Synthetic Topological Qubits in Conventional Bilayer Quantum Hall Systems

Abstract

The idea of topological quantum computation is to build powerful and robust quantum computers with certain macroscopic quantum states of matter called topologically ordered states. These systems have degenerate ground states that can be used as robust "topological qubits" to store and process quantum information. However, a topological qubit has not been realized since the proposed systems either require sophisticated topologically ordered states that are not available yet, or require complicated geometries that are too difficult to realize. In this paper, we propose a new experimental setup which can realize topological qubits in a simple bilayer fractional quantum Hall (FQH) system with proper electric gate configurations. Compared to previous works, our proposal is accessible with current experimental techniques and only involves well-established topological states. Our system can realize a large class of topological qubits, generalizing the Majorana zero modes studied in the recent literature to more computationally powerful possibilities. We propose three tunneling and interferometry experiments to detect the existence and non-local topological properties of the topological qubits.

6 pages (text + refs) + 8 pages appendix

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• Matrix product operator symmetries and intertwiners in string-nets with domain walls
• Boundary Criticality of the 3D O($N$) Model: From Normal to Extraordinary
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• Abelian and Non-Abelian States in $\nu =2/3$ Bilayer Fractional Quantum Hall Systems
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• Symmetry Enrichment in Three-Dimensional Topological Phases
• Anyonic Symmetries and Topological Defects in Abelian Topological Phases: an application to the $ADE$ Classification
• Designer non-Abelian anyon platforms: from Majorana to Fibonacci
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• Topological phase, supercritical point and emergent phenomena in extended ${\mathbb{Z}}_3$ parafermion chain
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• Electron-Tunneling-Assisted Non-Abelian Braiding of Rotating Majorana Bound States
• Fermion Parity Flips and Majorana Bound States at twist defects in Superconducting Fractional Topological Phases
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• Duality between open systems and closed bilayer systems: Thermofield double states as quantum many-body scars
• Do Rydberg chains yield Fibonacci anyons?
• Commuting-projector Hamiltonians for chiral topological phases built from parafermions
• The ordinary surface universality class of the three-dimensional O($N$) model
• Projective symmetry group classification of $Z_3$ parafermion spin liquids on a honeycomb lattice
• Universal finite-size scaling in the extraordinary-log boundary phase of three-dimensional $O(N)$ model
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• Theory of topological defects and textures in two-dimensional quantum orders with spontaneous symmetry breaking
• Dihedral twist liquid models from emergent Majorana fermions
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