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Quantum Error Correction :. Andrew Landahl David Gottesman Dr. Wu And others. Stabilizer measurement??. Z 1. This is implementing a measurement (interpreting 0 as +1, and 1 as –1). Stabilizer measurement??. Z 1. Z 2. This is implementing a measurement. - PowerPoint PPT Presentation
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Quantum ErrorCorrection:
• Andrew Landahl• David Gottesman• Dr. Wu• And others
Stabilizer measurement?? Stabilizer measurement??
0
This is implementing a measurement (interpreting 0 as +1, and 1 as –1)
1Z
Z1
0
This is implementing a measurement
21ZZ
Stabilizer measurement?? Stabilizer measurement??
Z1
Z2
Stabilizer measurement??
0
This is implementing a measurement
21XX
H H
Stabilizer measurement?? Stabilizer measurement??
Notation clarification Notation clarification
For an n-qubit system denotes
E.g. n=3, then
jZ
jnj
IIZIII
1
IZZIZIIIZZZ 21
What does it mean Z1 Z2?
The Shor The Shor Code as a Code as a Stabilizer Stabilizer
code code
Stabilizer codesStabilizer codes
Stabilizer Codes by Stabilizer Codes by Gottesman, 1997Gottesman, 1997
Classical (7,4,3) Hamming Classical (7,4,3) Hamming Code CCode C11
Stabilizer for Steane code
Steane code: based on Hamming code
Vector Space under Symplectic Inner Products
Weight and Distance
Theorem for Existence of Additive QECC
Stabilizer for 5-qubit [5,1,3] codeStabilizer for 5-qubit [5,1,3] code
Symplectic Form for Stabilizer
Commuting Group
Linear Block Codes
Standard Symplectic Form
Encoder for Stabilizer Codes
[5,1,3] Quantum Encoder (X part)
(5,1,3) code(5,1,3) code
Complete [5,1,3] Quantum Encoder
(5,1,3) code(5,1,3) code