  Bell-state measurement (BSM) on entangled states shared between quantum
repeaters is the fundamental operation used to route entanglement in quantum
networks. Performing BSMs on Werner states shared between repeaters leads to
exponential decay in the fidelity of the end-to-end Werner state with the
number of repeaters, necessitating entanglement distillation. Generally,
entanglement routing protocols use \emph{probabilistic} distillation techniques
based on local operations and classical communication. In this work, we use
quantum error correcting codes (QECCs) for \emph{deterministic} entanglement
distillation to route Werner states on a chain of repeaters. To maximize the
end-to-end distillable entanglement, which depends on the number and fidelity
of end-to-end Bell pairs, we utilize global link-state knowledge to determine
the optimal policy for scheduling distillation and BSMs at the repeaters. We
analyze the effect of the QECC's properties on the entanglement rate and the
number of quantum memories. We observe that low-rate codes produce
high-fidelity end-to-end states owing to their excellent error-correcting
capability, whereas high-rate codes yield a larger number of end-to-end states
but of lower fidelity. The number of quantum memories used at repeaters
increases with the code rate as well as the classical computation time of the
QECC's decoder.
