PIRSA:13010101 Scientific Series Quantum Foundations

DOI10.48660/13010101

Series: Perimeter Institute Quantum Discussions

Yoshida, B. (2013). Exotic topological order from quantum fractal code. Perimeter Institute. https://pirsa.org/13010101

Yoshida, Beni. Exotic topological order from quantum fractal code. Perimeter Institute, Jan. 14, 2013, https://pirsa.org/13010101 

@misc{ pirsa_PIRSA:13010101,
  doi = {10.48660/13010101},
  url = {https://pirsa.org/13010101},
  author = {Yoshida, Beni},
  keywords = {Quantum Foundations},
  language = {en},
  title = {Exotic topological order from quantum fractal code},
  publisher = {Perimeter Institute},
  year = {2013},
  month = {jan},
  note = {PIRSA:13010101 see, \url{https://pirsa.org}}
}

Abstract

We present a family of three-dimensional local quantum codes with pairs of fractal logical operators. It has two polynomials over finite fields as input parameters which generate fractal shapes of anti-commuting logical operators, and possesses exotic topological order with quantum glassiness which is beyond descriptions of conventional topological field theory. A necessary and sufficient condition for being free from string-like logical operators is obtained under which the model works as marginally self-correcting quantum memory. We also provide theoretical tools to analyze physical and coding properties of translation symmetric stabilizer Hamiltonians.

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