Local Quantum Codes from Subdivided Manifolds

PIRSA ID: 23030111
Série : Perimeter Institute Quantum Discussions
Event Type: Seminar
Domaine(s) scientifique(s) :
Quantum Information
Date de fin :
Speaker(s):
  • Elia Portnoy, Massachusetts Institute of Technology (MIT)
March 22, 2023 at 11:00 AM Other/External

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