Computer simulation methods in theoretical physics

Jerome H. Weiner, Attila Aşkar

Jincheng Zhang

Quantum topology, a burgeoning field of theoretical physics, proposes a novel approach to simulating physical systems by exploiting the properties of quantum entanglement. This paper explores the potential of utilizing quantum topology to develop a powerful new simulation technique, offering a pathway towards highly accurate and computationally efficient models of complex phenomena. We outline the core mechanism, detailing how entanglement can be leveraged to represent and manipulate fundamental connections within a system, ultimately aiming to overcome the limitations of traditional simulation methods. This work addresses the challenge of simulating intricate physical systems with reduced computational demands, presenting a fundamentally new methodology for achieving this goal. The paper will discuss the theoretical foundations, potential applications, and preliminary results obtained through simulations, highlighting the unique advantages of this approach.

Richard P. Feynman

Jan Brandejs

Title: Optimizing quantum simulations and the DMRG method Author: Jan Brandejs Department: Department of Chemical Physics and Optics Supervisor: doc. Dr. rer. nat. Jiří Pittner, DSc., J. Heyrovský Institute of Physical Chemistry of the Czech Academy of Sciences Abstract: In this work, we explore the quantum information theoretical aspects of simulation of quantum systems on classical computers, in particular the many- electron strongly correlated wave functions. We describe a way how to reduce the amount of data required for storing the wavefunction by a lossy compression of quantum information. For this purpose, we describe the measures of quantum entanglement for the density matrix renormalization group method. We imple- ment the computation of multi-site generalization of mutual information within the DMRG method and investigate entanglement patterns of strongly correlated chemical systems. We present several ways how to optimize the ground state calculation in the DMRG method. The theoretical conclusions are supported by numerical simulations of the diborane molecule, exhibiting chemically interest- ing electronic structure, like the 3-centered 2-electron bonds. In the theoretical part, we give a brief introduction to the principles of the DMRG method. Then we explain the quantum informational...

Jincheng Zhang

Quantum simulation is a promising field of research that leverages the principles of quantum mechanics to simulate the behavior of complex physical systems. This paper explores the development of a novel quantum simulation method based on the principle of physical field values, aiming to enhance simulation accuracy and provide new insights into fundamental physics. We present a detailed explanation of the method's architecture, focusing on the utilization of quantum computation to emulate physical fields and construct a robust quantum simulation model. The core claim highlights the potential of this approach to overcome limitations of traditional quantum simulation and facilitate the validation of theoretical physics. This work will demonstrate the efficacy of this technique through illustrative examples and analysis of its potential impact on various physical systems.

Таврійський державний агротехнологічний університет імені Дмитра Моторного, Natalya L. Sosnickaya, M. V. Morozov Morozov +3 more