Designing Majorana Quasiparticles in InAsP Quantum Dots in InP Nanowires with Variational Quantum Eigenvalue Solver

TL;DR

This paper explores the design of Majorana zero modes in InAsP quantum dots within InP nanowires, employing advanced quantum algorithms like VQE to accurately model topological states and their spectra.

Contribution

It introduces a variational quantum algorithm tailored for modeling Majorana modes in semiconductor nanostructures, demonstrating its effectiveness through classical and quantum simulations.

Findings

VQE accurately reproduces many-body spectra in topological phases.

The variational ansatz captures ground state and topological properties.

Classical simulations validate the quantum algorithm's effectiveness.

Abstract

This work presents steps toward the design of Majorana zero modes (MZM) in InAsP quantum dots (QD) embedded in an InP semiconducting nanowire in contact with a p-type superconductor described by the Kitaev Hamiltonian. The single particle spectrum is obtained from million atom atomistic calculations with QNANO and many-electron spectra using exact diagonalization (ED) and the hybrid Variational Quantum Eigensolver (VQE) method. A variational ansatz is constructed to capture the ground state of the system by utilizing a generalized form of the analytical solution for a particular set of parameters. By systematically deviating from the analytically solvable regime while maintaining the system in the topological phase (TP), the effectiveness of the variational function in reproducing the correct ground state and topological properties of the system is evaluated. This is done through a quantum algorithm for a many-body state containing MZM. The results are compared with exact solution in topological phase and demonstrate the capability of VQE, along with classical simulations, to accurately model the many-body spectra in topologically nontrivial state.