  Topological quantum error correcting codes have emerged as leading candidates
towards the goal of achieving large-scale fault-tolerant quantum computers.
However, quantifying entanglement in these systems of large size in the
presence of noise is a challenging task. In this paper, we provide two
different prescriptions to characterize noisy stabilizer states, including the
surface and the color codes, in terms of localizable entanglement over a subset
of qubits. In one approach, we exploit appropriately constructed entanglement
witness operators to estimate a witness-based lower bound of localizable
entanglement, which is directly accessible in experiments. In the other recipe,
we use graph states that are local unitary equivalent to the stabilizer state
to determine a computable measurement-based lower bound of localizable
entanglement. If used experimentally, this translates to a lower bound of
localizable entanglement obtained from single-qubit measurements in specific
bases to be performed on the qubits outside the subsystem of interest. Towards
computing these lower bounds, we discuss in detail the methodology of obtaining
a local unitary equivalent graph state from a stabilizer state, which includes
a new and scalable geometric recipe as well as an algebraic method that applies
to general stabilizer states of arbitrary size. Moreover, as a crucial step of
the latter recipe, we develop a scalable graph-transformation algorithm that
creates a link between two specific nodes in a graph using a sequence of local
complementation operations. We develop open-source Python packages for these
transformations, and illustrate the methodology by applying it to a noisy
topological color code, and study how the witness and measurement-based lower
bounds of localizable entanglement varies with the distance between the chosen
qubits.
