Abstract:
Majorana edge states have been a focus of condensed matter research for their potential applications in topological quantum computation, which appear in the topological DIII-class superconducting chains protected by both the particle-hole and time reversal symmetries. We utilize two charge-qubit arrays to explicitly simulate one type of DIII-class superconducting chains and the universal quantum operations performed on the Majorana edge states. It is shown that combined with one braiding operation, universal single-qubit operations on a Majorana-based qubit can be implemented by a controllable inductive coupling between two charge qubits at the ends of the arrays. It is further shown that in a similar way, a controlled-NOT gate for two topological qubits can be simulated in four charge-qubit arrays. We elaborate that the operations in charge-qubit arrays are indeed robust against certain local perturbations.
Weyl semimetals possess nontrivial Fermi surface topology in that the pair of Weyl points with opposite topological charges is separated from each other in momentum space. By studying the chiral anomaly via the path integral measure, we reach a deeper understanding of the exotic transport phenomena in Weyl semimetals.