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

Hiding qubits from the noise y y ground state throw away exact!

Classical information theory

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.

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

Minimum distance d ) correct up to (d-1)/2 errors. Example: G= 1010101 H = 1010101 0110011 0110011 0001111 0001111 1111111 C = 0000000, 1010101, 0110011, 1100110, 0001111, 1011010, 0111100, 1101001 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.

Dual codes Some codes contain their duals.

Quasi-classical code

} “correction” results in  correct

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