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Quantum Engineering Year 1: Quantum Mechanics Core Month 24Day 664

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Year 1·Month 24·Week 3

Day 664: Stabilizer Formalism Preview

Day 664 of 2,016~9 min read

Learning Objectives

•**Introduce** the Pauli group and stabilizer formalism
•**Define** stabilizer codes using group generators
•**Reformulate** the 3-qubit and Shor codes as stabilizer codes
•**Understand** the connection between stabilizers and syndromes
•**Preview** the CSS code construction

Today's Schedule (7 hours)

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On this page

1 Motivation A Systematic Framework 2 The Pauli Group 3 Key Properties of Pauli Operators 4 Stabilizer Definition 5 Generators 6 Three-Qubit Bit-Flip as Stabilizer Code 7 Three-Qubit Phase-Flip as Stabilizer Code 8 Shor Code Stabilizers 9 Syndrome Measurement as Stabilizer Eigenvalues 10 Error Correction Condition Stabilizer Version 11 Logical Operators 12 Code Distance 13 CSS Codes Preview 14 Advantages of Stabilizer Formalism Worked Example

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