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Quantum Engineering Year 2: Advanced Quantum Science Month 36Day 984

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Year 2·Month 36·Week 1

Day 984: Panteleev-Kalachev & Quantum Tanner Codes

Day 984 of 2,016~19 min read

Learning Objectives

•Explain the lifted product construction using group algebras
•Describe how Cayley graphs provide the expansion needed
•Construct quantum Tanner codes from left-right Cayley complexes
•Calculate code parameters from the underlying graph structure
•Compare the Panteleev-Kalachev and Leverrier-Zémor approaches
•Appreciate the algebraic machinery behind good qLDPC codes

Today's Schedule (7 hours)

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On this page

1 The Key Insight Lifting 2 Group Algebras 3 Cayley Graphs and Expansion 4 The Lifted Product Construction 5 Distance Improvement via Expansion 6 Quantum Tanner Codes Leverrier-Zmor 2022 7 Explicit Example Small Lifted Product 8 Code Parameters Summary Practical Applications Path to Implementation

Day 983Day 984 of 2,016Day 985