Majorana zero modes on a 1D chain for quantum computation

Abstract

Numerical calculations for Majorana zero modes on a one-dimensional chain are performed using the technique of block diagonalization for general parameter settings. It is found that Majorana zero modes occur near the ends of the chain and decay exponentially away from the ends. The phase diagrams show that Majorana zero modes of a long-enough chain indeed have a parameter domain of $2t>|\mu |$ as predicted from the bulk property of the chain, but a short chain has a much smaller parameter domain than the prediction. Through a numerical simulation Majorana zero modes are found to be robust under the disturbance of noise. Finally the reversion of the parity of the ground states is studied by applying a bias voltage on the quantum dot at an end of the chain. It is found that for a weak coupling between a chain and a quantum dot the parity of the ground states can be reversed through adiabatically tuning the bias voltage.

5 figures, 4 pages

References in corpus (14)

• Anyons in an exactly solved model and beyond
• Unpaired Majorana fermions in quantum wires
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Search for Majorana fermions in superconductors
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Fermionic quantum computation
• Introduction to topological superconductivity and Majorana fermions
• Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
• Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems
• Universal Quantum Computation with the nu=5/2 Fractional Quantum Hall State
• Non-Abelian operations on Majorana fermions via single charge control
• Charge detection enables free-electron quantum computation
• Topological Superfluids with Finite Momentum Pairing and Majorana Fermions

Cited by in corpus (3)

• Aharonov-Bohm interference as a probe of Majorana fermions
• Topological phase transition driven by magnetic field in one-dimensional topological superconductor rings
• Interfacing a topological qubit with a spin qubit in a hybrid quantum system