  Distributing quantum states reliably among distant locations is a key
challenge in the field of quantum networks. One-way quantum networks address
this by using one-way communication and quantum error correction. Here, we
analyze quantum circuit switching as a protocol to distribute quantum states in
one-way quantum networks. In quantum circuit switching, pairs of users can
request the delivery of multiple quantum states from one user to the other.
After waiting for approval from the network, the states can be distributed
either sequentially, forwarding one at a time along a path of quantum
repeaters, or in parallel, sending batches of quantum states from repeater to
repeater. Since repeaters can only forward a finite number of quantum states at
a time, a pivotal question arises: is it advantageous to send them sequentially
(allowing for multiple requests simultaneously) or in parallel (reducing
processing time but handling only one request at a time)? We compare both
approaches in a quantum network with a star topology. Using tools from queuing
theory, we show that requests are met at a higher rate when packets are
distributed in parallel, although sequential distribution can generally provide
service to a larger number of users simultaneously. We also show that using a
large number of quantum repeaters to combat channel losses limits the maximum
distance between users, as each repeater introduces additional processing
delays. These findings provide insight into the design of protocols for
distributing quantum states in one-way quantum networks.
