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SUMMARY:Elia Portnoy (MIT)
DTSTART:20241203T213000Z
DTEND:20241203T223000Z
DTSTAMP:20260423T021127Z
UID:MathPic/137
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MathPic/137/
 ">Quantum error-correcting codes\, systolic geometry\, and quantitative em
 beddings</a>\nby Elia Portnoy (MIT) as part of Mathematical Picture Langua
 ge Seminar\n\nLecture held in Jefferson 356 and Zoom https://harvard.zoom.
 us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09.\n\nAbstract\nThere ha
 ve been several recent breakthroughs constructing good quantum codes which
  have N qubits with distance and dimension Ω(N). However\, these codes ca
 nnot be implemented in 3 dimensions - there is no way to place the qubits 
 on a lattice so that every check only involves the qubits in some small ba
 ll. Bravyi and Terhal have shown that such 3d codes with  qubits can have 
 distance at most O(N^2/3) and dimension at most O(N^1/3)\, given that dist
 ance. In this talk I'll discuss how to construct 3d codes with parameters 
 that match these bounds. This relies on the known good codes\, a connectio
 n between codes and systolic geometry made by Freedman-Hastings\, and a qu
 antitative embedding theorem.\n\nPasscode: 657361\n
LOCATION:https://researchseminars.org/talk/MathPic/137/
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