Local Quantum Codes from Subdivided Manifolds

PIRSA ID: 23030111
Event Type: Seminar
Scientific Area(s):
Quantum Information
End date:
  • Elia Portnoy, Massachusetts Institute of Technology (MIT)

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