  Quantum error correction is the building block for constructing
fault-tolerant quantum processors that can operate reliably even if its
constituting elements are corrupted by decoherence. In this context, real-time
decoding is a necessity for implementing arbitrary quantum computations on the
logical level. In this work, we present a new decoder for Quantum Low Density
Parity Check (QLDPC) codes, named the closed-branch decoder, with a worst-case
complexity loosely upper bounded by
$\mathcal{O}(n\text{max}_{\text{gr}}\text{max}_{\text{br}})$, where
$\text{max}_{\text{gr}}$ and $\text{max}_{\text{br}}$ are tunable parameters
that pose the accuracy versus speed trade-off of decoding algorithms. For the
best precision, the $\text{max}_{\text{gr}}\text{max}_{\text{br}}$ product
increases exponentially as $\propto dj^d$, where $d$ indicates the distance of
the code and $j$ indicates the average row weight of its parity check matrix.
Nevertheless, we numerically show that considering small values that are
polynomials of the code distance are enough for good error correction
performance. The decoder is described to great extent and compared with the
Belief Propagation Ordered Statistics Decoder (BPOSD) operating over data
qubit, phenomenological and circuit-level noise models for the class of
Bivariate Bicycle (BB) codes. The results showcase a promising performance of
the decoder, obtaining similar results with much lower complexity than BPOSD
when considering the smallest distance codes, but experiencing some logical
error probability degradation for the larger ones. Ultimately, the performance
and complexity of the decoder depends on the product
$\text{max}_{\text{gr}}\text{max}_{\text{br}}$, which can be considered taking
into account benefiting one of the two aspects at the expense of the other.
