  Quantum network communication is challenging, as the No-Cloning theorem in
quantum regime makes many classical techniques inapplicable. For long-distance
communication, the only viable approach is teleportation of quantum states,
which requires a prior distribution of entangled pairs (EPs) of qubits.
Establishment of EPs across remote nodes can incur significant latency due to
the low probability of success of the underlying physical processes. To reduce
EP generation latency, prior works have looked at selection of efficient
entanglement-routing paths and simultaneous use of multiple such paths for EP
generation. In this paper, we propose and investigate a complementary technique
to reduce EP generation latency--to pre-distribute EPs over certain
(pre-determined) pairs of network nodes; these pre-distributed EPs can then be
used to generate EPs for the requested pairs, when needed, with lower
generation latency. For such an pre-distribution approach to be most effective,
we need to address an optimization problem of selection of node-pairs where the
EPs should be pre-distributed to minimize the generation latency of expected EP
requests, under a given cost constraint. In this paper, we appropriately
formulate the above optimization problem and design two efficient algorithms,
one of which is a greedy approach based on an approximation algorithm for a
special case. Via extensive evaluations over the NetSquid simulator, we
demonstrate the effectiveness of our approach and developed techniques; we show
that our developed algorithms outperform a naive approach by up to an order of
magnitude.
