Non-Abelian statistics and topological quantum information processing in 1D wire networks

By J. Alicea, Y. Oreg, G. Refael, F. von Oppen, Matthew Fisher. 2010

1,412 citations recorded by the source corpus.

The synthesis of a quantum computer remains an ongoing challenge in modern physics. Whereas decoherence stymies most approaches, topological quantum computation schemes evade decoherence at the hardware level by storing quantum information non-locally. Here we establish that a key operation—braiding of non-Abelian anyons—can be implemented using one-dimensional semiconducting wires. Such wires can be driven into a topological phase supporting long-sought particles known as Majorana fermions that can encode topological qubits. We show that in wire networks, Majorana fermions can be meaningfully braided by simply adjusting gate voltages, and that they exhibit non-Abelian statistics like vortices in a p+ip superconductor. We propose experimental set-ups that enable probing of the Majorana fusion rules and the efficient exchange of arbitrary numbers of Majorana fermions. This work should open a new direction in topological quantum computation that benefits from physical transparency and experimental feasibility.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/3c5fa7110b2b93259a744608905d617c2cd665f2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. John Preskill
2. Peter Zoller
3. J. Alicea
4. M. B. Hastings
5. Matthew Fisher
6. Y. Oreg
7. S. Diehl
8. G. Refael

In Atomic and Molecular Physics, and Optics

1. Masatoshi Sato
2. C. Beenakker
3. J. Alicea
4. K. Kawabata
5. Masahito Ueda
6. C. Nayak
7. A. Stern
8. K. Flensberg

Citations in the corpus

• Quantum computing and the entanglement frontier (2012, background): “64 In most such proposals, the anyon braiding by itself is not sufficient for universal quantum computing, but can be supplemented by unprotected (and possibly quite noisy) nontopologi-cal operations to realize a universal gate set.”
• Geometric phase from Aharonov–Bohm to Pancharatnam–Berry and beyond (2019, background): “ndom matrix theory (190) for disordered systems. Finally, we wish to mention the promising role of geometric phase and in particular non-Abelian geometric phase in quantum information and computation (191,192,193,194,195,196,197,198,199). Implementations of quantum gates based on the geometric phase”
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states (2012, background): “to the operations proposed for the Majorana case [38,40]).”
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device (2012, background): “Cooper pairs can transport between the two Nb contacts via the Majorana fermion states, leading to an enhancement in the zero-bias conductance [7, 18].”
• Topology by dissipation in atomic quantum wires (2011, background): “The pair of Majorana edge modes represents a non-local fermion, which is a promising building block to encode topological qubit”
• Two-dimensional epitaxial superconductor-semiconductor heterostructures: A platform for topological superconducting networks (2015, background): “[19] Jason Alicea, Yuval Oreg, Gil Refael, Felix von Oppen, and Matthew P.”