  Iterative decoders for finite length quantum low-density parity-check (QLDPC)
codes are attractive because their hardware complexity scales only linearly
with the number of physical qubits. However, they are impacted by short cycles,
detrimental graphical configurations known as trapping sets (TSs) present in a
code graph as well as symmetric degeneracy of errors. These factors
significantly degrade the decoder decoding probability performance, and cause
so-called error floor. In this paper, we establish a systematic methodology by
which one can identify and classify quantum trapping sets (QTSs) according to
their topological structure and decoder used. Conventional definition of a TS
from classical error correction is generalized to address the syndrome decoding
scenario for QLDPC codes. We show that the knowledge of QTSs can be used to
design better QLDPC code and decoder. Frame error rate improvements of two
orders of magnitude in the error floor regime are demonstrated for some
practical finite-length QLDPC codes without requiring any post-processing.
