High-Dimensional Quantum Walks for Field Theory Simulations

Abstract

There are many problems in physics that are not well understood due to the complexity of the underlying theory. For example, many-particle physics is difficult to study through theoretical analysis or the inefficiency of conventional classical computers as the system size grows. Quantum Simulations then become a necessary alternate step to understanding these problems. Discrete Quantum Walks, the quantum analogue of the classical random walk, has proven to be a promising quantum simulation technique and are also physically implemented in different setups. In this thesis, we provide a comprehensive review of Discrete Quantum Walk on a line and its capability to mimic the dynamics of massless free (1+1)D Dirac Hamiltonian in both flat space-time and curved space-time spacetime. We extend this model to two dimensions and study the dynamics of the walker under random disordered media. By restricting the disorder to one dimension, we have studied its effect on the distribution and the entanglement in the associated dimension. We further study the system using analytical methods in search of reasons for the behaviour under restrictive disorder. We also find the continuous limit of the model considered, which reduces to a (1+2)D Dirac-like equation.