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.