Resources required for topological quantum factoring

Baraban, M.; Bonesteel, N. E.; Simon, Steven H.

doi:10.1103/physreva.81.062317

Cited by 13 publications

(16 citation statements)

References 23 publications

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“…Not all anyon models, such as Ising anyons, provide universality by braiding alone (Sarma et al, 2015). Such computers need to be supplemented by non-topological operations in order to achieve universality (Baraban et al, 2010;Bravyi, 2006;Pachos, 2012). There even exist schemes for topological quantum computing which entirely replace braiding with different topological operations such as measurement (Bonderson et al, 2008).…”

Section: Using Fibonacci Anyons For Computingmentioning

confidence: 99%

Introduction to topological quantum computation with non-Abelian anyons

Field

Simula

2018

Quantum Sci. Technol.

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Topological quantum computers promise a fault tolerant means to perform quantum computation. Topological quantum computers use particles with exotic exchange statistics called non-Abelian anyons, and the simplest anyon model which allows for universal quantum computation by particle exchange or braiding alone is the Fibonacci anyon model. One classically hard problem that can be solved efficiently using quantum computation is finding the value of the Jones polynomial of knots at roots of unity. We aim to provide a pedagogical, self-contained, review of topological quantum computation with Fibonacci anyons, from the braiding statistics and matrices to the layout of such a computer and the compiling of braids to perform specific operations. Then we use a simulation of a topological quantum computer to explicitly demonstrate a quantum computation using Fibonacci anyons, evaluating the Jones polynomial of a selection of simple knots. In addition to simulating a modular circuit-style quantum algorithm, we also show how the magnitude of the Jones polynomial at specific points could be obtained exactly using Fibonacci or Ising anyons. Such an exact algorithm seems ideally suited for a proof of concept demonstration of a topological quantum computer.

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Section: Using Fibonacci Anyons For Computingmentioning

confidence: 99%

Introduction to topological quantum computation with non-Abelian anyons

Field

Simula

2018

Quantum Sci. Technol.

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“…For a π/8 phase gate with 99% fidelity, factoring a 128-bit number would consequently require ≈ 10 9 Ising anyons in the scheme analyzed in Ref. 96 [98]. Thus overcoming the nontrivial fabrication challenges involved could prove enormously beneficial for quantum information applications.…”

Section: Introductionmentioning

confidence: 99%

Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure

et al. 2014

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Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Green's observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional p + ip superconductor both support so-called Ising non-Abelian anyons. Here we establish a similar correspondence between the Z3 Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge-2e Cooper pairs are built from fractionalized quasiparticles. In particular, both phases harbor Fibonacci anyons that-unlike Ising anyons-allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kane's construction of non-Abelian phases from weakly coupled chains, we provide a blueprint for such a superconductor using Abelian quantum Hall states interlaced with an array of superconducting islands. Fibonacci anyons appear as neutral deconfined particles that lead to a two-fold ground-state degeneracy on a torus. In contrast to a p + ip superconductor, vortices do not yield additional particle types yet depending on non-universal energetics can serve as a trap for Fibonacci anyons. These results imply that one can, in principle, combine well-understood and widely available phases of matter to realize non-Abelian anyons with universal braid statistics. Numerous future directions are discussed, including speculations on alternative realizations with fewer experimental requirements. arXiv:1307.4403v2 [cond-mat.str-el]

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“…1 & 2 1 [ Ω] 2 [ Ω] Formation of a conducting domain wall at a boundary between unpolarized and polarized ν = 2/3 regions is shown in Fig. 3.…”

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confidence: 99%