Ground-State-Based Model Reduction with Unitary Circuits

• URL: http://arxiv.org/abs/2504.10774v2
• Date: Mon, 21 Apr 2025 00:40:52 GMT
• Title: Ground-State-Based Model Reduction with Unitary Circuits
• Authors: Shengtao Jiang, Steven R. White,
• Abstract summary: We numerically obtain low-energy effective models based on a unitary transformation of the ground state.<n>We test our method on the one-dimensional and two-dimensional square-lattice Hubbard model at half-filling.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a method to numerically obtain low-energy effective models based on a unitary transformation of the ground state. The algorithm finds a unitary circuit that transforms the ground state of the original model to a projected wavefunction with only the low-energy degrees of freedom. The effective model can then be derived using the unitary transformation encoded in the circuit. We test our method on the one-dimensional and two-dimensional square-lattice Hubbard model at half-filling, and obtain more accurate effective spin models than the standard perturbative approach.

Related papers

• MAP Image Recovery with Guarantees using Locally Convex Multi-Scale Energy (LC-MUSE) Model [12.218356507147583]
  We propose a multi-scale deep energy model that is strongly convex in the local neighbourhood around the data manifold.<n>We use the learned energy model in image-based inverse problems, where the formulation offers several desirable properties.<n>In the context of parallel Magnetic Resonance (MR) image reconstruction, we show that the proposed method performs better than the state-of-the-art convex regularizers.
  arXiv  Detail & Related papers  (2025-02-05T16:00:55Z)
• Bayesian Model Parameter Learning in Linear Inverse Problems with Application in EEG Focal Source Imaging [49.1574468325115]
  Inverse problems can be described as limited-data problems in which the signal of interest cannot be observed directly. We studied a linear inverse problem that included an unknown non-linear model parameter. We utilized a Bayesian model-based learning approach that allowed signal recovery and subsequently estimation of the model parameter.
  arXiv  Detail & Related papers  (2025-01-07T18:14:24Z)
• Latent Space Energy-based Neural ODEs [73.01344439786524]
  This paper introduces novel deep dynamical models designed to represent continuous-time sequences.<n>We train the model using maximum likelihood estimation with Markov chain Monte Carlo.<n> Experimental results on oscillating systems, videos and real-world state sequences (MuJoCo) demonstrate that our model with the learnable energy-based prior outperforms existing counterparts.
  arXiv  Detail & Related papers  (2024-09-05T18:14:22Z)
• Non-intrusive data-driven model order reduction for circuits based on Hammerstein architectures [0.8192907805418581]
  We develop a parsimonious Hammerstein model for a non-linear CMOS differential amplifier. We train this model on a combination of direct current (DC) and transient Spice (Xyce) circuit simulation data. Simulation results show that the Hammerstein model is an effective surrogate for the differential amplifier circuit.
  arXiv  Detail & Related papers  (2024-05-30T15:47:48Z)
• On the Trajectory Regularity of ODE-based Diffusion Sampling [79.17334230868693]
  Diffusion-based generative models use differential equations to establish a smooth connection between a complex data distribution and a tractable prior distribution. In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models.
  arXiv  Detail & Related papers  (2024-05-18T15:59:41Z)
• Diffeomorphic Template Registration for Atmospheric Turbulence Mitigation [50.16004183320537]
  We describe a method for recovering the irradiance underlying a collection of images corrupted by atmospheric turbulence. We select one of the images as a reference, and model the deformation in this image by the aggregation of the optical flow from it to other images. We achieve state-of-the-art performance despite its simplicity.
  arXiv  Detail & Related papers  (2024-05-06T17:39:53Z)
• Flat-band engineering of quasi-one-dimensional systems via supersymmetric transformations [0.0]
  We introduce a systematic method to spectrally design quasi-one-dimensional crystal models. The method is based on the supersymmetric transformation applied to an initially known pseudo-spin-1/2 model. The results are illustrated in two examples where the Su-Schriefer-Heeger chain is locally converted into a lattice stub.
  arXiv  Detail & Related papers  (2024-02-16T09:03:28Z)
• Predicting Ordinary Differential Equations with Transformers [65.07437364102931]
  We develop a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from irregularly sampled and noisy observations of a single solution trajectory. Our method is efficiently scalable: after one-time pretraining on a large set of ODEs, we can infer the governing law of a new observed solution in a few forward passes of the model.
  arXiv  Detail & Related papers  (2023-07-24T08:46:12Z)
• Counting Phases and Faces Using Bayesian Thermodynamic Integration [77.34726150561087]
  We introduce a new approach to reconstruction of the thermodynamic functions and phase boundaries in two-parametric statistical mechanics systems. We use the proposed approach to accurately reconstruct the partition functions and phase diagrams of the Ising model and the exactly solvable non-equilibrium TASEP.
  arXiv  Detail & Related papers  (2022-05-18T17:11:23Z)
• Unraveling correlated material properties with noisy quantum computers: Natural orbitalized variational quantum eigensolving of extended impurity models within a slave-boson approach [0.0]
  We propose a method for computing space-resolved correlation properties of the two-dimensional Hubbard model within a quantum-classical embedding strategy. We solve a two-impurity embedded model requiring eight qubits with an advanced hybrid scheme on top of the Variational Quantum Eigensolver algorithm. This paves the way to a controlled solution of the Hubbard model with larger and larger embedded problems solved by quantum computers.
  arXiv  Detail & Related papers  (2021-08-24T14:58:14Z)
• Interpolation Technique to Speed Up Gradients Propagation in Neural ODEs [71.26657499537366]
  We propose a simple literature-based method for the efficient approximation of gradients in neural ODE models. We compare it with the reverse dynamic method to train neural ODEs on classification, density estimation, and inference approximation tasks.
  arXiv  Detail & Related papers  (2020-03-11T13:15:57Z)

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.