nLab
topological quantum computation

Contents

Context

Constructivism, Realizability, Computability

Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Contents

Idea

In topological quantum computation one aims to make use of quantum systems described by topological quantum field theory for quantum computation.

For the time being see at quantum computation for more.

References

General:

Specifically via Chern-Simons theory and anyons/quantum Hall effect:

  • Alexei Kitaev, Fault-tolerant quantum computation by anyons, Annals Phys. 303 (2003) 2-30 (arXiv:quant-ph/9707021)

  • Michael Freedman, Michael Larsen, Zhenghan Wang, A modular functor which is universal for quantum computation, Communications in Mathematical Physics. 2002, Vol 227, Num 3, pp 605-622 (arXiv:quant-ph/0001108)

  • Samuel J. Lomonaco Jr., Louis Kauffman, Topological Quantum Computing and the Jones Polynomial, Proc. SPIE 6244, Quantum Information and Computation IV, 62440Z (12 May 2006) (arXiv:quant-ph/0605004)

  • 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)

  • D. Melnikov, A. Mironov, S. Mironov, A. Morozov, An. Morozov, A modular functor which is universal for quantum computation, Nucl. Phys. B926 (2018) 491-508 (arXiv:1703.00431)

  • Eric C. Rowell, Zhenghan Wang, Mathematics of Topological Quantum Computing, Bull. Amer. Math. Soc. 55 (2018), 183-238 (arXiv:1705.06206, doi:10.1090/bull/1605)

Last revised on February 14, 2020 at 09:31:24. See the history of this page for a list of all contributions to it.