t b a b a

protect such a stream only by cutting it into successive K-qubit blocks. Some introduction
and details can be found in [Cha98, Cha99, OT03, OT04].
Quantum Codes for Burst Error: Most quantum error correction codes assume
the ”independent qubit decoherence”(IQD) model in which the decoherence of each qubit
is uncorrelated to the decoherence of any other qubit as they all interact with separate
reservoirs. If this is not true, the errors are space-correlated, typically shown as a burst of
errors. Many approaches are introduced for burst error correction, such as Quantum cyclic
code [VRA99], Quantum interleaver [Kaw00].
Quantum Reed-Solomon Code [GGB99]: a classical [N; K; d] Reed-Solomon code
over GF (2 k ) with length N = 2 k − 1, distance d, and dimension K = N − d + 1, is a cyclic
code with the generator polynomial:
g(x) = (x − β j )(x − β j+1 · · · (x − β j+d−2 ))
with β a primitive element of GF (2 k ) of order N.
The quantum Reed-Solomon [N; K; d] code encodes k(2N-K) qubits in states | ϕ1〉, |
ϕ2〉 · · · | ϕk(2N−K)〉into kN qubits.
It can be constructed as a family of Calderbank-Shor-Steane (CSS) codes.
81