Density Matrix Renormalization Group Study of Domain Wall Qubits

Nanoscale magnetic domain walls (DWs) have emerged as promising candidates for qubits in scalable quantum computing architectures¹, owing to their topologically robust spin textures and ability to exhibit macroscopic quantum phenomena². Previous theoretical studies have primarily focused on the continuum limit of Heisenberg models, often relying on semiclassical approximations, while numerical simulations of quantum DWs remain largely unexplored. However, Traditional micromagnetic simulations, while effective in capturing classical magnetic dynamics, fall short in describing the quantum nature of DW qubits. In this work, we apply the density-matrix renormalization group (DMRG) method to explore coupled spin-1/2 ferromagnetic Heisenberg chains, providing a deeper understanding of quantum effects in DW qubits. Our simulations reveal that the anisotropic g-factor of DW qubits can be effectively tuned using external magnetic fields, allowing precise control over qubit operations. We demonstrate that entanglement between DW qubits can be achieved through dipolar-type interactions between two quantum spin chains. Furthermore, mobile DWs interacting on coupled spin ladders enable the implementation of two-qubit gates by adjusting their velocities. Single-qubit gates are implemented through Rabi-driven oscillations using oscillating magnetic fields. The combined tunability and robustness of DW qubits make them promising candidates for realizing universal quantum computation.