Quantum Error Correction :

1. Quantum ErrorCorrection: • Andrew Landahl • David Gottesman • Dr. Wu • And others

4. Stabilizer measurement?? Z1 • This is implementing a measurement (interpreting 0 as +1, and 1 as –1)

5. Stabilizer measurement?? Z1 Z2 • This is implementing a measurement

6. Stabilizer measurement?? Stabilizer measurement?? • This is implementing a measurement

7. Notation clarification • For an n-qubit system denotes • E.g. n=3, then What does it mean Z1 Z2?

8. The Shor Code as a Stabilizer code

10. Stabilizer codes

11. Stabilizer Codes by Gottesman, 1997

24. Classical (7,4,3) Hamming Code C1

25. Stabilizer for Steane code

26. Steane code: based on Hamming code

34. Vector Space under Symplectic Inner Products

35. Weight and Distance

36. Theorem for Existence of Additive QECC

37. Stabilizer for 5-qubit [5,1,3] code

38. Symplectic Form for Stabilizer

39. Commuting Group

40. Linear Block Codes

41. Standard Symplectic Form

42. Encoder for Stabilizer Codes

43. (5,1,3) code [5,1,3] Quantum Encoder (X part)

44. (5,1,3) code Complete [5,1,3] Quantum Encoder