Tensor Network Methods in Quantum Simulation of the Transverse Field Ising Model

Sammanfattning

This thesis explores the use of tensor network methods—specifically the imaginary Time-evolving Block Decimation (iTeBD) algorithm—to evolve one-dimensional finite transverse field Ising model (TFIM) spin chains and compute their ground state energies. Using the Matrix Product State (MPS) formalism, a compact representation of the system state is implemented, so that operations on the state can be performed efficiently. After simulating the evolution for different chain lengths, the computed ground state energies are compared with the known analytical solutions. The method demonstrates high accuracy and linear error scaling with system size, outperforming brute-force diagonalization.