1. Quantum Error Correction
a tutorial
A.M. Steane
Oxford University

2. Hiding qubits from the noisey y
ground state
throw away
exact!

3. Classical information theory

4. The simple repetition idea can achieve good quality (i. e
The simple repetition idea can achieve good quality (i.e. low noise) communication, but it makes inefficient use of the bits.
To do better, we look in detail at how bit flips affect bit strings.

5. Classical Error Correcting Codes
100
001
010
110
011
111
000
A code is also a group under addition

6. Minimum distance d ) correct up to (d-1)/2 errors.
Example:
G= H =
C = , , , ,
, , ,
7 bits, 23 = 8 members, minimum weight 4
Minimum distance d ) correct up to (d-1)/2 errors.
For a linear code, the minimum distance between
members is also the minimum weight.

7. Dual codes
Some codes contain their duals.

9. Quasi-classical code

11. }
“correction”
results in
 correct

12.  to pdf