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Preparing the ground state of the Fermi-Hubbard model is challenging, in part due to the exponentially large Hilbert space, which complicates efficiently finding a path from an initial state to the ground state using the variational…
Quantum reservoir computing is a neuro-inspired machine learning approach harnessing the rich dynamics of quantum systems to solve temporal tasks. It has gathered attention for its suitability for NISQ devices, for easy and fast…
Fast Fourier Transforms (FFT) are widely used to reduce memory and computational costs in deep learning. However, existing implementations, including standard FFT and real FFT (rFFT), cannot achieve true in-place computation. In particular,…
In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…
Traditional neural networks require enormous amounts of data to build their complex mappings during a slow training procedure that hinders their abilities for relearning and adapting to new data. Memory-augmented neural networks enhance…
Energy system optimization models are increasing in scope and resolution, yielding large and challenging linear programs. For a long time, the standard way to address such problems has relied on shared-memory interior-point methods (IPM),…
Models of interacting complex systems provide the fundamental statistical physics reference frame for the study and the understanding of associative memories, machine learning, and the dynamics of neural networks. On the other hand,…
State-space models (SSMs) have recently attention as an efficient alternative to computationally expensive attention-based models for sequence modeling. They rely on linear recurrences to integrate information over time, enabling fast…
Effective Hamiltonians are usually constructed by using canonical transformations or projection techniques. In contrast to this, we present a method for systems with arbitrary Hilbert space based on the introduction of cumulants. Cumulants…
A new efficient numerical algorithm for interacting fermion systems is proposed and examined in detail. The ground state is expressed approximately by a linear combination of numerically chosen basis states in a truncated Hilbert space. Two…
We show that phase memory can be much longer than energy relaxation in systems with exponentially large dimensions of Hilbert space; this finding is documented by fifty years of nuclear experiments, though the information is somewhat…
The stateless architecture of Large Language Models inherently lacks the mechanism to preserve dynamic context, compelling agents to redundantly reprocess history to maintain long-horizon autonomy. While latent memory offers a solution,…
Quantum many-body simulation provides a straightforward way to understand fundamental physics and connect with quantum information applications. However, suffering from exponentially growing Hilbert space size, characterization in terms of…
While isolated quantum systems generally thermalize after long-time evolution, there are several exceptions defying thermalization. A notable mechanism of such nonergodicity is the Hilbert space fragmentation (HSF), where the Hamiltonian…
Fermi acceleration is the process of energy transfer from massive objects in slow motion to light objects that move fast. The model for such process is a time-dependent Hamiltonian system. As the parameters of the system change with time,…
This paper applies the Recursive Projection Method (RPM) to the problem of finding the effective mechanical response of a periodic heterogeneous solid. Previous works apply the Fast Fourier Transform (FFT) in combination with various…
Many phenomena of strongly correlated materials are encapsulated in the Fermi-Hubbard model whose thermodynamical properties can be computed from its grand canonical potential according to standard procedures. In general, there is no closed…
Based on a recent work on traveling waves in spatially nonlocal reaction-diffusion equations, we investigate the existence of traveling fronts in reaction-diffusion equations with a memory term. We will explain how such memory terms can…
Modern computing systems are capable of exascale calculations, which are revolutionizing the development and application of high-fidelity numerical models in computational science and engineering. While these systems continue to grow in…
We consider the theory of four-fermion interactions with N-component fermions in de Sitter space. It is found that the effective potential for a composite operator in the theory is calculable in the leading order of the 1/N expansion. The…