Majorana Zero Modes in Networks of Cooper-Pair Boxes: Topologically Ordered States and Topological Quantum Computation

Yuval Oreg; Felix Von Oppen

doi:10.1146/annurev-conmatphys-031218-013618

Majorana Zero Modes in Networks of Cooper-Pair Boxes: Topologically Ordered States and Topological Quantum Computation

Yuval Oreg, Felix Von Oppen

Department of Condensed Matter Physics

Research output: Contribution to journal › Review article › peer-review

49 Citations (Scopus)

Abstract

Recent experimental progress introduced devices that can combine topological superconductivity with Coulomb-blockade effects. Experiments with these devices have already provided additional evidence for Majorana zero modes in proximity-coupled semiconductor wires. They also stimulated numerous ideas for how to exploit interactions between Majorana zero modes generated by Coulomb charging effects in networks of Majorana wires. Coulomb effects promise to become a powerful tool in the quest for a topological quantum computer as well as for driving topological superconductors into topologically ordered insulating states. Here, we present a focused review of these recent developments, including discussions of recent experiments, designs of topological qubits, Majorana-based implementations of universal quantum computation, and topological quantum error correction. Motivated by the analogy between a qubit and a spin-1/2 degree of freedom, we also review how coupling between Cooper-pair boxes leads to emergent topologically ordered insulating phases.

Original language	English
Pages (from-to)	397-420
Number of pages	24
Journal	Annual Review of Condensed Matter Physics
Volume	11
Early online date	3 Dec 2019
DOIs	https://doi.org/10.1146/annurev-conmatphys-031218-013618
Publication status	Published - 10 Mar 2020

Funding

We are indebted to our collaborators who contributed to works related to the topic of this review, including Jason Alicea, Bela Bauer, Erez Berg, Parsa Bonderson, Piet Brouwer, Hiromi Ebisu, Jens Eisert, Matthew Fisher, Karsten Flensberg, Michael Freedman, Leonid Glazman, Arbel Haim, Bert Halperin, Matthew Hastings, Torsten Karzig, Markus Kesselring, Thomas Kiendl, Christina Knapp, Daniel Litinski, Roman Lutchyn, Charlie Marcus, Ryan Mishmash, Chetan Nayak, Yang Peng, Falko Pientka, Stephan Plugge, Gil Refael, Eran Sagi, Eran Sela, Ady Stern, Yukio Tanaka, and Yizhi You. We also acknowledge support by the European Union's Horizon 2020 research and innovation program under the LEGOTOP grant agreement No. 788715, the DFG (CRC/Transregio 183 and CRC 910), QuantERA (TOPOQUANT), the Israel Science Foundation, and the Binational Science Foundation

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Cite this

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title = "Majorana Zero Modes in Networks of Cooper-Pair Boxes: Topologically Ordered States and Topological Quantum Computation",

abstract = "Recent experimental progress introduced devices that can combine topological superconductivity with Coulomb-blockade effects. Experiments with these devices have already provided additional evidence for Majorana zero modes in proximity-coupled semiconductor wires. They also stimulated numerous ideas for how to exploit interactions between Majorana zero modes generated by Coulomb charging effects in networks of Majorana wires. Coulomb effects promise to become a powerful tool in the quest for a topological quantum computer as well as for driving topological superconductors into topologically ordered insulating states. Here, we present a focused review of these recent developments, including discussions of recent experiments, designs of topological qubits, Majorana-based implementations of universal quantum computation, and topological quantum error correction. Motivated by the analogy between a qubit and a spin-1/2 degree of freedom, we also review how coupling between Cooper-pair boxes leads to emergent topologically ordered insulating phases. ",

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AB - Recent experimental progress introduced devices that can combine topological superconductivity with Coulomb-blockade effects. Experiments with these devices have already provided additional evidence for Majorana zero modes in proximity-coupled semiconductor wires. They also stimulated numerous ideas for how to exploit interactions between Majorana zero modes generated by Coulomb charging effects in networks of Majorana wires. Coulomb effects promise to become a powerful tool in the quest for a topological quantum computer as well as for driving topological superconductors into topologically ordered insulating states. Here, we present a focused review of these recent developments, including discussions of recent experiments, designs of topological qubits, Majorana-based implementations of universal quantum computation, and topological quantum error correction. Motivated by the analogy between a qubit and a spin-1/2 degree of freedom, we also review how coupling between Cooper-pair boxes leads to emergent topologically ordered insulating phases.

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Majorana Zero Modes in Networks of Cooper-Pair Boxes: Topologically Ordered States and Topological Quantum Computation

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