomial number of measurements, one ends up with a trivial model where the predictions on unseen inputs are independent of the input data. We identify four sources that can lead to concentration including expressivity of data embedding, global measurements, entanglement and noise. For each source, an associated concentration bound of quantum kernels is analytically derived. Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration. Our results are verified through numerical simulations for several QML tasks. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods.

A Vision for the Future of Multiscale Modeling

The rise of modern computer science enabled physical chemistry to make enormous progresses in understanding and harnessing natural and artificial phenomena. Nevertheless, despite the advances achieved over past decades, computational resources are still insufficient to thoroughly simulate extended systems from first principles. Indeed, countless biological, catalytic and photophysical processes require ab initio treatments to be properly described, but the breadth of length and time scales involved makes it practically unfeasible. A way to address these issues is to couple theories and algorithms working at different scales by dividing the system into domains treated at different levels of approximation, ranging from quantum mechanics to classical molecular dynamics, even including continuum electrodynamics. This approach is known as multiscale modeling and its use over the past 60 years has led to remarkable results. Considering the rapid advances in theory, algorithm design, and computing power, we believe multiscale modeling will massively grow into a dominant research methodology in the forthcoming years. Hereby we describe the main approaches developed within its realm, highlighting their achievements and current drawbacks, eventually proposing a plausible direction for future developments considering also the emergence of new computational techniques such as machine learning and quantum computing. We then discuss how advanced multiscale modeling methods could be exploited to address critical scientific challenges, focusing on the simulation of complex light-harvesting processes, such as natural photosynthesis. While doing so, we suggest a cutting-edge computational paradigm consisting in performing simultaneous multiscale calculations on a system allowing the various domains, treated with appropriate accuracy, to move and extend while they properly interact with each other. Although this vision is very ambitious, we believe the quick development of computer science will lead to both massive improvements and widespread use of these techniques, resulting in enormous progresses in physical chemistry and, eventually, in our society.

Generation of true quantum random numbers with on-demand probability distributions via single-photon quantum walks

Random numbers are at the heart of diverse fields, ranging from simulations of stochastic processes to classical and quantum cryptography. The requirement for true randomness in these applications has motivated various proposals for generating random numbers based on the inherent randomness of quantum systems. The generation of true random numbers with arbitrarily defined probability distributions is highly desirable for applications, but it is very challenging. Here we show that single-photon quantum walks can generate multi-bit random numbers with on-demand probability distributions, when the required "coin" parameters are found with the gradient descent (GD) algorithm. Our theoretical and experimental results exhibit high fidelity for various selected distributions. This GD-enhanced single-photon system provides a convenient way for building flexible and reliable quantum random number generators. Multi-bit random numbers are a necessary resource for high-dimensional quantum key distribution.

Improved clinical data imputation via classical and quantum determinantal point processes

Imputing data is a critical issue for machine learning practitioners, including in the life sciences domain, where missing clinical data is a typical situation and the reliability of the imputation is of great importance. Currently, there is no canonical approach for imputation of clinical data and widely used algorithms introduce variance in the downstream classification. Here we propose novel imputation methods based on determinantal point processes (DPP) that enhance popular techniques such as the multivariate imputation by chained equations and MissForest. Their advantages are twofold: improving the quality of the imputed data demonstrated by increased accuracy of the downstream classification and providing deterministic and reliable imputations that remove the variance from the classification results. We experimentally demonstrate the advantages of our methods by performing extensive imputations on synthetic and real clinical data. We also perform quantum hardware experiments by applying the quantum circuits for DPP sampling since such quantum algorithms provide a computational advantage with respect to classical ones. We demonstrate competitive results with up to 10 qubits for small-scale imputation tasks on a state-of-the-art IBM quantum processor. Our classical and quantum methods improve the effectiveness and robustness of clinical data prediction modeling by providing better and more reliable data imputations. These improvements can add significant value in settings demanding high precision, such as in pharmaceutical drug trials where our approach can provide higher confidence in the predictions made.

Meta-optimization of resources on quantum computers

The current state of quantum computing is commonly described as the Noisy Intermediate-Scale Quantum era. Available computers contain a few dozens of qubits and can perform a few dozens of operations before the inevitable noise erases all information encoded in the calculation. Even if the technology advances fast within the next years, any use of quantum computers will be limited to short and simple tasks, serving as subroutines of more complex classical procedures. Even for these applications the resource efficiency, measured in the number of quantum computer runs, will be a key parameter. Here we suggest a general meta-optimization procedure for hybrid quantum-classical algorithms that allows finding the optimal approach with limited quantum resources. This method optimizes the usage of resources of an existing method by testing its capabilities and setting the optimal resource utilization. We demonstrate this procedure on a specific example of variational quantum algorithm used to find the ground state energy of a hydrogen molecule.

Transition role of entangled data in quantum machine learning

Entanglement serves as the resource to empower quantum computing. Recent progress has highlighted its positive impact on learning quantum dynamics, wherein the integration of entanglement into quantum operations or measurements of quantum machine learning (QML) models leads to substantial reductions in training data size, surpassing a specified prediction error threshold. However, an analytical understanding of how the entanglement degree in data affects model performance remains elusive. In this study, we address this knowledge gap by establishing a quantum no-free-lunch (NFL) theorem for learning quantum dynamics using entangled data. Contrary to previous findings, we prove that the impact of entangled data on prediction error exhibits a dual effect, depending on the number of permitted measurements. With a sufficient number of measurements, increasing the entanglement of training data consistently reduces the prediction error or decreases the required size of the training data to achieve the same prediction error. Conversely, when few measurements are allowed, employing highly entangled data could lead to an increased prediction error. The achieved results provide critical guidance for designing advanced QML protocols, especially for those tailored for execution on early-stage quantum computers with limited access to quantum resources.

Quantum annealing of a frustrated magnet

Quantum annealing, which involves quantum tunnelling among possible solutions, has state-of-the-art applications not only in quickly finding the lowest-energy configuration of a complex system, but also in quantum computing. Here we report a single-crystal study of the frustrated magnet α-CoV2O6, consisting of a triangular arrangement of ferromagnetic Ising spin chains without evident structural disorder. We observe quantum annealing phenomena resulting from time-reversal symmetry breaking in a tiny transverse field. Below ~ 1 K, the system exhibits no indication of approaching the lowest-energy state for at least 15 hours in zero transverse field, but quickly converges towards that configuration with a nearly temperature-independent relaxation time of ~ 10 seconds in a transverse field of ~ 3.5 mK. Our many-body simulations show qualitative agreement with the experimental results, and suggest that a tiny transverse field can profoundly enhance quantum spin fluctuations, triggering rapid quantum annealing process from topological metastable Kosterlitz-Thouless phases, at low temperatures.

Immediate fall prevention: the missing key to a comprehensive solution for falling hazard in older adults

The world is witnessing an unprecedented demographic shift due to increased life expectancy and declining birth rates. By 2050, 20% of the global population will be over 60, presenting significant challenges like a shortage of caregivers, maintaining health and independence, and funding extended retirement. The technology that caters to the needs of older adults and their caregivers is the most promising candidate to tackle these issues. Although multiple companies and startups offer various aging solutions, preventive technology, which could prevent trauma, is not a big part of it. Trauma is the leading cause of morbidity, disability, and mortality in older adults, and statistics constitute traumatic fall accidents as its leading cause. Therefore, an immediate preventive technology that anticipates an accident on time and prevents it must be the first response to this hazard category to decrease the gap between life expectancy and the health/wellness expectancy of older adults. The article outlines the challenges of the upcoming aging crisis and introduces falls as one major challenge. After that, falls and their mechanisms are investigated, highlighting the cognitive functions and their relation to falls. Moreover, since understanding predictive cognitive mechanisms is critical to an effective prediction-interception design, they are discussed in more detail, signifying the role of cognitive decline in balance maintenance. Furthermore, the landscape of available solutions for falling and its shortcomings is inspected. Finally, immediate fall prevention, the missing part of a wholesome solution, and its barriers are introduced, and some promising methodologies are proposed.

The Dilemma of Quantum Neural Networks

The core of quantum machine learning is to devise quantum models with good trainability and low generalization error bounds than their classical counterparts to ensure better reliability and interpretability. Recent studies confirmed that quantum neural networks (QNNs) have the ability to achieve this goal on specific datasets. In this regard, it is of great importance to understand whether these advantages are still preserved on real-world tasks. Through systematic numerical experiments, we empirically observe that current QNNs fail to provide any benefit over classical learning models. Concretely, our results deliver two key messages. First, QNNs suffer from the severely limited effective model capacity, which incurs poor generalization on real-world datasets. Second, the trainability of QNNs is insensitive to regularization techniques, which sharply contrasts with the classical scenario. These empirical results force us to rethink the role of current QNNs and to design novel protocols for solving real-world problems with quantum advantages.

Harvesting Chemical Understanding with Machine Learning and Quantum Computers

It is tenable to argue that nobody can predict the future with certainty, yet one can learn from the past and make informed projections for the years ahead. In this Perspective, we overview the status of how theory and computation can be exploited to obtain chemical understanding from wave function theory and density functional theory, and then outlook the likely impact of machine learning (ML) and quantum computers (QC) to appreciate traditional chemical concepts in decades to come. It is maintained that the development and maturation of ML and QC methods in theoretical and computational chemistry represent two paradigm shifts about how the Schrödinger equation can be solved. New chemical understanding can be harnessed in these two new paradigms by making respective use of ML features and QC qubits. Before that happens, however, we still have hurdles to face and obstacles to overcome in both ML and QC arenas. Possible pathways to tackle these challenges are proposed. We anticipate that hierarchical modeling, in contrast to multiscale modeling, will emerge and thrive, becoming the workhorse of in silico simulations in the next few decades.

Understanding quantum machine learning also requires rethinking generalization

Quantum machine learning models have shown successful generalization performance even when trained with few data. In this work, through systematic randomization experiments, we show that traditional approaches to understanding generalization fail to explain the behavior of such quantum models. Our experiments reveal that state-of-the-art quantum neural networks accurately fit random states and random labeling of training data. This ability to memorize random data defies current notions of small generalization error, problematizing approaches that build on complexity measures such as the VC dimension, the Rademacher complexity, and all their uniform relatives. We complement our empirical results with a theoretical construction showing that quantum neural networks can fit arbitrary labels to quantum states, hinting at their memorization ability. Our results do not preclude the possibility of good generalization with few training data but rather rule out any possible guarantees based only on the properties of the model family. These findings expose a fundamental challenge in the conventional understanding of generalization in quantum machine learning and highlight the need for a paradigm shift in the study of quantum models for machine learning tasks.

Generative Quantum Machine Learning via Denoising Diffusion Probabilistic Models

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.

Hybrid Quantum Image Classification and Federated Learning for Hepatic Steatosis Diagnosis

In the realm of liver transplantation, accurately determining hepatic steatosis levels is crucial. Recognizing the essential need for improved diagnostic precision, particularly for optimizing diagnosis time by swiftly handling easy-to-solve cases and allowing the expert time to focus on more complex cases, this study aims to develop cutting-edge algorithms that enhance the classification of liver biopsy images. Additionally, the challenge of maintaining data privacy arises when creating automated algorithmic solutions, as sharing patient data between hospitals is restricted, further complicating the development and validation process. This research tackles diagnostic accuracy by leveraging novel techniques from the rapidly evolving field of quantum machine learning, known for their superior generalization abilities. Concurrently, it addresses privacy concerns through the implementation of privacy-conscious collaborative machine learning with federated learning. We introduce a hybrid quantum neural network model that leverages real-world clinical data to assess non-alcoholic liver steatosis accurately. This model achieves an image classification accuracy of 97%, surpassing traditional methods by 1.8%. Moreover, by employing a federated learning approach that allows data from different clients to be shared while ensuring privacy, we maintain an accuracy rate exceeding 90%. This initiative marks a significant step towards a scalable, collaborative, efficient, and dependable computational framework that aids clinical pathologists in their daily diagnostic tasks.

Employing neural density functionals to generate potential energy surfaces

CONTEXT

With the union of machine learning (ML) and quantum chemistry, amid the debate between machine-learned functionals and human-designed functionals in density functional theory (DFT), this paper aims to demonstrate the generation of potential energy surfaces using computations with machine-learned density functional approximation (ML-DFA). A recent research trend is the application of ML in quantum sciences in the design of density functionals such as DeepMind's Deep Learning model (DeepMind21, DM21). Though science reported the state-of-the-art performance of DM21, the opportunity to utilize DeepMind's pretrained DM21 neural networks in computations in quantum chemistry has not yet been tapped. So far in the literature, the Deep Learning density functionals (DM21) have not been applied to generate potential energy surfaces. While the superior accuracy of DM21 has been reported, there is still a scarcity of publications that apply DM21 in calculations in the field. In this context, for the first time in literature, neural density functionals inferring 2D potential energy surfaces (ML-DFA-PES) based on machine-learned DFA-based computational method is contributed in this paper. This paper reports the ML-DFA-generated PES for C4H8, H2O, H2, and H2+ by employing a pretrained DM21m TensorFlow model with cc-pVDZ basis set. In addition, we also analyze the long-range behavior of DM21 based PES to investigate the ability to describe a system at long ranges. Furthermore, we compare PES diagrams from DM21 with popular DFT functionals (b3lyp/ PW6B95) and CCSD(T).

METHODS

In this method, 2D potential energy surfaces are obtained using a method that relies upon the neural network's ability to accurately learn the mapping between 3D electron density and exchange-correlation potential. By inserting Deep Learning inference in DFT with a pretrained neural network, self-consistent field (SCF) energy at different geometries along the coordinates of interest is computed, and then, potential energy surfaces are plotted. In this method, first, the electron density is computed mathematically, and this computed 3D electron density is used as a ML feature vector to predict the exchange correlation potential as a ML inference computed by a forward pass of pre-trained DM21 TensorFlow computational graph, followed by the computation of self-consistent field energy at multiple geometries, and then, SCF energies at different bond lengths/angles are plotted as 2D PES. We implement this in a python source code using frameworks such as PySCF and DM21. This paper contributes this implementation in open source. The source code and DM21-DFA-based PES are contributed at https://sites.google.com/view/MLfunctionals-DeepMind-PES .

Quantum-parallel vectorized data encodings and computations on trapped-ion and transmon QPUs

Compact data representations in quantum systems are crucial for the development of quantum algorithms for data analysis. In this study, we present two innovative data encoding techniques, known as QCrank and QBArt, which exhibit significant quantum parallelism via uniformly controlled rotation gates. The QCrank method encodes a series of real-valued data as rotations on data qubits, resulting in increased storage capacity. On the other hand, QBArt directly incorporates a binary representation of the data within the computational basis, requiring fewer quantum measurements and enabling well-established arithmetic operations on binary data. We showcase various applications of the proposed encoding methods for various data types. Notably, we demonstrate quantum algorithms for tasks such as DNA pattern matching, Hamming weight computation, complex value conjugation, and the retrieval of a binary image with 384 pixels, all executed on the Quantinuum trapped-ion QPU. Furthermore, we employ several cloud-accessible QPUs, including those from IBMQ and IonQ, to conduct supplementary benchmarking experiments.

Application of machine learning in atmospheric pollution research: A state-of-art review

Machine learning (ML) is an artificial intelligence technology that has been used in atmospheric pollution research due to their powerful fitting ability. In this review, 105 articles related to ML and the atmospheric pollution research are critically reviewed. Applications of ML in the prediction of atmospheric pollution (mainly particulate matters) are systematically described, including the principle of prediction, influencing factors and improvement measures. Researchers can improve the accuracy of the prediction model through three main aspects, namely considering the geographical features of the study area into the model, introducing the physical characteristics of pollutants, matching and optimizing ML models. And by using interpretable ML tools, researchers are able to understand the mechanism of the model and gain in-depth information. Then, the state-of-art applications of ML in the source apportionment of atmospheric particulate matter and the effect of atmospheric pollutants on human health are also described. In addition, the advantages and disadvantages of the current applications of ML in atmospheric pollution research are summarized, and the application perspective of ML in this field is elucidated. Given the scarcity of source apportionment applications and human health research, standardized research methods and specialized ML methods are required in atmospheric pollution research to connect these two disciplines.

Efficient Quantum Image Classification Using Single Qubit Encoding

The domain of image classification has been seen to be dominated by high-performing deep-learning (DL) architectures. However, the success of this field, as seen over the past decade, has resulted in the complexity of modern methodologies scaling exponentially, commonly requiring millions of parameters. Quantum computing (QC) is an active area of research aimed toward greatly reducing problems of complexity faced in classical computing. With growing interest toward quantum machine learning (QML) for applications of image classification, many proposed algorithms require usage of numerous qubits. In the noisy intermediate-scale quantum (NISQ) era, these circuits may not always be feasible to execute effectively; therefore, we should aim to use each qubit as effectively and efficiently as possible, before adding additional qubits. This article proposes a new single-qubit-based deep quantum neural network for image classification that mimics traditional convolutional neural network (CNN) techniques, resulting in a reduced number of parameters compared with previous works. Our aim is to prove the concept of the initial proposal by demonstrating classification performance of the single-qubit-based architecture, as well as to provide a tested foundation for further development. To demonstrate this, our experiments were conducted using various datasets including MNIST, Fashion-MNIST, and ORL face datasets. To further our proposal in the context of the NISQ era, our experiments were intentionally conducted in noisy simulation environments. Initial test results appear promising, with classification accuracies of 94.6%, 89.5%, and 82.5% achieved on the subsets of MNIST, FMNIST, and ORL face datasets, respectively. In addition, proposals for further investigation and development were considered, where it is hoped that these initial results can be improved.

Correlated optical convolutional neural network with "quantum speedup"

Compared with electrical neural networks, optical neural networks (ONNs) have the potentials to break the limit of the bandwidth and reduce the consumption of energy, and therefore draw much attention in recent years. By far, several types of ONNs have been implemented. However, the current ONNs cannot realize the acceleration as powerful as that indicated by the models like quantum neural networks. How to construct and realize an ONN with the quantum speedup is a huge challenge. Here, we propose theoretically and demonstrate experimentally a new type of optical convolutional neural network by introducing the optical correlation. It is called the correlated optical convolutional neural network (COCNN). We show that the COCNN can exhibit "quantum speedup" in the training process. The character is verified from the two aspects. One is the direct illustration of the faster convergence by comparing the loss function curves of the COCNN with that of the traditional convolutional neural network (CNN). Such a result is compatible with the training performance of the recently proposed quantum convolutional neural network (QCNN). The other is the demonstration of the COCNN's capability to perform the QCNN phase recognition circuit, validating the connection between the COCNN and the QCNN. Furthermore, we take the COCNN analog to the 3-qubit QCNN phase recognition circuit as an example and perform an experiment to show the soundness and the feasibility of it. The results perfectly match the theoretical calculations. Our proposal opens up a new avenue for realizing the ONNs with the quantum speedup, which will benefit the information processing in the era of big data.

Verifying Quantum Advantage Experiments with Multiple Amplitude Tensor Network Contraction

The quantum supremacy experiment, such as Google Sycamore [F. Arute et al., Nature (London) 574, 505 (2019).NATUAS0028-083610.1038/s41586-019-1666-5], poses a great challenge for classical verification due to the exponentially increasing compute cost. Using a new-generation Sunway supercomputer within 8.5 d, we provide a direct verification by computing 3×10^{6} exact amplitudes for the experimentally generated bitstrings, obtaining a cross-entropy benchmarking fidelity of 0.191% (the estimated value is 0.224%). The leap of simulation capability is built on a multiple-amplitude tensor network contraction algorithm which systematically exploits the "classical advantage" (the inherent "store-and-compute" operation mode of von Neumann machines) of current supercomputers, and a fused tensor network contraction algorithm which drastically increases the compute efficiency on heterogeneous architectures. Our method has a far-reaching impact in solving quantum many-body problems, statistical problems, as well as combinatorial optimization problems.

Stabilized quantum-enhanced SIEM architecture and speed-up through Hoeffding tree algorithms enable quantum cybersecurity analytics in botnet detection

For the first time, we enable the execution of hybrid quantum machine learning (HQML) methods on real quantum computers with 100 data samples and real-device-based simulations with 5000 data samples, thereby outperforming the current state of research of Suryotrisongko and Musashi from 2022 who were dealing with 1000 data samples and quantum simulators (pure software-based emulators) only. Additionally, we beat their reported accuracy of 76.8% by an average accuracy of 91.2%, all within a total execution time of 1687 s. We achieve this significant progress through two-step strategy: Firstly, we establish a stable quantum architecture that enables us to execute HQML algorithms on real quantum devices. Secondly, we introduce new hybrid quantum binary classifiers (HQBCs) based on Hoeffding decision tree algorithms. These algorithms speed up the process via batch-wise execution, reducing the number of shots required on real quantum devices compared to conventional loop-based optimizers. Their incremental nature serves the purpose of online large-scale data streaming for domain generation algorithm (DGA) botnet detection, and allows us to apply HQML to the field of cybersecurity analytics. We conduct our experiments using the Qiskit library with the Aer quantum simulator, and on three different real quantum devices from Azure Quantum: IonQ, Rigetti, and Quantinuum. This is the first time these tools are combined in this manner.

Exploring the Potential of Artificial Intelligence in Adolescent Suicide Prevention: Current Applications, Challenges, and Future Directions

ObjectiveThe global surge in adolescent suicide necessitates the development of innovative and efficacious preventive measures. Traditionally, various approaches have been used, but with limited success. However, with the rapid advancements in artificial intelligence (AI), new possibilities have emerged. This paper reviews the potentials and challenges of integrating AI into suicide prevention strategies, focusing on adolescents. Method: This narrative review assesses the impact of AI on suicide prevention strategies, the strategies and cases of AI applications in adolescent suicide prevention, as well as the challenges faced. Through searches on the PubMed, web of science, PsycINFO, and EMBASE databases, 19 relevant articles were included in the review. Results: AI has significantly improved risk assessment and predictive modeling for identifying suicidal behavior. It has enabled the analysis of textual data through natural language processing and fostered novel intervention strategies. Although AI applications, such as chatbots and monitoring systems, show promise, they must navigate challenges like data privacy and ethical considerations. The research underscores the potential of AI to enhance future suicide prevention efforts through personalized interventions and integration with emerging technologies. Conclusion: AI possesses transformative potential for adolescent suicide prevention by offering targeted and adaptive solutions, while they also raise crucial ethical and practical considerations. Looking forward, AI can play a critical role in mitigating adolescent suicide rates, marking a new frontier in mental health care.

Quantum discriminator for binary classification

Quantum computers have the unique ability to operate relatively quickly in high-dimensional spaces-this is sought to give them a competitive advantage over classical computers. In this work, we propose a novel quantum machine learning model called the Quantum Discriminator, which leverages the ability of quantum computers to operate in the high-dimensional spaces. The quantum discriminator is trained using a quantum-classical hybrid algorithm in [Formula: see text] time, and inferencing is performed on a universal quantum computer in [Formula: see text] time. The quantum discriminator takes as input the binary features extracted from a given datum along with a prediction qubit, and outputs the predicted label. We analyze its performance on the Iris and Bars and Stripes data sets, and show that it can attain 99% accuracy in simulation.

Towards provably efficient quantum algorithms for large-scale machine-learning models

Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that fault-tolerant quantum computing could possibly provide provably efficient resolutions for generic (stochastic) gradient descent algorithms, scaling as [Formula: see text], where n is the size of the models and T is the number of iterations in the training, as long as the models are both sufficiently dissipative and sparse, with small learning rates. Based on earlier efficient quantum algorithms for dissipative differential equations, we find and prove that similar algorithms work for (stochastic) gradient descent, the primary algorithm for machine learning. In practice, we benchmark instances of large machine learning models from 7 million to 103 million parameters. We find that, in the context of sparse training, a quantum enhancement is possible at the early stage of learning after model pruning, motivating a sparse parameter download and re-upload scheme. Our work shows solidly that fault-tolerant quantum algorithms could potentially contribute to most state-of-the-art, large-scale machine-learning problems.

Machine learning assisted rational design of antimicrobial peptides based on human endogenous proteins and their applications for cosmetic preservative system optimization

Preservatives are essential components in cosmetic products, but their safety issues have attracted widespread attention. There is an urgent need for safe and effective alternatives. Antimicrobial peptides (AMPs) are part of the innate immune system and have potent antimicrobial properties. Using machine learning-assisted rational design, we obtained a novel antibacterial peptide, IK-16-1, with significant antibacterial activity and maintaining safety based on β-defensins. IK-16-1 has broad-spectrum antimicrobial properties against Escherichia coli, Staphylococcus aureus, Pseudomonas aeruginosa, and Candida albicans, and has no haemolytic activity. The use of IK-16-1 holds promise in the cosmetics industry, since it can serve as a preservative synergist to reduce the amount of other preservatives in cosmetics. This study verified the feasibility of combining computational design with artificial intelligence prediction to design AMPs, achieving rapid screening and reducing development costs.

The Future of Drug Development with Quantum Computing

Novel medication development is a time-consuming and expensive multistage procedure. Recent technology developments have lowered timeframes, complexity, and cost dramatically. Current research projects are driven by AI and machine learning computational models. This chapter will introduce quantum computing (QC) to drug development issues and provide an in-depth discussion of how quantum computing may be used to solve various drug discovery problems. We will first discuss the fundamentals of QC, a review of known Hamiltonians, how to apply Hamiltonians to drug discovery challenges, and what the noisy intermediate-scale quantum (NISQ) era methods and their limitations are.We will further discuss how these NISQ era techniques can aid with specific drug discovery challenges, including protein folding, molecular docking, AI-/ML-based optimization, and novel modalities for small molecules and RNA secondary structures. Consequently, we will discuss the latest QC landscape's opportunities and challenges.

Synergistic pretraining of parametrized quantum circuits via tensor networks

Parametrized quantum circuits (PQCs) represent a promising framework for using present-day quantum hardware to solve diverse problems in materials science, quantum chemistry, and machine learning. We introduce a "synergistic" approach that addresses two prominent issues with these models: the prevalence of barren plateaus in PQC optimization landscapes, and the difficulty to outperform state-of-the-art classical algorithms. This framework first uses classical resources to compute a tensor network encoding a high-quality solution, and then converts this classical output into a PQC which can be further improved using quantum resources. We provide numerical evidence that this framework effectively mitigates barren plateaus in systems of up to 100 qubits using only moderate classical resources, with overall performance improving as more classical or quantum resources are employed. We believe our results highlight that classical simulation methods are not an obstacle to overcome in demonstrating practically useful quantum advantage, but rather can help quantum methods find their way.

An Explainable MRI-Radiomic Quantum Neural Network to Differentiate Between Large Brain Metastases and High-Grade Glioma Using Quantum Annealing for Feature Selection

Solitary large brain metastases (LBM) and high-grade gliomas (HGG) are sometimes hard to differentiate on MRI. The management differs significantly between these two entities, and non-invasive methods that help differentiate between them are eagerly needed to avoid potentially morbid biopsies and surgical procedures. We explore herein the performance and interpretability of an MRI-radiomics variational quantum neural network (QNN) using a quantum-annealing mutual-information (MI) feature selection approach. We retrospectively included 423 patients with HGG and LBM (> 2 cm) who had a contrast-enhanced T1-weighted (CE-T1) MRI between 2012 and 2019. After exclusion, 72 HGG and 129 LBM were kept. Tumors were manually segmented, and a 5-mm peri-tumoral ring was created. MRI images were pre-processed, and 1813 radiomic features were extracted. A set of best features based on MI was selected. MI and conditional-MI were embedded into a quadratic unconstrained binary optimization (QUBO) formulation that was mapped to an Ising-model and submitted to D'Wave's quantum annealer to solve for the best combination of 10 features. The 10 selected features were embedded into a 2-qubits QNN using PennyLane library. The model was evaluated for balanced-accuracy (bACC) and area under the receiver operating characteristic curve (ROC-AUC) on the test set. The model performance was benchmarked against two classical models: dense neural networks (DNN) and extreme gradient boosting (XGB). Shapley values were calculated to interpret sample-wise predictions on the test set. The best 10-feature combination included 6 tumor and 4 ring features. For QNN, DNN, and XGB, respectively, training ROC-AUC was 0.86, 0.95, and 0.94; test ROC-AUC was 0.76, 0.75, and 0.79; and test bACC was 0.74, 0.73, and 0.72. The two most influential features were tumor Laplacian-of-Gaussian-GLRLM-Entropy and sphericity. We developed an accurate interpretable QNN model with quantum-informed feature selection to differentiate between LBM and HGG on CE-T1 brain MRI. The model performance is comparable to state-of-the-art classical models.

Predicting Gas Adsorption without the Knowledge of Pore Structures: A Machine Learning Method Based on Classical Density Functional Theory

Predicting gas adsorption from the pore structure is an intuitive and widely used methodology in adsorption. However, in real-world systems, the structural information is usually very complicated and can only be approximately obtained from the characterization data. In this work, we developed a machine learning (ML) method to predict gas adsorption form the raw characterization data of N2 adsorption. The ML method is modeled by a convolutional neural network and trained by a large number of data that are generated from a classical density functional theory, and the model gives a very accurate prediction of Ar adsorption. Though the training set is limited to modeling slit pores, the model can be applied to three-dimensional structured pores and real-world materials. The good agreements suggest that there is a universal relationship among adsorption isotherms of different adsorbates, which could be captured by the ML model.

Implementation and empirical evaluation of a quantum machine learning pipeline for local classification

In the current era, quantum resources are extremely limited, and this makes difficult the usage of quantum machine learning (QML) models. Concerning the supervised tasks, a viable approach is the introduction of a quantum locality technique, which allows the models to focus only on the neighborhood of the considered element. A well-known locality technique is the k-nearest neighbors (k-NN) algorithm, of which several quantum variants have been proposed; nevertheless, they have not been employed yet as a preliminary step of other QML models. Instead, for the classical counterpart, a performance enhancement with respect to the base models has already been proven. In this paper, we propose and evaluate the idea of exploiting a quantum locality technique to reduce the size and improve the performance of QML models. In detail, we provide (i) an implementation in Python of a QML pipeline for local classification and (ii) its extensive empirical evaluation. Regarding the quantum pipeline, it has been developed using Qiskit, and it consists of a quantum k-NN and a quantum binary classifier, both already available in the literature. The results have shown the quantum pipeline's equivalence (in terms of accuracy) to its classical counterpart in the ideal case, the validity of locality's application to the QML realm, but also the strong sensitivity of the chosen quantum k-NN to probability fluctuations and the better performance of classical baseline methods like the random forest.

Quantum-aided secure deep neural network inference on real quantum computers

Deep neural networks (DNNs) are phenomenally successful machine learning methods broadly applied to many different disciplines. However, as complex two-party computations, DNN inference using classical cryptographic methods cannot achieve unconditional security, raising concern on security risks of DNNs' application to sensitive data in many domains. We overcome such a weakness by introducing a quantum-aided security approach. We build a quantum scheme for unconditionally secure DNN inference based on quantum oblivious transfer with an untrusted third party. Leveraging DNN's noise tolerance, our approach enables complex DNN inference on comparatively low-fidelity quantum systems with limited quantum capacity. We validated our method using various applications with a five-bit real quantum computer and a quantum simulator. Both theoretical analyses and experimental results demonstrate that our approach manages to operate on existing quantum computers and achieve unconditional security with a negligible accuracy loss. This may open up new possibilities of quantum security methods for deep learning.

Targeting high performance of perovskite solar cells by combining electronic, manufacturing and environmental features in machine learning techniques

This study employs Machine Learning (ML) techniques to optimize the performance of Perovskite Solar Cells (PSCs) by identifying the ideal materials and properties for high Power Conversion Efficiency (PCE). Utilizing a dataset of 3000 PSC samples from previous experiments, the Random Forest (RF) technique classifies and predicts PCE as the target variable. The dataset includes various features encompassing cell architecture, substrate materials, electron transport layer (ETL) attributes, perovskite characteristics, hole transport layer (HTL) properties, back contact specifics, and encapsulation materials. ML-driven analysis reveals novel, highly efficient PSC configurations, such as Fe2O3/CsPbBrI2/NiO-mp/Carbon, CdS/FAMAPbI3/NiO-C/Au, and PCBM-60/Phen-NaDPO/MAPbI3/asy-PBTBDT/Ag. Additionally, the study investigates the impact of crucial parameters like perovskite bandgap, ETL thickness, thermal annealing temperature, and back contact thickness on device performance. The predictive model exhibits high accuracy (86.4 % R2) and low mean square error (1.3 MSE). Notably, the ML-recommended structure, SnO2/CsFAMAPbBrI/Spiro-OmeTAD/Au, achieves an impressive efficiency of around 23 %. Beyond performance improvements, the research explores the integration of ML into the manufacturing and quality control processes of PSCs. These findings hold promise for enhancing conversion yields, reducing defects, and ensuring consistent PSC performance, contributing to the advancement of this renewable energy technology.

Deep Learning in Mechanical Metamaterials: From Prediction and Generation to Inverse Design

Mechanical metamaterials are meticulously designed structures with exceptional mechanical properties determined by their microstructures and constituent materials. Tailoring their material and geometric distribution unlocks the potential to achieve unprecedented bulk properties and functions. However, current mechanical metamaterial design considerably relies on experienced designers' inspiration through trial and error, while investigating their mechanical properties and responses entails time-consuming mechanical testing or computationally expensive simulations. Nevertheless, recent advancements in deep learning have revolutionized the design process of mechanical metamaterials, enabling property prediction and geometry generation without prior knowledge. Furthermore, deep generative models can transform conventional forward design into inverse design. Many recent studies on the implementation of deep learning in mechanical metamaterials are highly specialized, and their pros and cons may not be immediately evident. This critical review provides a comprehensive overview of the capabilities of deep learning in property prediction, geometry generation, and inverse design of mechanical metamaterials. Additionally, this review highlights the potential of leveraging deep learning to create universally applicable datasets, intelligently designed metamaterials, and material intelligence. This article is expected to be valuable not only to researchers working on mechanical metamaterials but also those in the field of materials informatics.

Curriculum-Based Deep Reinforcement Learning for Quantum Control

Deep reinforcement learning (DRL) has been recognized as an efficient technique to design optimal strategies for different complex systems without prior knowledge of the control landscape. To achieve a fast and precise control for quantum systems, we propose a novel DRL approach by constructing a curriculum consisting of a set of intermediate tasks defined by fidelity thresholds, where the tasks among a curriculum can be statically determined before the learning process or dynamically generated during the learning process. By transferring knowledge between two successive tasks and sequencing tasks according to their difficulties, the proposed curriculum-based DRL (CDRL) method enables the agent to focus on easy tasks in the early stage, then move onto difficult tasks, and eventually approaches the final task. Numerical comparison with the traditional methods [gradient method (GD), genetic algorithm (GA), and several other DRL methods] demonstrates that CDRL exhibits improved control performance for quantum systems and also provides an efficient way to identify optimal strategies with few control pulses.

Quantum neural networks for the discovery and implementation of quantum error-correcting codes

We implement and use quantum neural networks that exploit bit-flip quantum error-correcting codes that correct bit-flip errors in arbitrary logical qubit states. We introduce conjugate layer quantum autoencoders and use them in order to restore states impacted by amplitude damping through the utilization of an approximative four-qubit error-correcting codeword. Our specific implementation avoids barren plateaus of the cost function and improves the training time. Moreover, we propose a strategy that allows one to discover new encryption protocols tailored for specific quantum channels. This is exemplified by learning to generate logical qubits explicitly for the bit-flip channel. Our modified quantum neural networks consistently outperform the standard implementations across all tasks.

Fragmented imaginary-time evolution for early-stage quantum signal processors

Simulating quantum imaginary-time evolution (QITE) is a significant promise of quantum computation. However, the known algorithms are either probabilistic (repeat until success) with unpractically small success probabilities or coherent (quantum amplitude amplification) with circuit depths and ancillary-qubit numbers unrealistically large in the mid-term. Our main contribution is a new generation of deterministic, high-precision QITE algorithms that are significantly more amenable experimentally. A surprisingly simple idea is behind them: partitioning the evolution into a sequence of fragments that are run probabilistically. It causes a considerable reduction in wasted circuit depth every time a run fails. Remarkably, the resulting overall runtime is asymptotically better than in coherent approaches, and the hardware requirements are even milder than in probabilistic ones. Our findings are especially relevant for the early fault-tolerance stages of quantum hardware.

QAmplifyNet: pushing the boundaries of supply chain backorder prediction using interpretable hybrid quantum-classical neural network

Supply chain management relies on accurate backorder prediction for optimizing inventory control, reducing costs, and enhancing customer satisfaction. Traditional machine-learning models struggle with large-scale datasets and complex relationships. This research introduces a novel methodological framework for supply chain backorder prediction, addressing the challenge of collecting large real-world datasets with 90% accuracy. Our proposed model demonstrates remarkable accuracy in predicting backorders on short and imbalanced datasets. We capture intricate patterns and dependencies by leveraging quantum-inspired techniques within the quantum-classical neural network QAmplifyNet. Experimental evaluations on a benchmark dataset establish QAmplifyNet's superiority over eight classical models, three classically stacked quantum ensembles, five quantum neural networks, and a deep reinforcement learning model. Its ability to handle short, imbalanced datasets makes it ideal for supply chain management. We evaluate seven preprocessing techniques, selecting the best one based on logistic regression's performance on each preprocessed dataset. The model's interpretability is enhanced using Explainable artificial intelligence techniques. Practical implications include improved inventory control, reduced backorders, and enhanced operational efficiency. QAmplifyNet also achieved the highest F1-score of 94% for predicting "Not Backorder" and 75% for predicting "backorder," outperforming all other models. It also exhibited the highest AUC-ROC score of 79.85%, further validating its superior predictive capabilities. QAmplifyNet seamlessly integrates into real-world supply chain management systems, empowering proactive decision-making and efficient resource allocation. Future work involves exploring additional quantum-inspired techniques, expanding the dataset, and investigating other supply chain applications. This research unlocks the potential of quantum computing in supply chain optimization and paves the way for further exploration of quantum-inspired machine learning models in supply chain management. Our framework and QAmplifyNet model offer a breakthrough approach to supply chain backorder prediction, offering superior performance and opening new avenues for leveraging quantum-inspired techniques in supply chain management.

The Nature of the Chemical Bonds of High-Valent Transition-Metal Oxo (M=O) and Peroxo (MOO) Compounds: A Historical Perspective of the Metal Oxyl-Radical Character by the Classical to Quantum Computations

This review article describes a historical perspective of elucidation of the nature of the chemical bonds of the high-valent transition metal oxo (M=O) and peroxo (M-O-O) compounds in chemistry and biology. The basic concepts and theoretical backgrounds of the broken-symmetry (BS) method are revisited to explain orbital symmetry conservation and orbital symmetry breaking for the theoretical characterization of four different mechanisms of chemical reactions. Beyond BS methods using the natural orbitals (UNO) of the BS solutions, such as UNO CI (CC), are also revisited for the elucidation of the scope and applicability of the BS methods. Several chemical indices have been derived as the conceptual bridges between the BS and beyond BS methods. The BS molecular orbital models have been employed to explain the metal oxyl-radical character of the M=O and M-O-O bonds, which respond to their radical reactivity. The isolobal and isospin analogy between carbonyl oxide R2C-O-O and metal peroxide LFe-O-O has been applied to understand and explain the chameleonic chemical reactivity of these compounds. The isolobal and isospin analogy among Fe=O, O=O, and O have also provided the triplet atomic oxygen (3O) model for non-heme Fe(IV)=O species with strong radical reactivity. The chameleonic reactivity of the compounds I (Cpd I) and II (Cpd II) is also explained by this analogy. The early proposals obtained by these theoretical models have been examined based on recent computational results by hybrid DFT (UHDFT), DLPNO CCSD(T0), CASPT2, and UNO CI (CC) methods and quantum computing (QC).

Exploring the Limitations of Hybrid Adiabatic Quantum Computing for Emission Tomography Reconstruction

Our study explores the feasibility of quantum computing in emission tomography reconstruction, addressing a noisy ill-conditioned inverse problem. In current clinical practice, this is typically solved by iterative methods minimizing a L2 norm. After reviewing quantum computing principles, we propose the use of a commercially available quantum annealer and employ corresponding hybrid solvers, which combine quantum and classical computing to handle more significant problems. We demonstrate how to frame image reconstruction as a combinatorial optimization problem suited for these quantum annealers and hybrid systems. Using a toy problem, we analyze reconstructions of binary and integer-valued images with respect to their image size and compare them to conventional methods. Additionally, we test our method's performance under noise and data underdetermination. In summary, our method demonstrates competitive performance with traditional algorithms for binary images up to an image size of 32×32 on the toy problem, even under noisy and underdetermined conditions. However, scalability challenges emerge as image size and pixel bit range increase, restricting hybrid quantum computing as a practical tool for emission tomography reconstruction until significant advancements are made to address this issue.

Recent Advances for Quantum Neural Networks in Generative Learning

Quantum computers are next-generation devices that hold promise to perform calculations beyond the reach of classical computers. A leading method towards achieving this goal is through quantum machine learning, especially quantum generative learning. Due to the intrinsic probabilistic nature of quantum mechanics, it is reasonable to postulate that quantum generative learning models (QGLMs) may surpass their classical counterparts. As such, QGLMs are receiving growing attention from the quantum physics and computer science communities, where various QGLMs that can be efficiently implemented on near-term quantum machines with potential computational advantages are proposed. In this paper, we review the current progress of QGLMs from the perspective of machine learning. Particularly, we interpret these QGLMs, covering quantum circuit Born machines, quantum generative adversarial networks, quantum Boltzmann machines, and quantum variational autoencoders, as the quantum extension of classical generative learning models. In this context, we explore their intrinsic relations and their fundamental differences. We further summarize the potential applications of QGLMs in both conventional machine learning tasks and quantum physics. Last, we discuss the challenges and further research directions for QGLMs.

QMLMaterial─A Quantum Machine Learning Software for Material Design and Discovery

Structural elucidation of chemical compounds is challenging experimentally, and theoretical chemistry methods have added important insight into molecules, nanoparticles, alloys, and materials geometries and properties. However, finding the optimum structures is a bottleneck due to the huge search space, and global search algorithms have been used successfully for this purpose. In this work, we present the quantum machine learning software/agent for materials design and discovery (QMLMaterial), intended for automatic structural determination in silico for several chemical systems: atomic clusters, atomic clusters and the spin multiplicity together, doping in clusters or solids, vacancies in clusters or solids, adsorption of molecules or adsorbents on surfaces, and finally atomic clusters on solid surfaces/materials or encapsulated in porous materials. QMLMaterial is an artificial intelligence (AI) software based on the active learning method, which uses machine learning regression algorithms and their uncertainties for decision making on the next unexplored structures to be computed, increasing the probability of finding the global minimum with few calculations as more data is obtained. The software has different acquisition functions for decision making (e.g., expected improvement and lower confidence bound). Also, the Gaussian process is available in the AI framework for regression, where the uncertainty is obtained analytically from Bayesian statistics. For the artificial neural network and support vector regressor algorithms, the uncertainty can be obtained by K-fold cross-validation or nonparametric bootstrap resampling methods. The software is interfaced with several quantum chemistry codes and atomic descriptors, such as the many-body tensor representation. QMLMaterial's capabilities are highlighted in the current work by its applications in the following systems: Na20, Mo6C3 (where the spin multiplicity was considered), H2O@CeNi3O5, Mg8@graphene, Na3Mg3@CNT (carbon nanotube).

Classical Surrogates for Quantum Learning Models

The advent of noisy intermediate-scale quantum computers has put the search for possible applications to the forefront of quantum information science. One area where hopes for an advantage through near-term quantum computers are high is quantum machine learning, where variational quantum learning models based on parametrized quantum circuits are discussed. In this work, we introduce the concept of a classical surrogate, a classical model which can be efficiently obtained from a trained quantum learning model and reproduces its input-output relations. As inference can be performed classically, the existence of a classical surrogate greatly enhances the applicability of a quantum learning strategy. However, the classical surrogate also challenges possible advantages of quantum schemes. As it is possible to directly optimize the Ansatz of the classical surrogate, they create a natural benchmark the quantum model has to outperform. We show that large classes of well-analyzed reuploading models have a classical surrogate. We conducted numerical experiments and found that these quantum models show no advantage in performance or trainability in the problems we analyze. This leaves only generalization capability as a possible point of quantum advantage and emphasizes the dire need for a better understanding of inductive biases of quantum learning models.

Variational quantum and quantum-inspired clustering

Here we present a quantum algorithm for clustering data based on a variational quantum circuit. The algorithm allows to classify data into many clusters, and can easily be implemented in few-qubit Noisy Intermediate-Scale Quantum devices. The idea of the algorithm relies on reducing the clustering problem to an optimization, and then solving it via a Variational Quantum Eigensolver combined with non-orthogonal qubit states. In practice, the method uses maximally-orthogonal states of the target Hilbert space instead of the usual computational basis, allowing for a large number of clusters to be considered even with few qubits. We benchmark the algorithm with numerical simulations using real datasets, showing excellent performance even with one single qubit. Moreover, a tensor network simulation of the algorithm implements, by construction, a quantum-inspired clustering algorithm that can run on current classical hardware.