PIRSA:23030111 Scientific Series Quantum Information

DOI10.48660/23030111

Series: Perimeter Institute Quantum Discussions

Portnoy, E. (2023). Local Quantum Codes from Subdivided Manifolds. Perimeter Institute. https://pirsa.org/23030111

Portnoy, Elia. Local Quantum Codes from Subdivided Manifolds. Perimeter Institute, Mar. 22, 2023, https://pirsa.org/23030111 

@misc{ pirsa_PIRSA:23030111,
  doi = {10.48660/23030111},
  url = {https://pirsa.org/23030111},
  author = {Portnoy, Elia},
  keywords = {Quantum Information},
  language = {en},
  title = {Local Quantum Codes from Subdivided Manifolds},
  publisher = {Perimeter Institute},
  year = {2023},
  month = {mar},
  note = {PIRSA:23030111 see, \url{https://pirsa.org}}
}

Abstract

For n≥3, we demonstrate the existence of quantum codes which are local in dimension n with V qubits, distance V^{(n−1)/n}, and dimension V^{(n−2)/n}, up to a polylog(V) factor. The distance is optimal up to the polylog factor. The dimension is also optimal for this distance up to the polylog factor. The proof combines the existence of asymptotically good quantum codes, a procedure to build a manifold from a code by Freedman-Hastings, and a quantitative embedding theorem by Gromov-Guth.

Zoom link:  https://pitp.zoom.us/j/96227350980?pwd=TEFtamRmTXg3dnBMNEhKUkpHbmVoZz09

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