  Inspired by classical polar codes, whose coding rate can asymptotically
achieve the Shannon capacity, researchers are trying to find its analogue in
quantum information field, which are called quantum polar codes. However, no
one has designed a quantum polar coding scheme which applies to quantum
computing yet. There are two intuitions in previous research. The first is that
directly converting classical polar coding circuits to quantum ones will
produce polarization phenomenon of pure quantum channel, which has been proved
in our previous work. The second is that based on this quantum polarization
phenomenon one can design a quantum polar coding scheme that applies to quantum
computing. There are several previous work following the second intuition, none
of which has been verified by experiments. In this paper, we follow the second
intuition and propose a more reasonable quantum polar stabilizer code
construction algorithm than any previous ones by using the theory of stabilizer
codes. Unfortunately, simulation experiments show that even the stabilizer
codes obtained from this more reasonable construction algorithm don't work,
which implies that the second intuition leads to a dead end. Based on the
analysis on why the second intuition don't work, we provide a possible future
direction of designing quantum stabilizer codes with high coding rate by
borrowing the idea of classical polar codes. following this direction, we find
a class of quantum stabilizer codes with coding rate 0.5 for pure Pauli X, Z
and Y noise.
