nLab Steven H. Simon

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Selected writings

On topological quantum computation with anyons:

• Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, Sankar Das Sarma, Non-Abelian Anyons and Topological Quantum Computation, Rev. Mod. Phys. 80, 1083 (2008) (arXiv:0707.1888)

• Steven H. Simon, Topological Quantum, 2021 $[$pdf, webpage$]$

On approximating (cf. the Solovay-Kitaev theorem) given quantum gates by (i.e. compiling them to) cicuits of anyon braid gates (generally considered for su(2)-anyons and here mostly for universal Fibonacci anyons, to some extent also for non-universal Majorana anyons):

• Nicholas E. Bonesteel, Layla Hormozi, Georgios Zikos, Steven H. Simon, Braid Topologies for Quantum Computation, Phys. Rev. Lett. 95 140503 (2005) $[$arXiv:quant-ph/0505065, doi:10.1103/PhysRevLett.95.140503$]$

• Layla Hormozi, Georgios Zikos, Nicholas E. Bonesteel, Steven H. Simon, Topological Quantum Compiling, Phys. Rev. B 75 165310 (2007) $[$arXiv:quant-ph/0610111, doi:10.1103/PhysRevB.75.165310$]$

• Layla Hormozi, Nicholas E. Bonesteel, Steven H. Simon, Topological Quantum Computing with Read-Rezayi States, Phys. Rev. Lett. 103 160501 (2009) $[$doi:10.1103/PhysRevLett.103.160501, arXiv:0903.2239$]$

• M. Baraban, Nicholas E. Bonesteel, Steven H. Simon, Resources required for topological quantum factoring, Phys. Rev. A 81 062317 (2010) $[$doi:10.1103/PhysRevA.81.062317, arXiv:1002.0537$]$

  (focus on compiling Shor's algorithm)

and particularly by just the “weaves” among all braids:

• Steven H. Simon, Nick E. Bonesteel, Michael H. Freedman, N. Petrovic, Layla Hormozi, Topological Quantum Computing with Only One Mobile Quasiparticle, Phys. Rev. Lett. 96 (2006) 070503 (arXiv:quant-ph/0509175, doi:10.1103/PhysRevLett.96.070503)

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