Density Matrix Renormalization Group Study of Domain Wall Qubits

TL;DR

This paper uses advanced quantum simulation techniques to demonstrate that domain wall spin textures in quantum chains can serve as robust qubits and form the basis for scalable quantum computing architectures.

Contribution

It provides the first fully quantum demonstration of domain wall qubits using DMRG, including effective Hamiltonians for single and two-qubit gates.

Findings

Domain wall chiralities form isolated low-energy states suitable for qubits.

Magnetic fields induce tunneling between chiral states, enabling gate operations.

Real-time simulations demonstrate single- and two-qubit gate implementations.

Abstract

Nanoscale topological spin textures in magnetic systems are emerging as promising candidates for scalable quantum architectures. Despite their potential as qubits, previous studies have been limited to semiclassical approaches, leaving a critical gap: the lack of a fully quantum demonstration. Here, we address this challenge by employing the density-matrix renormalization group (DMRG) method to establish domain wall (DW) qubits in coupled quantum spin-1/2 chains. We calculate the ground-state energies and excitation gaps of the system and find that DWs with opposite chiralities form a well-defined low-energy sector, distinctly isolated from higher excited states in the presence of anisotropies. This renders the chirality states suitable for encoding quantum information, serving as robust qubits. Interestingly, when a magnetic field is applied, we observe tunneling between quantum DW states with opposite chiralities. Through quantum simulations, we construct an effective qubit Hamiltonian that exhibits strongly anisotropic $g$-factors, offering a way to implement single-qubit gates. Furthermore, we obtain an effective interacting Hamiltonian for two mobile DWs in coupled quantum spin chains from DMRG simulations, enabling the implementation of two-qubit gates.Single-qubit and two-qubit gates are also demonstrated in real-time simulations using the time-dependent variational principle. Our work represents a critical step from semiclassical constructions to a fully quantum demonstration of the potential of DW textures for scalable quantum computing, establishing a solid foundation for future quantum architectures based on topological magnetic textures.