Approaching the Quantum Singleton Bound with Approximate Error Correction
summary
Constructs efficiently decodable approximate quantum codes of any constant rate R that correct adversarial errors up to nearly the quantum Singleton bound (≈(1−R)/2) with constant alphabet size and recovery error exponentially small in message length. Key ingredients are a new notion of quantum list decoding implemented via CSS codes built from folded quantum Reed‑Solomon codes plus an expander‑based alphabet reduction, and list filtering using randomness‑efficient purity testing codes or the keyless Pauli manipulation detection primitive together with robust secret sharing.
AI-written summary · about
chapters (12)
- 0:00Introduction
- 12:49Approaching the Singleton Bound
- 16:28Classically
- 21:25Recap
- 22:52List Decoding
- 27:46Quantum Alphabet Reduction
- 35:04Quantum LDPC
- 37:40Approximate Codes
- 41:14Quantum Production
- 44:29Message Fee
- 45:39Decoding
- 55:29Summary
related talks
51mPeaked quantum advantage using error correction
19mAvenues for Quantum Error Correction and Mitigation
01h 41mA 3D Self-Correcting Quantum Memory
43mDecoders for Good Quantum LDPC Codes
32mTowards local testability for quantum coding
49mQuantum Garbled Circuits
01h 07mIntroduction to qLDPC Codes
50mDecoding Quantum Low Density Parity Check Codes