Hybrid Quantum-classical Model Research Articles

A Hybrid Quantum-Classical Model for Stock Price Prediction Using Quantum-Enhanced Long Short-Term Memory

The stock markets have become a popular topic within machine learning (ML) communities, with one particular application being stock price prediction. However, accurately predicting the stock market is a challenging task due to the various factors within financial markets. With the introduction of ML, prediction techniques have become more efficient but computationally demanding for classical computers. Given the rise of quantum computing (QC), which holds great promise for being exponentially faster than current classical computers, it is natural to explore ML within the QC domain. In this study, we leverage a hybrid quantum-classical ML approach to predict a company’s stock price. We integrate classical long short-term memory (LSTM) with QC, resulting in a new variant called QLSTM. We initially validate the proposed QLSTM model by leveraging an IBM quantum simulator running on a classical computer, after which we conduct predictions using an IBM real quantum computer. Thereafter, we evaluate the performance of our model using the root mean square error (RMSE) and prediction accuracy. Additionally, we perform a comparative analysis, evaluating the prediction performance of the QLSTM model against several other classical models. Further, we explore the impacts of hyperparameters on the QLSTM model to determine the best configuration. Our experimental results demonstrate that while the classical LSTM model achieved an RMSE of 0.0693 and a prediction accuracy of 0.8815, the QLSTM model exhibited superior performance, achieving values of 0.0602 and 0.9736, respectively. Furthermore, the QLSTM outperformed other classical models in both metrics.

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.

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.

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.

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.

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.

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.

Quantum machine learning with differential privacy

Quantum machine learning (QML) can complement the growing trend of using learned models for a myriad of classification tasks, from image recognition to natural speech processing. There exists the potential for a quantum advantage due to the intractability of quantum operations on a classical computer. Many datasets used in machine learning are crowd sourced or contain some private information, but to the best of our knowledge, no current QML models are equipped with privacy-preserving features. This raises concerns as it is paramount that models do not expose sensitive information. Thus, privacy-preserving algorithms need to be implemented with QML. One solution is to make the machine learning algorithm differentially private, meaning the effect of a single data point on the training dataset is minimized. Differentially private machine learning models have been investigated, but differential privacy has not been thoroughly studied in the context of QML. In this study, we develop a hybrid quantum-classical model that is trained to preserve privacy using differentially private optimization algorithm. This marks the first proof-of-principle demonstration of privacy-preserving QML. The experiments demonstrate that differentially private QML can protect user-sensitive information without signficiantly diminishing model accuracy. Although the quantum model is simulated and tested on a classical computer, it demonstrates potential to be efficiently implemented on near-term quantum devices [noisy intermediate-scale quantum (NISQ)]. The approach’s success is illustrated via the classification of spatially classed two-dimensional datasets and a binary MNIST classification. This implementation of privacy-preserving QML will ensure confidentiality and accurate learning on NISQ technology.

Hybrid quantum-classical model of mechano-electrochemical effects on graphite-electrolyte interfaces in metal-ion batteries

Electrochemical double layer (EDL) in rechargeable metal-ion batteries is important to ion intercalation and deintercalation (IID) reactions. Mechanical factors of metal-ion batteries shape the local reaction condition in the EDL and further influence the kinetics of IID reactions. This so-called mechano-electrochemical (MEC) effects on IID reactions are treated in this work based on a hybrid quantum–classical (HQC) framework that accounts for the coupling of ion and electron transfer, EDL structure, and mechanical factors. Under well-defined approximations, an analytical expression for the activation energy of IID reactions is obtained, where the MEC effects are explicitly expressed. In particular, a mechano-electrostatic coupling coefficient is defined to describe how the mechanical deformation and structural size influence the IID reactions via changing the local reaction condition in the EDL. The present work represents a step towards microscopic understanding of the MEC effects on the kinetics of IID reactions in rechargeable metal-ion batteries.

Shot Optimization in Quantum Machine Learning Architectures to Accelerate Training

Quantum Machine Learning (QML) has recently emerged as a rapidly growing domain as an intersection of Quantum Computing (QC) and Machine Learning (ML) fields. Hybrid quantum-classical models have demonstrated exponential speedups in various machine learning tasks compared to their classical counterparts. On one hand, training of QML models on real hardware remains a challenge due to long wait queue and the access cost. On the other hand, simulation-based training is not scalable to large QML models due to exponentially growing simulation time. Since the measurement operation converts quantum information to classical binary data, the quantum circuit is executed multiple times (called shots) to obtain the basis state probabilities or qubit expectation values. Higher number of shots worsen the training time of QML models on real hardware and the access cost. Higher number of shots also increase the simulation-based training time. In this paper, we propose shot optimization method for QML models at the expense of minimal impact on model performance. We use classification task as a test case for MNIST and FMNIST datasets using a hybrid quantum-classical QML model. First, we sweep the number of shots for short and full versions of the dataset. We observe that training the full version provides 5-6% higher testing accuracy than short version of dataset with up to 10X higher number of shots for training. Therefore, one can reduce the dataset size to accelerate the training time. Next, we propose adaptive shot allocation on short version dataset to optimize the number of shots over training epochs and evaluate the impact on classification accuracy. We use a (a) linear function where the number of shots reduce linearly with epochs, and (b) step function where the number of shots reduce in step with epochs. We note around 0.01 increase in loss and ~4% (1%) reduction in testing accuracy for reduction in shots by up to 100X (10X) for linear (step) shot function compared to conventional constant shot function for MNIST dataset, and 0.05 increase in loss and ~5-7% (5-7%) reduction in testing accuracy with similar reduction in shots using linear (step) shot function on FMNIST dataset. For comparison, we also use the proposed shot optimization methods to perform ground state energy estimation of different molecules and observe that step function gives the best and most stable ground state energy prediction at 1000X less number of shots.

A HYBRID QUANTUM-PERFECTED MODEL OF ARTIFICIAL INTELLIGENCE IN THE PROBLEM OF AUTOMATIC RECOGNITION AND FAST CONVERSION OF UNSTRUCTURED TEXT INFORMATION INTO SPATIAL

Background. Efficiently converting large amounts of unstructured text data into spatial information is crucial for managing water distribution systems. This allows for the conversion of extensive sets of text information, such as reports, orders, letters, and other documents, into point classes of spatial objects in geographic information systems. To tackle this challenge, a promising new approach involves combining hybrid quantum-classical neural networks with geo-information technologies. Methods. The study utilized quantum-enhanced hybrid neural networks in combination with GIS methods to identify named entities such as personal accounts and balance sheet objects of Kyivvodokanal by their addresses and geocoding. This information was then published on a geoportal using the ArcGIS Enterprise platform in real-time, which holds great promise for effective water management. The performance of the developed model was evaluated by accuracy indicators, recall parameters, and weighted harmonic average of accuracy and recall. Results. The obtained results indicate that the developed hybrid quantum-classical model of artificial intelligence can be successfully applied to transform large volumes of unstructured textual information into spatial information. The model was integrated into GIS using ArcGIS Enterprise. By combining the obtained point classes of spatial objects with already existing data, methods of spatial connections, an interactive map with an update interval of every five minutes was developed. Conclusions. Taking advantage of quantum computing and combining it with classical hardware and classical AI models, it became possible to achieve similar and even better performance in various tasks compared to state-of-the-art methods. Quantum natural language processing is a promising new field that has the potential to revolutionize the way one analyzes and understands human language.

Multiclass classification using quantum convolutional neural networks with hybrid quantum-classical learning

Multiclass classification is of great interest for various applications, for example, it is a common task in computer vision, where one needs to categorize an image into three or more classes. Here we propose a quantum machine learning approach based on quantum convolutional neural networks for solving the multiclass classification problem. The corresponding learning procedure is implemented via TensorFlowQuantum as a hybrid quantum-classical (variational) model, where quantum output results are fed to the softmax activation function with the subsequent minimization of the cross entropy loss via optimizing the parameters of the quantum circuit. Our conceptional improvements here include a new model for a quantum perceptron and an optimized structure of the quantum circuit. We use the proposed approach to solve a 4-class classification problem for the case of the MNIST dataset using eight qubits for data encoding and four ancilla qubits; previous results have been obtained for 3-class classification problems. Our results show that the accuracy of our solution is similar to classical convolutional neural networks with comparable numbers of trainable parameters. We expect that our findings will provide a new step toward the use of quantum neural networks for solving relevant problems in the NISQ era and beyond.

Unbiasing fermionic quantum Monte Carlo with a quantum computer

Interacting many-electron problems pose some of the greatest computational challenges in science, with essential applications across many fields. The solutions to these problems will offer accurate predictions of chemical reactivity and kinetics, and other properties of quantum systems1–4. Fermionic quantum Monte Carlo (QMC) methods5,6, which use a statistical sampling of the ground state, are among the most powerful approaches to these problems. Controlling the fermionic sign problem with constraints ensures the efficiency of QMC at the expense of potentially significant biases owing to the limited flexibility of classical computation. Here we propose an approach that combines constrained QMC with quantum computation to reduce such biases. We implement our scheme experimentally using up to 16 qubits to unbias constrained QMC calculations performed on chemical systems with as many as 120 orbitals. These experiments represent the largest chemistry simulations performed with the help of quantum computers, while achieving accuracy that is competitive with state-of-the-art classical methods without burdensome error mitigation. Compared with the popular variational quantum eigensolver7,8, our hybrid quantum-classical computational model offers an alternative path towards achieving a practical quantum advantage for the electronic structure problem without demanding exceedingly accurate preparation and measurement of the ground-state wavefunction.

Hilbert bundles as quantum-classical continua

A hybrid quantum–classical model is proposed whereby a micro-structured (Cosserat-type) continuum is construed as a principal Hilbert bundle. A numerical example demonstrates the possible applicability of the theory.

TensorFlow Quantum: Impacts of Quantum State Preparation on Quantum Machine Learning Performance

Learning methodologies on quantum devices have shown that there are advantages in utilizing quantum properties. A requirement for using quantum computing in machine learning techniques is the data representation as quantum states. In Quantum Machine Learning, quantum state preparation is paramount to attain a functional pipeline in a model. One state preparation method, amplitude encoding, allows a dataset to be mapped or encoded more robustly and enhances the learning of quantum models. Albeit more densely represented, a dataset which has been prepared by amplitude encoding provides a more learnable input to a model. The two main advantages from using amplitude encoding are an increase in classification accuracy and reduced variability of learning epoch to epoch. In this paper, we compare the basic implementations of TensorFlow Quantum’s Quantum Convolutional Neural Network and a hybrid quantum-classical network using angle encoding, with a third network of our design that utilizes amplitude encoding for enriched state preparation. Our results show there is a direct benefit in performing amplitude encoding before training a TensorFlow Quantum hybrid quantum-classical model. In the best case scenario, amplitude encoding made classifying the samples 8.9% more accurate.

Charge-transfer plasmons with narrow conductive molecular bridges: A quantum-classical theory.

We analyze a new type of plasmon system arising from small metal nanoparticles linked by narrow conductive molecular bridges. In contrast to the well-known charge-transfer plasmons, the bridge in these systems consists only of a narrow conductive molecule or polymer in which the electrons move in a ballistic mode, showing quantum effects. The plasmonic system is studied by an original hybrid quantum-classical model accounting for the quantum effects, with the main parameters obtained from first-principles density functional theory simulations. We have derived a general analytical expression for the modified frequency of the plasmons and have shown that its frequency lies in the near-infrared (IR) region and strongly depends on the conductivity of the molecule, on the nanoparticle-molecule interface, and on the size of the system. As illustrated, we explored the plasmons in a system consisting of two small gold nanoparticles linked by a conjugated polyacetylene molecule terminated by sulfur atoms. It is argued that applications of this novel type of plasmon may have wide ramifications in the areas of chemical sensing and IR deep tissue imaging.

A Hybrid Quantum-Classical Model of Electrostatics in Multiply Charged Quantum Dots

We present a general model for describing the properties of excess electrons in multiply charged quantum dots (QDs). Key factors governing Fermi-level energies and electron density distributions are investigated by treating carrier densities, charge compensation, and various material and dielectric medium properties as independently tunable parameters. Electronic interactions are described using a mean-field electrostatic potential calculable through Gauss's Law by treating the quantum dot as a sphere of uniform charge density. This classical approximation modifies the Particle in a Sphere'' Schrodinger equation for a square well potential and reproduces the broken degeneracy and Fermi-level energies expected from experiment and first-principles methods. Several important implications emerge from this model: (i) Excess electron density drifts substantially towards the QD surfaces with high electron densities and large radii, and when solvated by a high dielectric medium. (ii) The maximum density of condu...

Theoretical Shaping of Femtosecond Laser Pulses for Molecular Photodissociation with Control Techniques Based on Ehrenfest's Dynamics and Time-Dependent Density Functional Theory.

The combination of nonadiabatic Ehrenfest-path molecular dynamics (EMD) based on time-dependent density functional theory (TDDFT) and quantum optimal control formalism (QOCT) was used to optimize the shape of ultra-short laser pulses to achieve photodissociation of a hydrogen molecule and the trihydrogen cation H3 (+) . This work completes a previous one [A. Castro, ChemPhysChem, 2013, 14, 1488-1495], in which the same objective was achieved by demonstrating the combination of QOCT and TDDFT for many-electron systems on static nuclear potentials. The optimization model, therefore, did not include the nuclear movement and the obtained dissociation mechanism could only be sequential: fast laser-assisted electronic excitation to nonbonding states (during which the nuclei are considered to be static), followed by field-free dissociation. Here, in contrast, the optimization was performed with the QOCT constructed on top of the full dynamic model comprised of both electrons and nuclei, as described within EMD based on TDDFT. This is the first numerical demonstration of an optimal control formalism for a hybrid quantum-classical model, that is, a molecular dynamics method.