Measurement-Only Topological Quantum Computation via Anyonic Interferometry

Abstract

We describe measurement-only topological quantum computation using both projective and interferometrical measurement of topological charge. We demonstrate how anyonic teleportation can be achieved using "forced measurement" protocols for both types of measurement. Using this, it is shown how topological charge measurements can be used to generate the braiding transformations used in topological quantum computation, and hence that the physical transportation of computational anyons is unnecessary. We give a detailed discussion of the anyonics for implementation of topological quantum computation (particularly, using the measurement-only approach) in fractional quantum Hall systems.

57 pages, 5 figures; v2: minor corrections

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• How quickly can anyons be braided? Or: How I learned to stop worrying about diabatic errors and love the anyon
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• Proximity-induced low-energy renormalization in hybrid semiconductor-superconductor Majorana structures
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• Majorana bound states in semiconducting nanostructures
• Metaplectic Anyons, Majorana Zero Modes, and their Computational Power
• Braiding Majorana zero modes using quantum dots
• Splitting the Topological Degeneracy of non-Abelian Anyons
• Anyonic entanglement renormalization
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• Fault-Tolerant Quantum Error Correction for non-Abelian Anyons
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• Number conserving analysis of measurement-based braiding with Majorana zero modes
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• Modular transformations through sequences of topological charge projections
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• Interacting Valley Chern Insulator and its Topological Imprint on Moiré Superconductors
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• Measuring Topological Order
• Quantum computing with Octonions
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• 1D Error Correcting Code for Majorana Qubits
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