

Advance in quantum error correction - user_235711
http://newsoffice.mit.edu/2015/quantum-error-correction-0526

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scythe
It was already possible to correct a positive fraction of qubits as long as
you accept a constant distance; consider the Hamiltonian:

H = <a_i1|X|a_i2> \+ <a_i2|Z|a_i3> \+ <a_i1|Z|a_(i+1)1> \+ <a_i3|X|a_(i+1)3>
[i = 1..N]

This generates a [N, N/3, 2] code, with N/3 logical qubits per physical qubit.
The trouble is that a no-go theorem states that for codes defined by operators
which are local in any finite dimension, the code distance d = o(N); in
particular, in two dimensions, d = O(√N).

(IIRC; haven't done this in a while...)

