Explore fault tolerance in quantum computing through a comprehensive lecture on LDPC codes. Delve into the threshold theorem, surface codes, and the potential of high-rate low-density parity check codes to reduce overhead in quantum computers. Examine progress in code development, decoding algorithms, and fault-tolerant operations. Investigate hypergraph product codes, efficient decoding methods, and constant overhead fault tolerance. Compare the pros and cons of surface codes and high-rate LDPC codes, and consider open questions in the field. Gain insights from Daniel Gottesman of the Perimeter Institute in this Quantum Colloquium presented by the Simons Institute.
Fault Tolerance with LDPC Codes - Quantum Colloquium
Overview
Syllabus
Intro
The Threshold Theorem
Fault-Tolerant Protocols
Low Density Parity Check Codes
Fault-Tolerant Error Correction
Pros and Cons of Surface Codes
What other LDPC codes exist?
Hypergraph Product Codes
Typical Errors
Efficient Decoding Algorithm
Fault-Tolerant Gates
Making Ancillas
Don't Put All Qubits in One Basket
Constant Overhead Fault Tolerance
The (Almost) Precise Theorem
Pros and cons of High-Rate LDPC
Open Questions
Taught by
Simons Institute
