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We provide a current perspective on the rapidly developing field of Majorana zero modes in solid state systems. We emphasize the theoretical prediction, experimental realization, and potential use of Majorana zero modes in future information processing devices through braiding-based topological quantum computation. Well-separated Majorana zero modes should manifest non-Abelian braiding statistics suitable for unitary gate operations for topological quantum computation. Recent experimental work, following earlier theoretical predictions, has shown specific signatures consistent with the existence of Majorana modes localized at the ends of semiconductor nanowires in the presence of superconducting proximity effect. We discuss the experimental findings and their theoretical analyses, and provide a perspective on the extent to which the observations indicate the existence of anyonic Majorana zero modes in solid state systems. We also discuss fractional quantum Hall systems (the 5/2 state) in this context. We describe proposed schemes for carrying out braiding with Majorana zero modes as well as the necessary steps for implementing topological quantum computation.
We introduce a second-quantized representation of the ring of symmetric functions to further develop a purely second-quantized -- or lattice -- approach to the study of zero modes of frustration free Haldane-pseudo-potential-type Hamiltonians, which
We discuss the emergence of zero-energy Majorana modes in a disordered finite-length p-wave one-dimensional superconducting ring, pierced by a magnetic flux $Phi$ tuned at an appropriate value $Phi=Phi_*$. In the absence of fermion parity conservatio
We propose to use residual parafermions of the overscreened Kondo effect for topological quantum computation. A superconducting proximity gap of $Delta<T_K$ can be utilized to isolate the parafermion from the continuum of excitations and stabilize th
One of the main challenges for quantum computation is that while the number of gates required to perform a non-trivial quantum computation may be very large, decoherence and errors in realistic quantum architectures limit the number of physical gate
Among the major approaches that are being pursued for realizing quantum bits, the Majorana-based platform has been the most recent to be launched. It attempts to realize qubits which store quantum information in a topologically-protected manner. The