~/talk

Explicit Abelian Lifts and Quantum LDPC Codes

Talkat ITCS 2022 · 2022-01-31..02-03· [quantum-computing]

speakers

name:Fernando Granha Jeronimo

links:none on file

name:Tushant Mittal

links:none on file

name:Ryan O'Donnell

links:none on file

name:Pedro Paredes

links:none on file

name:Madhur Tulsiani

links:none on file

resources

video:https://youtu.be/X-YOL_o247E

slides:none on file

summary

Constructs polynomial-time explicit d-regular expanders that are Z_L lifts (and more generally transitive abelian lifts) for L up to about 2^{cN}, derandomizing prior existential results and producing explicit quasi-cyclic LDPC and quantum LDPC codes with distance nearly N^{1−α} (and almost linear distance in some regimes). Analysis uses the trace power/trace-bar method plus a new combinatorial count of hikes (singleton-free nonbacktracking walks) via compressed DFS encodings, yielding near-Ramanujan eigenvalue bounds in the stated ranges.

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