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, Oxford University Press (2023) [ISBN:9780198886723, pdf, webpage]

On topological quantum compilation and approximating (cf. the Solovay-Kitaev theorem) given quantum gates by (i.e. compiling them to) ciOcuits 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)

On “Gaffnian states” for quantum Hall systems:

• Steven H. Simon, Edward H. Rezayi, Nigel R. Cooper, I. Berdnikov: Construction of a paired wave function for spinless electrons at filling fraction $\nu = 2/5$, Phys. Rev. B 75 (2007) 075317 [doi:10.1103/PhysRevB.75.075317]

On fractional quantum Hall systems and description of its Laughlin wavefunctions as conformal blocks of 2d CFT:

• Thors H. Hansson, M. Hermanns, Steven H. Simon, S. F. Viefers: Quantum Hall Physics – hierarchies and CFT techniques, Rev. Mod. Phys. 89 (2017) 025005 [arXiv:1601.01697, doi:10.1103/RevModPhys.89.025005]

On Laughlin wavefunctions and its cousins, approximating ground states of fractional quantum Hall systems:

• Steven H. Simon: Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions, Chapter 8 of: Fractional Quantum Hall Effects eds. Halperin and Jain, World Scientific (2020) [arXiv:2107.00437, doi:10.1142/11751]

On topological phases of matter via higher lattice gauge theory:

• Joe Huxford, Steven H. Simon, Excitations in the Higher Lattice Gauge Theory Model for Topological Phases I: Overview [arXiv:2202.08294]

category: people