Quantum Algorithm and Tensor Network Simulations for Topological Many-Body Systems

Topological many-body systems are made of interacting particles whose global properties are determined not by local order parameters (for example, magnetization in ferromagnets), but by topological features. These systems can exhibit robustness against local perturbations and topological phases of matter, making them interesting with potential applications in quantum computing.

In particular, we consider two systems:

1) A Kitaev 1D p-wave superconducting chain of spinless fermions,

2) A 1D semiconducting chain with proximity s-wave superconductivity.

We use quantum-inspired algorithms and tensor network methods as numerical tools to study these systems. We look for the ground state representation among with the energy spectra and aim to compute quantities of interest, such as entanglement entropies.