COMBINING QUANTUM TRAJECTORIES AND TIME-DEPENDENT VARIATIONAL MONTE CARLO FOR MANY-BODY OPEN QUANTUM SYSTEMS

Simulating quantum systems is complex due to the “curse of dimensionality”, which is exacerbated in open quantum systems that interact with their environment. Indeed, tra- ditional computational methods struggle with the exponential growth of Hilbert space in these systems. This thesis introduces the Open-Time Variational Monte Carlo (otVMC) method, which combines the quantum trajectory formalism with Monte Carlo tech- niques to enable real-time simulations of open quantum systems. By exploiting stochas- tic Schrödinger equations and a variational approach, otVMC significantly reduces com- putational complexity. Applied to a dissipative many-body spin system with long-range interactions, this method successfully simulates up to 180 spins and provides insights into time evolution of the spin-squeezing parameter. Despite some limitations, such as potential biases and challenges with accuracy in the long-time evolution, otVMC offers a robust tool for studying the dynamics of large, strongly interacting systems and holds promise for future extensions to continuous and higher-dimensional systems.

Grantor dc:publisher

Università degli Studi di Milano

Year dc:date

2024

Author dc:creator

• D'ALBERTO, JACOPO

Contributors dc:contributor

• supervisore: D. E. Galli ; co-supervisore: G. Bertaina ; director of the school: A. Mennella
• J. D'Alberto
• GALLI, DAVIDE EMILIO
• MENNELLA, ANIELLO

• open quantum system
• quantum monte carlo
• quantum trajectorie
• variational method
• out-of-equilibrium
• spin system
• spin squeezing
• restricted boltzmann machines
• Settore PHYS-04/A - Fisica teorica della materia, modelli, metodi matematici e applicazioni
• Settore PHYS-03/A - Fisica sperimentale della materia e applicazioni

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

eng

Identifier

http://dx.doi.org/10.13130/d-alberto-jacopo_phd2024-12-18
10.13130/d-alberto-jacopo_phd2024-12-18

OAI identifier oai:identifier

oai:air.unimi.it:2434/1119575