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Dense Associative Memories or modern Hopfield networks permit storage and reliable retrieval of an exponentially large (in the dimension of feature space) number of memories. At the same time, their naive implementation is non-biological,…
We investigate the computational limits of the memory retrieval dynamics of modern Hopfield models from the fine-grained complexity analysis. Our key contribution is the characterization of a phase transition behavior in the efficiency of…
Bosonic quantum systems operate in an infinite-dimensional Hilbert space, unlike discrete-variable quantum systems. This distinct mathematical structure leads to fundamental differences in quantum information processing, such as an…
Understanding the behavior of interacting fermions is of fundamental interest in many fields ranging from condensed matter to high energy physics. Developing numerically efficient and accurate simulation methods is an indispensable part of…
Many-body fermionic quantum calculations performed on analog quantum computers are restricted by the presence of k-local terms, which represent interactions among more than two qubits. These originate from the fermion-to-qubit mapping…
We address the numerical challenge of solving the Hookean-type time-fractional Navier--Stokes--Fokker--Planck equation, a history-dependent system of PDEs defined on the Cartesian product of two $d$-dimensional spaces in the turbulent…
One approach for solving interacting many-fermion systems is the configuration-interaction method, also sometimes called the interacting shell model, where one finds eigenvalues of the Hamiltonian in a many-body basis of Slater determinants…
The inversion of extremely high order matrices has been a challenging task because of the limited processing and memory capacity of conventional computers. In a scenario in which the data does not fit in memory, it is worth to consider…
Quantum many-body systems out of equilibrium pose some of the most intriguing questions in physics. Unfortunately, numerically keeping track of time evolution of states under Hamiltonian dynamics constitutes a severe challenge for all known…
Several recent studies have demonstrated the utility of the quantum SWITCH as an important resource for enhancing the performance of various information processing tasks. In a quantum SWITCH, the advantages appear significantly due to the…
We present a nonparametric interpretation for deep learning compatible modern Hopfield models and utilize this new perspective to debut efficient variants. Our key contribution stems from interpreting the memory storage and retrieval…
The increasing complexity of transformer models in artificial intelligence expands their computational costs, memory usage, and energy consumption. Hardware acceleration tackles the ensuing challenges by designing processors and…
Although best-fit is known to be slow, it excels at optimizing memory space utilization. Interestingly, by keeping the free memory region at the top of the memory, the process of memory allocation and deallocation becomes approximately…
Memcomputing is a novel paradigm of computation that utilizes dynamical elements with memory to both store and process information on the same physical location. Its building blocks can be fabricated in hardware with standard electronic…
Few- and many-fermion systems on the verge of stability, and consisting of strongly interacting particles, appear in many areas of physics. The theoretical modeling of such systems is a very difficult problem. In this work we present a…
Quantum chemistry simulations on a quantum computer suffer from the overhead needed for encoding the fermionic problem in a bosonic system of qubits. By exploiting the block diagonality of a fermionic Hamiltonian, we show that the number of…
In order to reduce the computational complexity of large language models, great efforts have been made to to improve the efficiency of transformer models such as linear attention and flash-attention. However, the model size and…
We derive the effective Hamiltonian $H - \mu N$ for open quantum systems with varying particle number from first principles within the framework of non-relativistic quantum statistical mechanics. We prove that under physically motivated…
We examine what is an efficient and scalable nonlinear solver, with low work and memory complexity, for many classes of discretized partial differential equations (PDEs) - matrix-free Full multigrid (FMG) with a Full Approximation Storage…
Quantum lattice models with large local Hilbert spaces emerge across various fields in quantum many-body physics. Problems such as the interplay between fermions and phonons, the BCS-BEC crossover of interacting bosons, or decoherence in…