Quantum Model Research Articles

Extremely asymmetric absorption and reflection near the exceptional point for three-dimensional metamaterial

In recent years, particular physical phenomena enabled by non-Hermitian metamaterial systems have attracted significant research interests. In this paper, a non-Hermitian three-dimensional metamaterial near the exceptional point (EP) is proposed to demonstrate extremely asymmetric absorption and reflection. Unlike its conventional counterparts, this proposed metamaterial is constructed with a loss-assisted design. Localized losses are introduced into the structure by combining our technique of graphene-based resistive inks with conventional printed circuit board process. Extremely asymmetric absorption and reflection near the EP are experimentally observed by tuning the loss between split ring resonators in the meta-atoms. Simultaneously, by linking the equivalent circuit model (ECM) with the quantum model, an equivalent non-Hermitian transmission matrix is constructed. We show that tuning the structure parameters of the ECM produces a metamaterial system with EP response. Our system can be used in the design of unidirectional metamaterial absorbers. Our work contributes to future works on the manipulation of EP to develop precision sensing and other applications in the 3D metamaterial platform.

Quantum model regression for generating fuzzy numbers in adiabatic quantum computing

This paper addresses the problem of inherent fuzziness in real-world data, arising from uncertainties, complexities, and limitations of traditional statistical methods. We introduce a pioneering method leveraging Adiabatic Quantum Computing (AQC), based on an adiabatic quantum regression model, to generate fuzzy numbers—ideal tools owing to their extension of real numbers and robust arithmetic properties. This innovative approach overcomes challenges in Quantum Machine Learning (QML) and limitations of Noisy Intermediate-Scale Quantum (NISQ) computers, providing a solution superior to conventional statistical methods and addressing the crucial issue of exponential power increase. Unique to this work, we offer rare closed-form expressions to produce fuzzy numbers through AQC and emphasise the integration of random variables and fuzzy numbers to encapsulate uncertainty fully. We propose a novel transformation of the Cumulative Distribution Function (CDF) into triangular and trapezoidal fuzzy numbers using AQC, enabling a comprehensive description of probability distributions of random variables. Experimental results are detailed, demonstrating the significant applicability and breakthroughs of this research in addressing data fuzziness.

Comparing Natural Language Processing and Quantum Natural Processing approaches in text classification tasks

Quantum physics and mechanics have demonstrated significant advances and promising results in different areas using the current near-term devices. One emerging subarea in quantum machine learning is quantum natural language processing, which combines quantum computing advantages and speedups with language processing algorithms to create and perform natural language tasks such as text classification or generation. The libraries and toolboxes used in this subarea include DisCoPy and lambeq, which are used to transform sentences into string diagrams or monoidal functors, convert these diagrams into quantum circuits or ansatz and embed it into a quantum model. In this study, we used both libraries with different text-based datasets to perform sentiment analysis via classification. To do so, we create synthetic datasets to train the different models. After we obtain satisfactory results, we test the resulting models with known datasets. Despite its promising results, quantum natural language processing is far from achieving its full potential. To achieve this potential, the quantum software and hardware must be improved to make them suitable for use with more extensive and complex datasets and other tasks.

QUANTUM DISCORD AND ENTANGLEMENT FOR TWO ATOMS IN A KERR MEDIUM AND STARK SHIFT

. This study analyzes the effect of the Kerr medium and Stark shift on the entanglement between two two-level atoms and a single-mode cavity in a quantum model. The findings demonstrate that the entanglement between the atoms varies periodically over time, with the periods affected by the Kerr medium and Stark shift. The Kerr medium and Stark shift hinder atom disentanglement, resulting in a prolonged stationary entangled state. The Stark shift can also enhance atom-atom entanglement for partially entangled states. These findings reveal that the Kerr medium and Stark shift can effectively control the entanglement between two atoms. Moreover, weak measurement strength impacts quantum particles' entanglement, which decreases over time. Quantum discord is more affected by weak measurement strengths than entanglement, decreasing until a critical point and increasing with a further rise in weak measurement strengths.

Interpreting variational quantum models with active paths in parameterized quantum circuits

Variational quantum machine learning (VQML) models based on parameterized quantum circuits (PQC) have been expected to offer a potential quantum advantage for machine learning (ML) applications. However, comparison between VQML models and their classical counterparts is hard due to the lack of interpretability of VQML models. In this study, we introduce a graphical approach to analyze the PQC and the corresponding operation of VQML models to deal with this problem. In particular, we utilize the Stokes representation of quantum states to treat VQML models as network models based on the corresponding representations of basic gates. From this approach, we suggest the notion of active paths in the networks and relate the expressivity of VQML models with it. We investigate the growth of active paths in VQML models and observe that the expressivity of VQML models can be significantly limited for certain cases. Then we construct classical models inspired by our graphical interpretation of VQML models and show that they can emulate or outperform the outputs of VQML models for these cases. Our result provides a new way to interpret the operation of VQML models and facilitates the interconnection between quantum and classical ML areas.

Nonlinear solution of classical three-wave interaction via finite-dimensional quantum model

The quantum three-wave interaction, the lowest-order nonlinear interaction in plasma physics, describes energy–momentum transfer between three resonant waves in the quantum regime. We describe how it may also act as a finite-degree-of-freedom approximation to the classical three-wave interaction in certain circumstances. By promoting the field variables to operators, we quantize the classical system, show that the quantum system has more free parameters than the classical system and explain how these parameters may be selected to optimize either initial or long-term correspondence. We then numerically compare the long-time quantum–classical correspondence far from the fixed point dynamics. We discuss the Poincaré recurrence of the system and the mitigation of quantum scrambling.

Multi-Unitary Complex Hadamard Matrices

We analyze the set of real and complex Hadamard matrices with additional symmetry constrains. In particular, we link the problem of existence of maximally entangled multipartite states of [Formula: see text] subsystems with [Formula: see text] levels each to the set of complex Hadamard matrices of order [Formula: see text]. To this end, we investigate possible subsets of such matrices which are, dual, strongly dual ([Formula: see text] or [Formula: see text]), two-unitary ([Formula: see text] and [Formula: see text] are unitary), or [Formula: see text]-unitary. Here [Formula: see text] denotes reshuffling of a matrix [Formula: see text] describing a bipartite system, and [Formula: see text] its partial transpose. Such matrices find several applications in quantum many-body theory, tensor networks and classification of multipartite quantum entanglement and imply a broad class of analytically solvable quantum models in [Formula: see text] dimensions.

Dequantizing quantum machine learning models using tensor networks

Ascertaining whether a classical model can efficiently replace a given quantum model——is crucial in assessing the true potential of quantum algorithms. In this work, we introduced the dequantizability of the function class of variational quantum-machine-learning (VQML) models by employing the tensor network formalism, effectively identifying every VQML model as a subclass of matrix product state (MPS) model characterized by constrained coefficient MPS and tensor product-based feature maps. From this formalism, we identify the conditions for which a VQML model's function class is dequantizable or not. Furthermore, we introduce an efficient quantum kernel-induced classical kernel which is as expressive as given any quantum kernel, hinting at a possible way to dequantize quantum kernel methods. This presents a thorough analysis of VQML models and demonstrates the versatility of our tensor-network formalism to properly distinguish VQML models according to their genuine quantum characteristics, thereby unifying classical and quantum machine-learning models within a single framework. Published by the American Physical Society 2024

NoRA: A Tensor Network Ansatz for Volume-Law Entangled Equilibrium States of Highly Connected Hamiltonians

Motivated by the ground state structure of quantum models with all-to-all interactions such as mean-field quantum spin glass models and the Sachdev-Ye-Kitaev (SYK) model, we propose a tensor network architecture which can accomodate volume law entanglement and a large ground state degeneracy. We call this architecture the non-local renormalization ansatz (NoRA) because it can be viewed as a generalization of MERA, DMERA, and branching MERA networks with the constraints of spatial locality removed. We argue that the architecture is potentially expressive enough to capture the entanglement and complexity of the ground space of the SYK model, thus making it a suitable variational ansatz, but we leave a detailed study of SYK to future work. We further explore the architecture in the special case in which the tensors are random Clifford gates. Here the architecture can be viewed as the encoding map of a random stabilizer code. We introduce a family of codes inspired by the SYK model which can be chosen to have constant rate and linear distance at the cost of some high weight stabilizers. We also comment on potential similarities between this code family and the approximate code formed from the SYK ground space.

Multi-attribute quantum group interference decision model considering minimum constraint and information entropy

About multi-attribute group decision making process, the opinions of different decisions will interfere with each other, or be affected by the decision-making environment, resulting in an unobserved interference effect, which is regarded as quantum entanglement in quantum theory. In this paper, an interference effect model based on minimum constraint and information entropy is proposed to measure the interference value in quantum decision models. Firstly, considering the interference effects of decision makers’ opinions, the evaluation opinions of decision makers are aggregated using Quantum-like Bayesian Network (QLBN), which are regarded as wave functions superimposed in the quantum model. Secondly, due to the uncertainty of decision process, information entropy and minimum constraint are combined to solve the interference effect. The minimum constraint is used to limit the range of interference values and the information entropy represents the uncertainty in the decision process. The grey relational degree represents the conditional probability of the decision maker about the alternatives. Thirdly, the weights of attributes and the probabilities of the alternatives are aggregated about decision makers by the proposed interference effect model, and then the alternatives are ranked by the aggregated probabilities. Subsequently, a numerical example is used to verify the validity and rationality of the model. Comparative analyses and sensitivity analyses are also implemented to demonstrate the stability and reliability of our method.

Once-in-a-lifetime encounter models for neutrino media: From coherent oscillations to flavor equilibration

Collective neutrino oscillations are typically studied using the lowest-order quantum kinetic equation, also known as the mean-field approximation. However, some recent quantum many-body simulations suggest that quantum entanglement among neutrinos may be important and may result in flavor equilibration of the neutrino gas. In this work, we develop new quantum models for neutrino gases in which any pair of neutrinos can interact at most once in their lifetimes. A key parameter of our models is γ=μΔz, where μ is the neutrino coupling strength, which is proportional to the neutrino density, and Δz is the duration over which a pair of neutrinos can interact each time. Our models reduce to the mean-field approach in the limit γ→0 and achieve flavor equilibration in time t≫(γμ)−1. These models demonstrate the emergence of coherent flavor oscillations from the particle perspective and may help elucidate the role of quantum entanglement in collective neutrino oscillations. Published by the American Physical Society 2024

Hybrid quantum physics-informed neural networks for simulating computational fluid dynamics in complex shapes

Finding the distribution of the velocities and pressures of a fluid by solving the Navier–Stokes equations is a principal task in the chemical, energy, and pharmaceutical industries, as well as in mechanical engineering and in design of pipeline systems. With existing solvers, such as OpenFOAM and Ansys, simulations of fluid dynamics in intricate geometries are computationally expensive and require re-simulation whenever the geometric parameters or the initial and boundary conditions are altered. Physics-informed neural networks (PINNs) are a promising tool for simulating fluid flows in complex geometries, as they can adapt to changes in the geometry and mesh definitions, allowing for generalization across fluid parameters and transfer learning across different shapes. We present a hybrid quantum PINN (HQPINN) that simulates laminar fluid flow in 3D Y-shaped mixers. Our approach combines the expressive power of a quantum model with the flexibility of a PINN, resulting in a 21% higher accuracy compared to a purely classical neural network. Our findings highlight the potential of machine learning approaches, and in particular HQPINN, for complex shape optimization tasks in computational fluid dynamics. By improving the accuracy of fluid simulations in complex geometries, our research using hybrid quantum models contributes to the development of more efficient and reliable fluid dynamics solvers.

Cyber Risk in Insurance: A Quantum Modeling

In this research, we consider cyber risk in insurance using a quantum approach, with a focus on the differences between reported cyber claims and the number of cyber attacks that caused them. Unlike the traditional probabilistic approach, quantum modeling makes it possible to deal with non-commutative event paths. We investigate the classification of cyber claims according to different cyber risk behaviors to enable more precise analysis and management of cyber risks. Additionally, we examine how historical cyber claims can be utilized through the application of copula functions for dependent insurance claims. We also discuss classification, likelihood estimation, and risk-loss calculation within the context of dependent insurance claim data.

The quantum model of T-cell activation: Revisiting immune response theories.

Our understanding of the immune response is far from complete, missing out on more detailed explanations that could be provided by molecular insights. To bridge this gap, we introduce the quantum model of T-cell activation. This model suggests that the transfer of energy during protein phosphorylation within T cells is not a continuous flow but occurs in discrete bursts, or 'quanta', of phosphates. This quantized energy transfer is mediated by oscillating cycles of receptor phosphorylation and dephosphorylation, initiated by dynamic 'catch-slip' pulses in the peptide-major histocompatibility complex-T-cell receptor (pMHC-TcR) interactions. T-cell activation is predicated upon achieving a critical threshold of catch-slip pulses at the pMHC-TcR interface. Costimulation is relegated to a secondary role, becoming crucial only when the frequency of pMHC-TcR catch-slip pulses does not meet the necessary threshold for this quanta-based energy transfer. Therefore, our model posits that it is the quantum nature of energy transfer-not the traditional signal I or signal II-that plays the decisive role in T-cell activation. This paradigm shift highlights the importance of understanding T-cell activation through a quantum lens, offering a potentially transformative perspective on immune response regulation.

Quantum description of atomic diffraction by material nanostructures

We present a theoretical model of matter-wave diffraction through a material nanostructure. This model is based on the numerical solution of the time-dependent Schrödinger equation, which goes beyond the standard semiclassical approach. In particular, we consider the dispersion force interaction between the atoms and the material, which is responsible for high energy variations. The effect of such forces on the quantum model is investigated, along with a comparison with the semiclassical model. In particular, for atoms at low velocity and close to the material surface, the semiclassical approach fails, while the quantum model accurately describes the expected diffraction pattern. This description is thus relevant for slow and cold atom experiments where increased precision is required, e.g., for metrological applications. Published by the American Physical Society 2024

USE OF QUANTUM MODELS IN THE STUDY OF RELATIONSHIPS BETWEEN INNOVATIONS AND ECONOMIC DEVELOPMENT

The article analyzes the main aspects of the application of quantum models for the analysis of relationships between innovations and economic growth, which are a promising direction in economic science. The influence of trends and challenges of globalization and accelerated technological innovations, which play a key role in realizing competitive advantages and increasing productivity, is determined; in promoting the sustainable development of the economy. The author defines the dynamics of innovation processes, which causes the need for new approaches, such as the principles of quantum modeling, defines the content of quantum models in global business. In particular, the principles that allow for more accurate modeling of uncertainty and non-linear processes characteristic of innovative activity are considered. The author pays special attention to the use of quantum models for accurate forecasting and planning of economic development, development of effective strategies for scientific research and state policy in the field of innovation. The recommendations are aimed at carrying out a comprehensive analysis and assessment of the impact of quantum technologies on economic indicators of employment, indicators of investment activity and international trade. In further scientific developments, it is expected to improve the comparative analysis of classical and quantum economic models for determining effective approaches to innovation management. A promising direction of scientific research is the development of a methodical tool for optimizing investments in research and R&D to improve the mechanisms of state support for innovative activities. Emphasis is placed on the fact that research results will contribute to the creation of a new generation of economic strategies based on the principles of quantum economics, and will open up new horizons for the growth and development of the world market.

Quantum Vision Transformers for Quark–Gluon Classification

We introduce a hybrid quantum-classical vision transformer architecture, notable for its integration of variational quantum circuits within both the attention mechanism and the multi-layer perceptrons. The research addresses the critical challenge of computational efficiency and resource constraints in analyzing data from the upcoming High Luminosity Large Hadron Collider, presenting the architecture as a potential solution. In particular, we evaluate our method by applying the model to multi-detector jet images from CMS Open Data. The goal is to distinguish quark-initiated from gluon-initiated jets. We successfully train the quantum model and evaluate it via numerical simulations. Using this approach, we achieve classification performance almost on par with the one obtained with the completely classical architecture, considering a similar number of parameters.

Error estimation in current noisy quantum computers

One of the main important features of the noisy intermediate-scale quantum (NISQ) era is the correct evaluation and consideration of errors. In this paper, we analyse the main sources of errors in current (IBM) quantum computers and we present a useful tool (TED-qc) designed to facilitate the total error probability expected for any quantum circuit. We propose this total error probability as the best way to estimate a lower bound for the fidelity in the NISQ era, avoiding the necessity of comparing the quantum calculations with any classical one. In order to contrast the robustness of our tool we compute the total error probability that may occur in three different quantum models: 1) the Ising model, 2) the Quantum-Phase Estimation (QPE), and 3) the Grover’s algorithm. For each model, the main quantities of interest are computed and benchmarked against the reference simulator’s results as a function of the error probability for a representative and statistically significant sample size. The analysis is satisfactory in more than the 99%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$99\\%$$\\end{document} of the cases. In addition, we study how error mitigation techniques are able to eliminate the noise induced during the measurement. These results have been calculated for the IBM quantum computers, but both the tool and the analysis can be easily extended to any other quantum computer.

Accuracy vs memory advantage in the quantum simulation of stochastic processes

Many inference scenarios rely on extracting relevant information from known data in order to make future predictions. When the underlying stochastic process satisfies certain assumptions, there is a direct mapping between its exact classical and quantum simulators, with the latter asymptotically using less memory. Here we focus on studying whether such quantum advantage persists when those assumptions are not satisfied, and the model is doomed to have imperfect accuracy. By studying the trade-off between accuracy and memory requirements, we show that quantum models can reach the same accuracy with less memory, or alternatively, better accuracy with the same memory. Finally, we discuss the implications of this result for learning tasks.

Quantum model of galactic halos with an Navarro-Frenk-White dark matter profile

A quantum model of a cold dark matter galactic halo is developed. The model requires specifying the mass and radius of the halo as well as its density profile. The structure of the halo resulting from the theory is predicted and its physical properties are determined. Verification of these theoretical predictions by observations is proposed and discussed. The model is constructed by analytically solving the governing equation and using its time-independent solutions to determine the internal structure of a galactic halo with an Navarro-Frenk-White cold dark matter density profile. The governing equation that is the basis of the developed theory is derived from the irreducible representations of the extended Galilean group. The method of finding the solutions is analytical, even though an Navarro-Frenk-White density profile is used in the calculations. The theory predicts a halo with a core composed of free dark matter particles that move randomly with frequent collisions. It also predicts an envelope in which the particles are confined to their orbits, which are quantized. Except in the close vicinity of the core, the population of the orbits remains fixed, and physical reasons for the nonexistence of quantum jumps between these orbits are presented. A quantum model of a galactic cold dark matter halo with a given Navarro-Frenk-White density profile is constructed. It predicts a quantum structure of the halo that is significantly different than any previously known dark matter model. The quantum model naturally accounts for dark matter being collisionless, and it predicts that dark matter can only emit radiation of one fixed frequency. The values of this frequency are computed for dark matter particles of different masses. A potential observational verification of the theory is also discussed.