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Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications and data storage systems. SC codes are constructed by partitioning an…
We introduce an algorithm based on Generalized Dual Method (GDM) to efficiently study the dynamics of a particle in quasiperiodic environments without the need to use periodic approximations or to save the information of the vertices that…
We present exact methods for the numerical integration of the Wannier-Stark system in a many-body scenario including two Bloch bands. Our ab initio approaches allow for the treatment of a few-body problem with bosonic statistics and strong…
The Simplex tableau has been broadly used and investigated in the industry and academia. With the advent of the big data era, ever larger problems are posed to be solved in ever larger machines whose architecture type did not exist in the…
We propose a new scheme for parallel spatially multimode quantum memory for light. The scheme is based on the propagating in different directions quantum signal wave and strong classical reference wave, like in a classical volume hologram…
Low-rank approximations of original samples are playing more and more an important role in many recently proposed mathematical models from data science. A natural and initial requirement is that these representations inherit original…
The standard kinetic Monte Carlo algorithm is an extremely efficient method to carry out serial simulations of dynamical processes such as thin-film growth. However, in some cases it is necessary to study systems over extended time and…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
Iterative methods that operate with the full Hamiltonian matrix in the untrimmed Hilbert space of a finite system continue to be important tools for the study of one- and two-dimensional quantum spin models, in particular in the presence of…
An efficient parallelization approach to simulate optical properties of ensembles of quantum emitters in realistic electromagnetic environments is considered. It relies on balancing computing load of utilized processors and is built into…
Quantum computers are promising tools for the simulation of many-body systems, and among those, QCD stands out by its rich phenomenology. Every simulation starts with a codification, and here we succently review a newly developed compact…
We study the problem of learning the Hamiltonian of a quantum many-body system given samples from its Gibbs (thermal) state. The classical analog of this problem, known as learning graphical models or Boltzmann machines, is a well-studied…
With the rapid growth of large language models (LLMs), a wide range of methods have been developed to distribute computation and memory across hardware devices for efficient training and inference. While existing surveys provide descriptive…
Quantum algorithms have begun to surpass classical ones in several computation fields, yet practical application remains challenging due to hardware and software limitations. Here, we introduce a quantum algorithm that quadratically…
In this work we show that randomized (block) coordinate descent methods can be accelerated by parallelization when applied to the problem of minimizing the sum of a partially separable smooth convex function and a simple separable convex…
As compute power increases with time, more involved and larger simulations become possible. However, it gets increasingly difficult to efficiently use the provided computational resources. Especially in particle-based simulations with a…
We describe an algorithm for dynamic load balancing of geometrically parallelized synchronous Monte Carlo simulations of physical models. This algorithm is designed for a (heterogeneous) multiprocessor system of the MIMD type with…
In this thesis the variational optimisation of the density matrix is discussed as a method in many-body quantum mechanics. This is a relatively unknown technique in which one tries to obtain the two-particle reduced density matrix directly…
Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications. They also find application in various data storage systems because of their…
We demonstrate that general-purpose memory allocation involving many threads on many cores can be done with high performance, multicore scalability, and low memory consumption. For this purpose, we have designed and implemented scalloc, a…