Parallel simulations, finite bath: Parallelising numerical simulations for the time evolution of a finite spin bath coupled to a qubit

Abstract

At low energies, the environment of most open quantum systems can be represented by baths of harmonic oscillators or spins. Modelling and simulating an open quantum system requires substantial computational resources, and simulations on personal computers are limited to small models. Parallel computing architectures may allow expansion of the model size and enhance simulation capabilities. This thesis aims to optimise existing simulation code of an open quantum model for parallel execution. The model consists of an open quantum system, represented by a qubit, which interacts with an environment containing a finite number of weakly and randomly coupled spins. To reduce the dimension of its Hilbert space, the environment is mapped into an oscillator bath, producing a quadratic Hamiltonian. The time evolution of all particles is tracked through exact diagonalisation. The code is written in MATLAB and good scientific computing practices are followed. Primary optimisation takes place in a local computing environment using MATLAB Parallel Computing Toolbox. The analysis of this legacy code facilitates its modular restructuring with distinct physical processes or computational tasks assigned to specific functions. The modular version, which has been vectorised, shows an approximate 35% reduction in time consumption for a small model with 1500 spins. Optimisation for parallelism continues with dividing the code further into multicore and GPU parallelisms, with the latter indicating improved performance of about 23% over the modular version. Next, the optimised code was tested in Aalto Triton supercomputing cluster, achieving an approximate 99% improvement in time performance between the modular and the GPU versions for a model of 10000 spins, as well as an enlargement of the model by a factor of 20, to 30000 spins. Having being tested in two different computational environments, the aimed optimisation is considered successful. The structure of the code makes its adaptation simple for simulation of different models, enabling further exploration of its potential.