Quantum Error Correction:

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Quantum ErrorCorrection

• Andrew Landahl
• David Gottesman
• Dr. Wu
• And others

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Stabilizer measurement??
Z1

• This is implementing a measurement
  (interpreting 0 as 1, and 1 as 1)

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Stabilizer measurement??
Z1
Z2

• This is implementing a measurement

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Stabilizer measurement??
Stabilizer measurement??

• This is implementing a measurement

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Notation clarification

• For an n-qubit system denotes
• E.g. n3, then

What does it mean Z1 Z2?
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The Shor Code as a Stabilizer code
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Stabilizer codes
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Stabilizer Codes by Gottesman, 1997
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Classical (7,4,3) Hamming Code C1
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Stabilizer for Steane code
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Steane code based on Hamming code
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Vector Space under Symplectic Inner Products
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Weight and Distance
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Theorem for Existence of Additive QECC
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Stabilizer for 5-qubit 5,1,3 code
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Symplectic Form for Stabilizer
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Commuting Group
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Linear Block Codes
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Standard Symplectic Form
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Encoder for Stabilizer Codes
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5,1,3 Quantum Encoder (X part)
(5,1,3) code
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Complete 5,1,3 Quantum Encoder
(5,1,3) code
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