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Abstract:

We consider a hypothetical topological quantum computer composed of either Ising or Fibonacci anyons. For each case, we calculate the time and number of qubits (space) necessary to execute the most computationally expensive step of Shor's algorithm, modular exponentiation. For Ising anyons, we apply Bravyi's distillation method which combines topological and nontopological operations to allow for universal quantum computation. With reasonable restrictions on the physical parameters we find that factoring a 128-bit number requires approximately 103 Fibonacci anyons versus at least 3×109 Ising anyons. Other distillation algorithms could reduce the resources for Ising anyons substantially. © 2010 The American Physical Society.

Abstract:

We study charged excitations of the non-Abelian Moore-Read liquid at a filling factor ν=52, allowing for spin depolarization. Using a combination of numerical studies, and taking account of nonzero well widths, we find that at a sufficiently low Zeeman energy it is energetically favorable for charge e/4 quasiholes to bind into Skyrmions of charge e/2. We show that Skyrmion formation is further promoted by disorder, and argue that this can lead to a depolarized ν=52 ground state in realistic experimental situations. We comment on the consequences for the activated transport. © 2010 The American Physical Society.