Reduced-order modeling of two-dimensional turbulent Rayleigh-B\'enard flow by hybrid quantum-classical reservoir computing

• URL: http://arxiv.org/abs/2307.03053v2
• Date: Fri, 10 Nov 2023 22:09:58 GMT
• Title: Reduced-order modeling of two-dimensional turbulent Rayleigh-B\'enard flow by hybrid quantum-classical reservoir computing
• Authors: Philipp Pfeffer, Florian Heyder and J\"org Schumacher
• Abstract summary: Two hybrid quantum-classical reservoir computing models are presented to reproduce low-order statistical properties of a turbulent Rayleigh-B'enard convection flow. We show that both quantum algorithms are able to reconstruct the essential statistical properties of the turbulent convection flow successfully with similar performance compared to the classical reservoir network.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Two hybrid quantum-classical reservoir computing models are presented to reproduce low-order statistical properties of a two-dimensional turbulent Rayleigh-B\'enard convection flow at a Rayleigh number Ra=1e+5 and a Prandtl number Pr=10. These properties comprise the mean vertical profiles of the root mean square velocity and temperature and the turbulent convective heat flux. Both quantum algorithms differ by the arrangement of the circuit layers of the quantum reservoir, in particular the entanglement layers. The second of the two quantum circuit architectures, denoted as H2, enables a complete execution of the reservoir update inside the quantum circuit without the usage of external memory. Their performance is compared with that of a classical reservoir computing model. Therefore, all three models have to learn the nonlinear and chaotic dynamics of the turbulent flow at hand in a lower-dimensional latent data space which is spanned by the time-dependent expansion coefficients of the 16 most energetic Proper Orthogonal Decomposition (POD) modes. These training data are generated by a POD snapshot analysis from direct numerical simulations of the original turbulent flow. All reservoir computing models are operated in the reconstruction mode. We analyse different measures of the reconstruction error in dependence on the hyperparameters which are specific for the quantum cases or shared with the classical counterpart, such as the reservoir size and the leaking rate. We show that both quantum algorithms are able to reconstruct the essential statistical properties of the turbulent convection flow successfully with similar performance compared to the classical reservoir network. Most importantly, the quantum reservoirs are by a factor of 4 to 8 smaller in comparison to the classical case.

Related papers

• Latent Schrodinger Bridge: Prompting Latent Diffusion for Fast Unpaired Image-to-Image Translation [58.19676004192321]
  Diffusion models (DMs), which enable both image generation from noise and inversion from data, have inspired powerful unpaired image-to-image (I2I) translation algorithms. We tackle this problem with Schrodinger Bridges (SBs), which are differential equations (SDEs) between distributions with minimal transport cost. Inspired by this observation, we propose Latent Schrodinger Bridges (LSBs) that approximate the SB ODE via pre-trained Stable Diffusion. We demonstrate that our algorithm successfully conduct competitive I2I translation in unsupervised setting with only a fraction of cost required by previous DM-
  arXiv  Detail & Related papers  (2024-11-22T11:24:14Z)
• Memory-Augmented Hybrid Quantum Reservoir Computing [0.0]
  We present a hybrid quantum-classical approach that implements memory through classical post-processing of quantum measurements. We tested our model on two physical platforms: a fully connected Ising model and a Rydberg atom array.
  arXiv  Detail & Related papers  (2024-09-15T22:44:09Z)
• Towards Efficient Quantum Hybrid Diffusion Models [68.43405413443175]
  We propose a new methodology to design quantum hybrid diffusion models. We propose two possible hybridization schemes combining quantum computing's superior generalization with classical networks' modularity.
  arXiv  Detail & Related papers  (2024-02-25T16:57:51Z)
• Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search [77.34726150561087]
  We consider an environment formed by incoherent photons as a resource for controlling open quantum systems via an incoherent control. We exploit a coherent control in the Hamiltonian and an incoherent control in the dissipator which induces the time-dependent decoherence rates.
  arXiv  Detail & Related papers  (2023-02-28T07:36:02Z)
• A predictive physics-aware hybrid reduced order model for reacting flows [65.73506571113623]
  A new hybrid predictive Reduced Order Model (ROM) is proposed to solve reacting flow problems. The number of degrees of freedom is reduced from thousands of temporal points to a few POD modes with their corresponding temporal coefficients. Two different deep learning architectures have been tested to predict the temporal coefficients.
  arXiv  Detail & Related papers  (2023-01-24T08:39:20Z)
• Modeling the space-time correlation of pulsed twin beams [68.8204255655161]
  Entangled twin-beams generated by parametric down-conversion are among the favorite sources for imaging-oriented applications. We propose a semi-analytic model which aims to bridge the gap between time-consuming numerical simulations and the unrealistic plane-wave pump theory.
  arXiv  Detail & Related papers  (2023-01-18T11:29:49Z)
• Thermodynamics of bidirectional associative memories [0.0]
  We investigate the equilibrium properties of bidirectional associative memories (BAMs) introduced by Kosko in 1988 as a generalization of the Hopfield model to a bipartite structure. We characterize the computational capabilities of a extension of this model in the thermodynamic limit.
  arXiv  Detail & Related papers  (2022-11-17T17:35:37Z)
• Ternary unitary quantum lattice models and circuits in $2 + 1$ dimensions [0.0]
  We extend the concept of dual unitary quantum gates to quantum lattice models in $2 + 1$ dimensions. We study ternary unitary four-particle gates, which are unitary in time and both spatial dimensions.
  arXiv  Detail & Related papers  (2022-06-03T10:53:49Z)
• Hybrid quantum-classical reservoir computing of thermal convection flow [0.0]
  We simulate the chaotic dynamics of Lorenz-type models for a classical two-dimensional thermal convection flow with 3 and 8 degrees of freedom. The high-dimensional quantum reservoir dynamics are established by universal quantum gates that rotate and entangle the individual qubits of the tensor product quantum state. Our work thus opens the door to model the dynamics of classical complex systems in a high-dimensional phase space effectively with an algorithm that requires a small number of qubits.
  arXiv  Detail & Related papers  (2022-04-29T08:55:59Z)
• Continuous and time-discrete non-Markovian system-reservoir interactions: Dissipative coherent quantum feedback in Liouville space [62.997667081978825]
  We investigate a quantum system simultaneously exposed to two structured reservoirs. We employ a numerically exact quasi-2D tensor network combining both diagonal and off-diagonal system-reservoir interactions with a twofold memory for continuous and discrete retardation effects. As a possible example, we study the non-Markovian interplay between discrete photonic feedback and structured acoustic phononovian modes, resulting in emerging inter-reservoir correlations and long-living population trapping within an initially-excited two-level system.
  arXiv  Detail & Related papers  (2020-11-10T12:38:35Z)
• Reservoir computing model of two-dimensional turbulent convection [0.0]
  Reservoir computing is applied to model the large-scale evolution and the resulting low-order turbulence statistics. Our work demonstrates that the reservoir computing model is capable to model the large-scale structure and low-order statistics of turbulent convection.
  arXiv  Detail & Related papers  (2020-01-28T11:49:25Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.