相关论文: On the Discretization Error of the Discrete Genera…

Diffusion models have received wide attention in generation tasks. However, the expensive computation cost prevents the application of diffusion models in resource-constrained scenarios. Quantization emerges as a practical solution that…

Studies of the dynamics of a quantum system coupled to baths are typically performed by utilizing the Nakajima-Zwanzig memory kernel (${\mathcal{K}}$) or the influence functions ($\mathbf{{I}}$), especially when the dynamics exhibit memory…

We propose and analyse a spatial discretization of the non-local Quantum Drift Diffusion (nlQDD) model by Degond, M\`{e}hats and Ringhofer in one space dimension. With our approach, that uses consistently matrices on ${\mathbb C}^N$ instead…

Simulation of continuous time evolution requires time discretization on both classical and quantum computers. A finer time step improves simulation precision, but it inevitably leads to increased computational efforts. This is particularly…

The particles model, the collision model, the polynomial development used for the equilibrium distribution, the time discretization and the velocity discretization are factors that let the lattice Boltzmann framework (LBM) far away from its…

We develop an unconditionally energy-stable tensor-product space-time discretization framework for the solution of a linear kinetic transport equation in one space dimension. The kinetic equation is a simplified model of radiative transfer…

This paper introduces Discrete Markov Probabilistic Models (DMPMs), a novel discrete diffusion algorithm for discrete data generation. The algorithm operates in discrete bit space, where the noising process is a continuous-time Markov chain…

The traditional thermodynamic Bethe ansatz (TBA) equations for the XXZ model at $|\Delta|\ge 1$ are derived within the quantum transfer matrix (QTM) method. This provides further evidence of the equivalence of both methods. Most…

A discretization of a continuum theory with constraints or conserved quantities is called mimetic if it mirrors the conserved laws or constraints of the continuum theory at the discrete level. Such discretizations have been found useful in…

We present a generalized temporal transfer matrix method (TTMM) for time-varying media that accurately captures wave dynamics in media operating at exceptional points (EPs). The method expands wave fields in the canonical basis of each…

Latent Diffusion Models (LDMs) capture the dynamic evolution of latent variables over time, blending patterns and multimodality in a generative system. Despite the proficiency of LDM in various applications, such as text-to-image…

Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…

We derive an expression for the energy-momentum tensor in the discrete lattice formulation of pure glue QCD. The resulting expression satisfies the continuity equation for energy conservation up to numerical errors with a symmetric…

We introduce time-dependent density matrix renormalization group (tDMRG) as a solution to long standing problem in spintronics -- how to describe spin-transfer torque (STT) between flowing spins of conduction electrons and localized spins…

Diffusion transformers (DiTs) combine transformer architectures with diffusion models. However, their computational complexity imposes significant limitations on real-time applications and sustainability of AI systems. In this study, we aim…

It is shown that discrete-time quantum walks can be used to digitize, i.e., to time discretize fermionic models of continuous-time lattice gauge theory. The resulting discrete-time dynamics is thus not only manifestly unitary, but also…

In this work a practical scheme is developed for the first-principles study of time-dependent quantum transport. The basic idea is to combine the transport master-equation with the well-known time-dependent density functional theory. The…

Atomistic simulations with methods such as molecular dynamics are extremely powerful tools to understand nanoscale dynamical behavior. The resulting trajectories, by the virtue of being embedded in a high-dimensional configuration space,…

A new improved transfer matrix method (TMM) is presented. It is shown that the method not only overcomes the numerical instability found in the original TMM, but also greatly improves the scalability of computation. The new improved TMM has…

We describe a simple quantum mechanical method that can be used to obtain accurate numerical results over long time scales for the spin correlation tensor of an electron spin that is hyperfine coupled to a large number of nuclear spins.…