Overview of Quantum Error Correction - Victor Albert

Dive into a comprehensive lecture on quantum error correction delivered by Victor Albert from NIST/Maryland at the Noisy Intermediate-Scale Quantum Systems conference. Explore the origins, growth, and basics of quantum error correction, starting with repetition codes and progressing to more complex structures like stabilizer codes, surface codes, and bosonic codes. Examine the geometric perspective of error correction, discuss break-even points and threshold theorems, and learn about the hardness of decoding. Gain insights into recent experimental implementations, commercial proposals, and the explosion of quantum low-density parity-check (QLDPC) codes. Conclude with observations on notable codes and emerging opportunities in the field of quantum error correction.

Intro
GOAL OF ERROR CORRECTION
QEC: ORIGINS & GROWTH
BASICS OF ERROR CORRECTION: REPETITION CODE
MY FIRST QUANTUM CODE
ERROR SPACE STRUCTURE
GENERAL QEC CONDITIONS
FOUR-QUBIT CODE → CONCATENATED CODE
FOUR-QUBIT CODE → STABILIZER CODE
FOUR-QUBIT CODE → CSS CODE
FOUR-QUBIT CODE → SURFACE CODE
FOUR-QUBIT CODE → BINOMIAL CODE
GEOMETRIC PERSPECTIVE → BOSONIC CODES
USE CASES OF DIMENSIONS
BREAK EVEN & THRESHOLD THEOREM
HARDNESS OF DECODING
STABILIZER EXPERIMENTS
BOSONIC EXPERIMENTS
COMMERCIAL PROPOSALS
QLDPC EXPLOSION
OTHER NOTABLE CODES
OBSERVATIONS & OPPORTUNITIES