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Quantum Engineering Year 1: Quantum Mechanics Core Month 24Day 663

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Year 1·Month 24·Week 3

Day 663: Nine-Qubit Shor Code

Day 663 of 2,016~10 min read

Learning Objectives

•**Understand** concatenation of error correcting codes
•**Construct** the 9-qubit Shor code from bit-flip and phase-flip codes
•**Verify** that Shor code corrects arbitrary single-qubit errors
•**Analyze** syndrome measurement and correction procedures
•**Appreciate** the historical significance of this discovery

Today's Schedule (7 hours)

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On this page

1 The Problem with 3-Qubit Codes 2 The Concatenation Idea 3 Shor Code Construction 4 Full Shor Code States 5 Encoding Circuit 6 Bit-Flip Syndrome Operators 7 Phase-Flip Syndrome Operators 8 Complete Syndrome Table 9 Error Correction Procedure 10 Why It Works Knill-Laflamme Verification 11 Discretization of Errors 12 Code Parameters Worked Example

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