Quantum-classical Model Research Articles

Quantum Neural Networks: A New Frontier

Abstract. In recent years, there has been remarkable progress in improving the availability of resources and refining algorithms for quantum computing. Since the late 1980s, the scientific community has been fascinated by the idea of harnessing quantum phenomena to tackle computational problems. This article provides a comprehensive exploration of the foundational theories and practical applications of quantum neural networks (QNNs), highlighting their potential to transform machine learning through unique features like quantum parallelism and entanglement. It delves into various QNN architectures, such as quantum circuits and hybrid quantum-classical models, showcasing their effectiveness in handling intricate computational tasks more efficiently than traditional neural networks. Furthermore, the article examines the current challenges and future prospects in this rapidly advancing field, emphasizing the pivotal role of QNNs in driving forward research in both quantum computing and artificial intelligence. Quantum neural networks are poised to not only enhance computational capabilities but also pave the way for groundbreaking innovations in diverse technological domains.

Variational quantum algorithm for designing quantum information maskers

Abstract Since the concept of quantum information masking was proposed by Modi et al. [Phys. Rev. Lett. 120, 230501 (2018)], many interesting and significant results have been reported, both theoretically and experimentally. However, designing a quantum information masker is not an easy task, especially for larger systems. In this paper, we propose a variational quantum algorithm to resolve this problem. Specifically, our algorithm is a hybrid quantum-classical model, where the quantum device with adjustable parameters tries to mask quantum information and the classical device evaluates the performance of the quantum device and optimizes its parameters. After optimization, the quantum device behaves as an optimal masker. The loss value during optimization can be used to characterize the performance of the masker. In particular, if the loss value converges to zero, we obtain a perfect masker that masks completely the quantum information generated by the quantum information source, otherwise, the perfect masker does not exist and the subsystems always contain the original information. Nevertheless, these resulting maskers are still optimal. Quantum parallelism is utilized to reduce quantum state preparations and measurements. Our work paves the way for the wide applications of quantum information masking, and some of the techniques used in this work may have potential applications in quantum information processing.

Wavelet Based Financial Forecast Ensemble Featuring Hybrid Quantum-Classical LSTM Model

One of the most sought-after goals in the financial world is a reliable method by which investors can predict a stock price movement consistently. Advancements in stock prediction via the use of machine learning have improved the accuracy of such predictions and yielded better ideas about value investments in the stock market. However, with the addition of the state-of-art tool M-band wavelet transform as a preprocessing step, we can denoise our raw data set (prior stock prices) and refine it to make the forecast even more accurate. Following this preprocessing step, multiple machine learning techniques are deployed to construct a robust, non-parametric hybrid forecasting model. To demonstrate the novelty of our algorithm, we present a case study on stock price prediction employing a discrete 4-band wavelet transform integrated with a hybrid machine learning ensemble. Our results underscore the potential and importance of such ensemble methods in refining the accuracy and reliability of financial forecasts. Furthermore, in theory, quantum computing can further optimize these algorithms, potentially leading to more precise stock price forecasts. In particular, our ensemble will feature a hybrid quantumclassical LSTM Model to demonstrate the potential of both wavelets and quantum computing in stock forecasting.

Prerelaxation in quantum, classical, and quantum-classical two-impurity models

We numerically study the relaxation dynamics of impurity-host systems, focusing on the presence of long-lived metastable states in the nonequilibrium dynamics after an initial excitation of the impurities. In generic systems, an excited impurity coupled to a large bath at zero temperature is expected to relax and approach its ground state over time. However, certain exceptional cases exhibit metastability, where the system remains in an excited state on timescales largely exceeding the typical relaxation time. We study this phenomenon for three prototypical impurity models: a tight-binding quantum model of independent spinless fermions on a lattice with two stub impurities, a classical-spin Heisenberg model with two weakly coupled classical impurity spins, and a tight-binding quantum model of independent electrons with two classical impurity spins. Through numerical integration of the fundamental equations of motion, we find that all three models exhibit similar qualitative behavior: complete relaxation for nearest-neighbor impurities and incomplete or strongly delayed relaxation for next-nearest-neighbor impurities. The underlying mechanisms leading to this behavior differ between models and include impurity-induced bound states, emergent approximately conserved local observables, and exact cancellation of local and nonlocal dissipation effects. Published by the American Physical Society 2024

Theory of electrotuneable mechanical force of solid-liquid interfaces: A self-consistent treatment of short-range van der Waals forces and long-range electrostatic forces.

Elucidating the mechanical forces between two solid surfaces immersed in a communal liquid environment is crucial for understanding and controlling adhesion, friction, and electrochemistry in many technologies. Although traditional models can adequately describe long-range mechanical forces, they require substantial modifications in the nanometric region where electronic effects become important. A hybrid quantum-classical model is employed herein to investigate the separation-dependent disjoining pressure between two metal surfaces immersed in an electrolyte solution under potential control. We find that the pressure between surfaces transits from a long-range electrostatic interaction, attractive or repulsive depending on the charging conditions of surfaces, to a strong short-range van der Waals attraction and then an even strong Pauli repulsion due to the redistribution of electrons. The underlying mechanism of the transition, especially the attractive-repulsive one in the short-range region, is elucidated. This work contributes to the understanding of electrotunable friction and lubrication in a liquid environment.

A hybrid quantum-classical classification model based on branching multi-scale entanglement renormalization ansatz

Tensor networks are emerging architectures for implementing quantum classification models. The branching multi-scale entanglement renormalization ansatz (BMERA) is a tensor network known for its enhanced entanglement properties. This paper introduces a hybrid quantum-classical classification model based on BMERA and explores the correlation between circuit layout, expressiveness, and classification accuracy. Additionally, we present an autodifferentiation method for computing the cost function gradient, which serves as a viable option for other hybrid quantum-classical models. Through numerical experiments, we demonstrate the accuracy and robustness of our classification model in tasks such as image recognition and cluster excitation discrimination, offering a novel approach for designing quantum classification models.

Multiple dynamic modes of Bicoid morphogen gradient are explained by a quantum-classical model

Multiple dynamic modes of Bicoid morphogen gradient are explained by a quantum-classical model

Mixed quantum-classical modeling of exciton-phonon scattering in solids: Application to optical linewidths of monolayer MoS2.

We present a mixed quantum-classical framework for the microscopic and non-Markovian modeling of exciton-phonon scattering in solid-state materials and apply it to calculate the optical linewidths of monolayer MoS2. Within this framework, we combine reciprocal-space mixed quantum-classical dynamics with models for the quasiparticle band structure as well as the electron-hole and carrier-phonon interactions, parametrized against abinitio calculations, although noting that a direct interfacing with abinitio calculations is straightforward in principle. We introduce various parameters for truncating the Brillouin zone to select regions of interest. Variations of these parameters allow us to determine linewidths in the limit of asymptotic material sizes. The obtained asymptotic linewidths are found to agree favorably with experimental measurements across a range of temperatures. As such, our framework establishes itself as a promising route toward unraveling the non-Markovian and microscopic principles governing the nonadiabatic dynamics of solids.

Charge transfer plasmons in nanoparticle arrays on graphene: Theoretical development

The properties of charge transfer plasmons (CTPs) in periodic metallic nanoparticle arrays (PMNPAs) on the single-layer graphene surface are studied within a computationally efficient original hybrid quantum-classical model. The model is based on the proven assumption that the carrier charge density in doped graphene remains unchanged under plasmon oscillations. Calculated CTP frequencies for two PMNPA geometries are shown to lie within the THz range and to be factorized, i.e., presented as a product of two independent factors determined by the graphene charge density and the PMNPA geometry. Equations are derived for describing the CTP frequencies and eigenvectors, i.e., oscillating nanoparticle charge values. It is shown that the CTP plasmons having a band structure containing a wave vector and a band number, like to phonons in periodic media, can be divided into an acoustic mode and optical CTP modes. For the acoustic modes, the CTP group velocity tends to zero at k→0, but reaches a value of ∼VFermi in graphene inside the Brillouin zone, while for the optical modes, the group velocity dispersion is extremely weak, although their energy is higher than the acoustic plasmon energies. It is shown that the calculated dependence of CTP frequencies on the carrier concentration in graphene is in good agreement with experimental data. We believe that the proposed model can help in designing various graphene-based terahertz nanoplasmonic devices of complex geometry due to very high computational efficiency.

Nanoscale chemical reaction exploration with a quantum magnifying glass

Nanoscopic systems exhibit diverse molecular substructures by which they facilitate specific functions. Theoretical models of them, which aim at describing, understanding, and predicting these capabilities, are difficult to build. Viable quantum-classical hybrid models come with specific challenges regarding atomistic structure construction and quantum region selection. Moreover, if their dynamics are mapped onto a state-to-state mechanism such as a chemical reaction network, its exhaustive exploration will be impossible due to the combinatorial explosion of the reaction space. Here, we introduce a “quantum magnifying glass” that allows one to interactively manipulate nanoscale structures at the quantum level. The quantum magnifying glass seamlessly combines autonomous model parametrization, ultra-fast quantum mechanical calculations, and automated reaction exploration. It represents an approach to investigate complex reaction sequences in a physically consistent manner with unprecedented effortlessness in real time. We demonstrate these features for reactions in bio-macromolecules and metal-organic frameworks, diverse systems that highlight general applicability.

Quantum machine learning for image classification

Image classification, a pivotal task in multiple industries, faces computational challenges due to the burgeoning volume of visual data. This research addresses these challenges by introducing two quantum machine learning models that leverage the principles of quantum mechanics for effective computations. Our first model, a hybrid quantum neural network with parallel quantum circuits, enables the execution of computations even in the noisy intermediate-scale quantum era, where circuits with a large number of qubits are currently infeasible. This model demonstrated a record-breaking classification accuracy of 99.21% on the full MNIST dataset, surpassing the performance of known quantum–classical models, while having eight times fewer parameters than its classical counterpart. Also, the results of testing this hybrid model on a Medical MNIST (classification accuracy over 99%), and on CIFAR-10 (classification accuracy over 82%), can serve as evidence of the generalizability of the model and highlights the efficiency of quantum layers in distinguishing common features of input data. Our second model introduces a hybrid quantum neural network with a Quanvolutional layer, reducing image resolution via a convolution process. The model matches the performance of its classical counterpart, having four times fewer trainable parameters, and outperforms a classical model with equal weight parameters. These models represent advancements in quantum machine learning research and illuminate the path towards more accurate image classification systems.

Incorporating Electrolyte Correlation Effects into Variational Models of Electrochemical Interfaces.

We propose a way for obtaining a classical free energy density functional for electrolytes based on a first-principle many-body partition function. Via a one-loop expansion, we include coulombic correlations beyond the conventional mean-field approximation. To examine electrochemical interfaces, we integrate the electrolyte free energy functional into a hybrid quantum-classical model. This scheme self-consistently couples electronic, ionic, and solvent degrees of freedom and incorporates electrolyte correlation effects. The derived free energy functional causes a correlation-induced enhancement in interfacial counterion density and leads to an overall increase in capacitance. This effect is partially compensated by a reduction of the dielectric permittivity of interfacial water. At larger surface charge densities, ion crowding at the interface stifles these correlation effects. While scientifically intriguing already at planar interfaces, we anticipate these correlation effects to play an essential role for electrolytes in nanoconfinement.

Shallow hybrid quantum-classical convolutional neural network model for image classification

Shallow hybrid quantum-classical convolutional neural network model for image classification

Hybrid quantum-classical polarizability model for single molecule biosensing.

Optical whispering gallery mode biosensors are able to detect single molecules through effects of their polarizability. We address the factors that affect the polarizability of amino acids, which are the building blocks of life, via electronic structure theory. Amino acids are detected in aqueous environments, where their polarizability is different compared to the gasphase due to solvent effects. Solvent effects include structural changes, protonation and the local field enhancement through the solvent (water). We analyse the impact of these effects and find that all contribute to an increased effective polarizability in the solvent. We also address the excess polarizability relative to the displaced water cavity and develop a hybrid quantum-classical model that is in good agreement with self-consistent calculations. We apply our model to calculate the excess polarizability of 20 proteinogenic amino acids and determine the minimum resolution required to distinguish the different molecules and their ionised conformers based on their polarizability.

“Physicality”: A New Notion for Building a Quantum-Classical Hybrid Circuits Model

“Physicality”: A New Notion for Building a Quantum-Classical Hybrid Circuits Model

Hybrid Quantum-Classical Convolutional Neural Network Model for Image Classification.

Image classification plays an important role in remote sensing. Earth observation (EO) has inevitably arrived in the big data era, but the high requirement on computation power has already become a bottleneck for analyzing large amounts of remote sensing data with sophisticated machine learning models. Exploiting quantum computing might contribute to a solution to tackle this challenge by leveraging quantum properties. This article introduces a hybrid quantum-classical convolutional neural network (QC-CNN) that applies quantum computing to effectively extract high-level critical features from EO data for classification purposes. Besides that, the adoption of the amplitude encoding technique reduces the required quantum bit resources. The complexity analysis indicates that the proposed model can accelerate the convolutional operation in comparison with its classical counterpart. The model's performance is evaluated with different EO benchmarks, including Overhead-MNIST, So2Sat LCZ42, PatternNet, RSI-CB256, and NaSC-TG2, through the TensorFlow Quantum platform, and it can achieve better performance than its classical counterpart and have higher generalizability, which verifies the validity of the QC-CNN model on EO data classification tasks.

Hybrid quantum ResNet for car classification and its hyperparameter optimization

Image recognition is one of the primary applications of machine learning algorithms. Nevertheless, machine learning models used in modern image recognition systems consist of millions of parameters that usually require significant computational time to be adjusted. Moreover, adjustment of model hyperparameters leads to additional overhead. Because of this, new developments in machine learning models and hyperparameter optimization techniques are required. This paper presents a quantum-inspired hyperparameter optimization technique and a hybrid quantum-classical machine learning model for supervised learning. We benchmark our hyperparameter optimization method over standard black-box objective functions and observe performance improvements in the form of reduced expected run times and fitness in response to the growth in the size of the search space. We test our approaches in a car image classification task and demonstrate a full-scale implementation of the hybrid quantum ResNet model with the tensor train hyperparameter optimization. Our tests show a qualitative and quantitative advantage over the corresponding standard classical tabular grid search approach used with a deep neural network ResNet34. A classification accuracy of 0.97 was obtained by the hybrid model after 18 iterations, whereas the classical model achieved an accuracy of 0.92 after 75 iterations.

A topic-aware classifier based on a hybrid quantum-classical model

In the era of Large Language Models, there is still potential for improvement in current Natural Language Processing (NLP) methods in terms of verifiability and consistency. NLP classical approaches are computationally expensive due to their high-power consumption, computing power, and storage requirements. Another computationally efficient approach to NLP is categorical quantum mechanics, which combines grammatical structure and individual word meaning to deduce the sentence meaning. As both quantum theory and natural language use vector space to describe states which are more efficient on quantum hardware, QNLP models can achieve up to quadratic speedup over classical direct calculation methods. In recent years, there is significant progress in utilizing quantum features such as superposition and entanglement to represent linguistic meaning on quantum hardware. Earlier research work has already demonstrated QNLP’s potential quantum advantage in terms of speeding up search, enhancing classification tasks’ accuracy and providing an exponentially large quantum state space in which complex linguistic structures can be efficiently embedded. In this work, a QNLP model is used to determine if two sentences are related to the same topic or not. By comparing our QNLP model to a classical tensor network-based one, our model improved training accuracy by up to 45% and validation accuracy by 35%, respectively. The QNLP model convergence is also studied when varying: first, the problem size, second, parametrized quantum circuits used for model’s training, and last, the backend quantum simulator noise model. The experimental results show that strongly entangled ansatz designs result in fastest model convergence.

Physics simulation via quantum graph neural network

We develop and implement two realizations of quantum graph neural networks (QGNN), applied to the task of particle interaction simulation. The first QGNN is a speculative quantum-classical hybrid learning model that relies on the ability to directly utilize superposition states as classical information to propagate information between particles. The second is an implementable quantum-classical hybrid learning model that propagates particle information directly through the parameters of RX rotation gates. A classical graph neural network (CGNN) is also trained in the same task. Both the Speculative QGNN and CGNN act as controls against the Implementable QGNN. Comparison between classical and quantum models is based on the loss value and accuracy of each model. Overall, each model had a high learning efficiency, in which the loss value rapidly approached zero during training; however, each model was moderately inaccurate. Comparing performances, our results show that the Implementable QGNN has a potential advantage over the CGNN. Additionally, we show that a slight alteration in hyperparameters in the CGNN notably improves accuracy, suggesting that further fine tuning could mitigate the issue of moderate inaccuracy in each model.

A Quantum-Classical Model of Brain Dynamics.

The study of the human psyche has elucidated a bipartite structure of logic reflecting the quantum-classical nature of the world. Accordingly, we posited an approach toward studying the brain by means of the quantum-classical dynamics of a mixed Weyl symbol. The mixed Weyl symbol can be used to describe brain processes at the microscopic level and, when averaged over an appropriate ensemble, can provide a link to the results of measurements made at the meso and macro scale. Within this approach, quantum variables (such as, for example, nuclear and electron spins, dipole momenta of particles or molecules, tunneling degrees of freedom, and so on) can be represented by spinors, whereas the electromagnetic fields and phonon modes can be treated either classically or semi-classically in phase space by also considering quantum zero-point fluctuations. Quantum zero-point effects can be incorporated into numerical simulations by controlling the temperature of each field mode via coupling to a dedicated Nosé-Hoover chain thermostat. The temperature of each thermostat was chosen in order to reproduce quantum statistics in the canonical ensemble. In this first paper, we introduce a general quantum-classical Hamiltonian model that can be tailored to study physical processes at the interface between the quantum and the classical world in the brain. While the approach is discussed in detail, numerical calculations are not reported in the present paper, but they are planned for future work. Our theory of brain dynamics subsumes some compatible aspects of three well-known quantum approaches to brain dynamics, namely the electromagnetic field theory approach, the orchestrated objective reduction theory, and the dissipative quantum model of the brain. All three models are reviewed.