Exact Simulation Research Articles

Exact Simulation of Quadratic Intensity Models

We develop efficient algorithms of exact simulation for quadratic stochastic intensity models that have become increasingly popular for modeling events arrivals, especially in economics, finance, and insurance. They have huge potential to be applied to many other areas such as operations management, queueing science, biostatistics, and epidemiology. Our algorithms are developed by the principle of exact distributional decomposition, which lies in a fully analytical expression for the joint Laplace transform of quadratic process and its integral newly derived in this paper. They do not involve any numerical Laplace inversion, have been validated by extensive numerical experiments, and substantially outperform all existing alternatives in the literature. Moreover, our algorithms are extendable to multidimensional point processes and beyond Cox processes to additionally incorporate two-sided random jumps with arbitrarily distributed sizes in the intensity for capturing self-exciting and self-correcting effects in event arrivals. Applications to portfolio loss modeling are provided to demonstrate the applicability and flexibility of our algorithms. History: Accepted by Bruno Tuffin, Area Editor for Simulation. Funding: This work was supported by the Beijing University of Posts and Telecommunications [Grant 2022RC58], the Shanghai University of Finance and Economics [Grant 2020110930], the National Natural Science Foundation of China [Grant 71401147], and Graduate Innovation Fund of Shanghai University of Finance and Economics [CXJJ-2023-387]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0323 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0323 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Extending Non-Perturbative Simulation Techniques for Open-Quantum Systems to Excited-State Proton Transfer and Ultrafast Non-Adiabatic Dynamics.

Excited state proton transfer is an ubiquitous phenomenon in biology and chemistry, spanning from the ultrafast reactions of photobases and acids to light-driven, enzymatic catalysis and photosynthesis. However, the simulation of such dynamics involves multiple challenges, since high-dimensional, out-of-equilibrium vibronic states play a crucial role, while a fully quantum description of the proton's dissipative, real-space dynamics is also required. In this work, we extend the powerful matrix product state approach to open quantum systems (TEDOPA) to study these demanding dynamics, and also more general nonadiabatic processes that can appear in complex photochemistry subject to strong laser driving. As an illustration, we initially consider an open model of a four-level electronic system interacting with hundreds of intramolecular vibrations that drive ultrafast excited state proton transfer, as well as an explicit photonic environment that allows us to directly monitor the resulting dual fluorescence in this system. We then demonstrate how to include a continuous "reaction coordinate" of the proton transfer that allows numerically exact simulations that can be understood, visualized and interpreted in the familiar language of diabatic and adiabatic dynamics on potential surfaces, while also retaining an exact quantum treatment of dissipation and driving effects that could be used to study diverse problems in ultrafast photochemistry.

An Exact Stochastic Simulation Method for Fractional Order Compartment Models

An Exact Stochastic Simulation Method for Fractional Order Compartment Models

Efficient simulation of open quantum systems coupled to a reservoir through multiple channels.

It is challenging to simulate open quantum systems that are connected to a reservoir through multiple channels. For example, vibrations may induce fluctuations in both energy gaps and electronic couplings, which represent two independent channels of system-bath couplings. Systems of this kind are ubiquitous in the processes of excited state radiationless decay. Combined with density matrix renormalization group (DMRG) and matrix product states (MPS) methods, we develop an interaction-picture chain mapping strategy for vibrational reservoirs to simulate the dynamics of these open systems, resulting in time-dependent spatially local system-bath couplings in the chain-mapped Hamiltonian. This transformation causes the entanglement generated by the system-bath interactions to be restricted within a narrow frequency window of vibrational modes, enabling efficient DMRG/MPS dynamical simulations. We demonstrate the utility of this approach by simulating singlet fission dynamics using a generalized spin-boson Hamiltonian with both diagonal and off-diagonal system-bath couplings. This approach generalizes an earlier interaction-picture chain mapping scheme, allowing for efficient and exact simulation of systems with multi-channel system-bath couplings using matrix product states, which may further our understanding of nonlocal exciton-phonon couplings in exciton transport and the non-Condon effect in energy and electron transfer.

Coupled Thermal and Power Transport of Optical Waveguide Arrays: Photonic Wiedemann-Franz Law and Rectification Effect.

In isolated nonlinear optical waveguide arrays, simultaneous conservation of longitudinal momentum flow ("internal energy") and optical power ("particle number") of the optical modes enables study of coupled thermal and particle transport in the negative temperature regime. Based on exact numerical simulation and rationale from Landauer formalism, we predict generic photonic version of the Wiedemann-Franz law in such systems, with the Lorenz number L∝|T|^{-2}. This is rooted in the spectral decoupling of thermal and particle current, and their different temperature dependence. In addition, in asymmetric junctions, relaxation of the system toward equilibrium shows apparent asymmetry for positive and negative biases, indicating rectification behavior. This Letter illustrates the possibility of simulate nonequilibrium transport processes using optical networks, in parameter regimes difficult to reach in natural condensed matter or atomic gas systems. It also provides new insights in manipulating power and momentum flow of optical waves in artificial waveguide arrays.

A stochastic Schrödinger equation and matrix product state approach to carrier transport in organic semiconductors with nonlocal electron-phonon interaction.

Evaluation of the charge transport property of organic semiconductors requires exact quantum dynamics simulation of large systems. We present a numerically nearly exact approach to investigate carrier transport dynamics in organic semiconductors by extending the non-Markovian stochastic Schrödinger equation with complex frequency modes to a forward-backward scheme and by solving it using the matrix product state (MPS) approach. By utilizing the forward-backward formalism for noise generation, the bath correlation function can be effectively treated as a temperature-independent imaginary part, enabling a more accurate decomposition with fewer complex frequency modes. Using this approach, we study the carrier transport and mobility in the one-dimensional Peierls model, where the nonlocal electron-phonon interaction is taken into account. The reliability of this approach was validated by comparing carrier diffusion motion with those obtained from the hierarchical equations of motion method across various parameter regimes of the phonon bath. The efficiency was demonstrated by the modest virtual bond dimensions of MPS and the low scaling of the computational time with the system size.

Theory and quantum dynamics simulations of exciton-polariton motional narrowing.

The motional narrowing effect has been extensively studied for cavity exciton-polariton systems in recent decades both experimentally and theoretically, which is featured by (1) the subaverage behavior and (2) the asymmetric linewidths for the upper polariton and the lower polariton. However, a minimal theoretical model that is clear and adequate to address all these effects as well as the linewidth scaling relations remains missing. In this work, based on the single mode 1D Holstein-Tavis-Cummings (HTC) model, we studied the motional narrowing effect of the polariton linear absorption spectra via both semi-analytic derivations and numerically exact quantum dynamics simulations using the hierarchical equations of motion approach. The results reveal that under collective light-matter coupling between a cavity mode and N molecules, the polariton linewidth scales as 1/N under the slow limit, while scales as 1/N under the fast limit, due to the polaron decoupling effect. Furthermore, by varying the detunings, the polariton linewidths exhibit significant motional narrowing, covering both characters mentioned above. Our analytic linewidth expressions [Eqs. (34) and (35)] agree well with the numerical exact simulations in all the parameter regimes we explored. These results indicate that the physics of motional narrowing is adequately accounted for by the single-mode 1D HTC model. We envision that both the numerical results and the analytic polariton linewidths expression presented in this work will offer great theoretical value for providing a better understanding of the exciton-polariton motional narrowing based on the HTC model.

Artificial Intelligence Applied to Microwave Heating Systems: Prediction of Temperature Profile through Convolutional Neural Networks

Microwave heating, which is caused by the interaction of electromagnetic radiation and materials, has become an important component in industrial operations across numerous industries. Despite their importance, conventional numerical simulations of microwave heating are computationally intensive. Concurrently, advances in artificial intelligence (AI), particularly machine learning algorithms, have transformed data processing by increasing accuracy while decreasing computational time. This study tackles the difficulty of efficient and accurate modelling in microwave heating by combining convolutional neural networks (CNNs) with traditional simulation techniques. The major goal of this research is to use CNNs to forecast temperature profiles in a variety of industrial materials, including susceptors, semi-transparent, and microwave-transparent materials, under varying power settings and heating periods. This unique strategy greatly reduces prediction times, with up to 60-fold speed increases over standard methods. Our research is based on examining the electromagnetic and thermal responses of these materials under microwave heating. This study’s findings emphasise the need for extensive datasets and show the transformational potential of CNNs in optimising material processing. It uses artificial intelligence to pave the way for more effective and exact simulations, supporting breakthroughs in industrial microwave heating applications.

Toward Accurate Calculation of Excitation Energies on Quantum Computers with ΔADAPT-VQE: A Case Study of BODIPY Derivatives.

Quantum chemistry simulations offer a cost-effective way to computationally design BODIPY photosensitizers. However, accurate predictions of excitation energies pose a challenge for time-dependent density functional theory and equation-of-motion coupled-cluster singles and doubles methods. By contrast, reliable predictions can be achieved by multireference quantum chemistry methods; unfortunately, their computational cost increases exponentially with the number of electrons. Alternatively, quantum computing holds potential for an exact simulation of the photophysical properties in a computationally more efficient way. Herein, we introduce the state-specific ΔUCCSD-VQE (unitary coupled-cluster singles and doubles-variational quantum eigensolver) and ΔADAPT-VQE methods in which the electronically excited state is calculated via a non-Aufbau configuration. We show for six BODIPY derivatives that the proposed methods predict accurate excitation energies that are in good agreement with those from experiments. Due to its performance and simplicity, we believe that ΔADAPT will become a useful approach for the simulation of BODIPY photosensitizers on near-term quantum devices.

An efficient method for solving high-dimension stationary FPK equation of strongly nonlinear systems under additive and/or multiplicative white noise

Engineering structures may suffer from drastic nonlinear random vibrations in harsh environments. Random vibration has been extensively studied since 1960s, but is still an open problem for large-scale strongly nonlinear systems. In this paper, a random vibration analysis method based on the Neural Networks for large-scale strongly nonlinear systems under additive and/or multiplicative Gaussian white noise (GWN) excitations is proposed. In the proposed method, the high-dimensional steady-state Fokker–Planck-Kolmogorov (FPK) equation governing the state’s probability density function (PDF) is firstly reduced to low-dimensional FPK equation involving only the interested state variables, generally one or two dimensions. The equivalent drift coefficients (EDCs) and diffusion coefficients (EDFs) in the low-dimensional FPK equation are proven to be the conditional mean of the coefficients given the interested variables. Furthermore, it is shown that the conditional mean can be optimally estimated by regression. Subsequently, the EDCs and EDFs, as functions of the retained variables, are approximated by the semi-analytical Radial Basis Functions Neural Networks trained with samples generated by a few deterministic analyses. Finally, the Physics Informed Neural Network is employed to solve the reduced steady-state FPK equation, and the PDF of the system responses is obtained. Four typical examples under additive and/or multiplicative GWN excitations are used to examine the accuracy and efficiency of the proposed method by comparing its results with the exact solution (if available) or Monte Carlo simulations. The proposed method also exhibits greater accuracy than the globally-evolving-based generalized density evolution equation scheme, a similar method of its kind, especially for strongly nonlinear systems. Notably, even though steady-state systems are applied in this paper, there is no obstacle to extending the proposed framework to transient systems.

Does the Correlation between 2MRS Galaxies and the CMB Indicate an Unmodeled CMB Foreground?

We revisit the claimed detection of a new cosmic microwave background (CMB) foreground based on the correlation between low-redshift Two Micron All Sky Survey Redshift Survey (2MRS) galaxies and CMB temperature maps from the Planck and Wilkinson Microwave Anisotropy Probe missions. We reproduce the reported measurements but argue that the original analysis significantly underestimated the uncertainties. We cross-correlate the 2MRS galaxy positions with simulated CMB maps and show that the correlation measured with the real data for late-type spiral galaxies at angular scales θ ≥ 0.°1 and redshift cz < 4500 km s−1 is consistent with zero at the 1.7σ level or less, depending on the exact CMB map and simulation construction. This was the sample that formed the basis for the original detection claim. For smaller angular separations the results are not robust to galaxy type or CMB cleaning method, and we are unable to draw firm conclusions. The original analysis did not propose a specific, falsifiable physical correlation mechanism, and it is impossible to rule out any contribution from an underlying physical effect. However, given our calculations, the lack of signal from expanding the redshift range, and the lack of corroboration from other galaxy surveys, we do not find the evidence for a new CMB foreground signal compelling.

Bath-induced interactions and transient dynamics in open quantum systems at strong coupling: Effective Hamiltonian approach.

Understanding the dynamics of dissipative quantum systems, particularly beyond the weak coupling approximation, is central to various quantum applications. While numerically exact methods provide accurate solutions, they often lack the analytical insight provided by theoretical approaches. In this study, we employ the recently developed method dubbed the effective Hamiltonian theory to understand the dynamics of system-bath configurations without resorting to a perturbative description of the system-bath coupling energy. Through a combination of mapping steps and truncation, the effective Hamiltonian theory offers both analytical insights into signatures of strong couplings in open quantum systems and a straightforward path for numerical simulations. To validate the accuracy of the method, we apply it to two canonical models: a single spin immersed in a bosonic bath and two noninteracting spins in a common bath. In both cases, we study the transient regime and the steady state limit at nonzero temperature and spanning system-bath interactions from the weak to the strong regime. By comparing the results of the effective Hamiltonian theory with numerically exact simulations, we show that although the former overlooks non-Markovian features in the transient equilibration dynamics, it correctly captures non-perturbative bath-generated couplings between otherwise non-interacting spins, as observed in their synchronization dynamics and correlations. Altogether, the effective Hamiltonian theory offers a powerful approach for understanding strong coupling dynamics and thermodynamics, capturing the signatures of such interactions in both relaxation dynamics and in the steady state limit.

Understanding Central Spin Decoherence Due to Interacting Dissipative Spin Baths.

We propose a new approach to simulate the decoherence of a central spin coupled to an interacting dissipative spin bath with cluster-correlation expansion techniques. We benchmark the approach on generic 1D and 2D spin baths and find excellent agreement with numerically exact simulations. Our calculations show a complex interplay between dissipation and coherent spin exchange, leading to increased central spin coherence in the presence of fast dissipation. Finally, we model near-surface nitrogen-vacancy centers in diamond and show that accounting for bath dissipation is crucial to understanding their decoherence. Our method can be applied to a variety of systems and provides a powerful tool to investigate spin dynamics in dissipative environments.

Fast Exact Simulation of the First Passage of a Tempered Stable Subordinator Across a Non-Increasing Function

Fast Exact Simulation of the First Passage of a Tempered Stable Subordinator Across a Non-Increasing Function

Efficient Large-Scale Many-Body Quantum Dynamics via Local-Information Time Evolution

During time evolution of many-body systems entanglement grows rapidly, limiting exact simulations to small-scale systems or small timescales. Quantum information tends, however, to flow towards larger scales without returning to local scales, such that its detailed large-scale structure does not directly affect local observables. This allows for the removal of large-scale quantum information in a way that preserves all local observables and gives access to large-scale and large-time quantum dynamics. To this end, we use the recently introduced to organize quantum information into different scales, allowing us to define and that we employ to systematically discard long-range quantum correlations in a controlled way. Our approach relies on decomposing the system into subsystems up to a maximum scale and time evolving the subsystem density matrices by solving the subsystem von Neumann equations in parallel. Importantly, the information flow needs to be preserved during the discarding of large-scale information. To achieve this without the need to make assumptions about the microscopic details of the information current, we introduce a second scale at which information is discarded, while using the state at the maximum scale to accurately obtain the information flow. The resulting algorithm, which we call local-information time evolution, is highly versatile and suitable for investigating many-body quantum dynamics in both closed and open quantum systems with diverse hydrodynamic behaviors. We present results for the energy transport in the mixed-field Ising model and the magnetization transport in the XX spin chain with onsite dephasing where we accurately determine the power-law exponent and the diffusion coefficients. Furthermore, the information lattice framework employed here promises to offer insightful results about the spatial and temporal behavior of entanglement in many-body systems. Published by the American Physical Society 2024

Simplifying the simulation of local Hamiltonian dynamics

Local Hamiltonians Hk describe nontrivial k-body interactions in quantum many-body systems. Here, we address the dynamical simulatability of a k-local Hamiltonian by a simpler one Hk′ with k′&lt;k, under the realistic constraint that both Hamiltonians act on the same Hilbert space. When it comes to exact simulation, we build upon known methods to derive examples of Hk and Hk′ that simulate the same physics. We also address the most realistic case of approximate simulation. There, we upper-bound the error up to which a Hamiltonian can simulate another one, regardless of their internal structure, and show an example suggesting that the accuracy of a (k′=2)-local Hamiltonian to simulate Hk with k&gt;2 increases with k. Finally, we propose a method to search for the k′-local Hamiltonian that simulates, with the highest possible precision, the short time dynamics of a given Hk Hamiltonian. Published by the American Physical Society 2024

Classical and quantum theory of fluctuations for many‐particle systems out of equilibrium

AbstractCorrelated classical and quantum many‐particle systems out of equilibrium are of high interest in many fields, including dense plasmas, correlated solids, and ultracold atoms. Accurate theoretical description of these systems is challenging both, conceptionally and with respect to computational resources. While for classical systems, in principle, exact simulations are possible via molecular dynamics, this is not the case for quantum systems. Alternatively, one can use many‐particle approaches such as hydrodynamics, kinetic theory, or nonequilibrium Green functions (NEGF). However, NEGF exhibit a very unfavorable cubic scaling of the CPU time with the number of time steps. An alternative is the G1–G2 scheme [N. Schlünzen et al., Phys. Rev. Lett. 124, 076601 (2020)] which allows for NEGF simulations with time linear scaling, however, at the cost of large memory consumption. The reason is the need to store the two‐particle correlation function. This problem can be overcome for a number of approximations by reformulating the kinetic equations in terms of fluctuations – an approach that was developed, for classical systems, by Yu.L. Klimontovich [JETP 33, 982 (1957)]. Here, we present an overview of his ideas and extend them to quantum systems. In particular, we demonstrate that this quantum fluctuations approach can reproduce the nonequilibrium GW approximation [E. Schroedter et al., Cond. Matt. Phys. 25, 23401 (2022)] promising high accuracy at low computational cost which arises from an effective semiclassical stochastic sampling procedure. We also demonstrate how to extend the approach to the two‐time exchange‐correlation functions and the density response properties. [E. Schroedter et al., Phys. Rev. B 108, 205109 (2023)]. The results are equivalent to the Bethe–Salpeter equation for the two‐time exchange‐correlation function when the generalized Kadanoff‐Baym ansatz with Hartree‐Fock propagators is applied [E. Schroedter and M. Bonitz, phys. stat. sol. (b) 2024, 2300564].

Hilbert Space Delocalization under Random Unitary Circuits.

The unitary dynamics of a quantum system initialized in a selected basis state yield, generically, a state that is a superposition of all the basis states. This process, associated with the quantum information scrambling and intimately tied to the resource theory of coherence, may be viewed as a gradual delocalization of the system's state in the Hilbert space. This work analyzes the Hilbert space delocalization under the dynamics of random quantum circuits, which serve as a minimal model of the chaotic dynamics of quantum many-body systems. We employ analytical methods based on the replica trick and Weingarten calculus to investigate the time evolution of the participation entropies which quantify the Hilbert space delocalization. We demonstrate that the participation entropies approach, up to a fixed accuracy, their long-time saturation value in times that scale logarithmically with the system size. Exact numerical simulations and tensor network techniques corroborate our findings.

Investigation of the Effect of Heat Transfer during Friction Stir Welding (FSW) of AZ80A Mg Alloy Plates using a Pin Tool by Conducting Finite Elements Analysis

Friction stir welding (FSW) is an innovative solid-state welding process that has attracted substantial attention due to its potential for combining problematic materials such magnesium alloys, such as AZ80A. In order to better understand the impact of heat transport during FSW of AZ80A magnesium alloy plates using a pin tool, this study used finite element analysis (FEA). The welding process's thermal features, such as temperature distribution, thermal stresses, and material flow patterns, are the major focus of this analysis. The first step of the study is to conduct a comprehensive literature evaluation to lay a firm groundwork and pinpoint knowledge gaps. The thermal conductivity, specific heat, density, and mechanical characteristics of AZ80A magnesium alloy are measured and recorded as part of the material characterisation process. To ensure an exact simulation of real-world welding circumstances, a comprehensive 3D model of the welding setup is built, including the AZ80A magnesium alloy plates and the pin tool. In order to accurately record temperature variations, a tiny mesh is used, particularly in the welding zone. By include boundary conditions that mimic the real-world welding characteristics, such as the rotation of the pin tool and the clamping or fixturing of the plates, finite element analysis is used to model the FSW procedure. To simulate the heat input produced by FSW, a heat source or heat production model is used.

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.