  A multiple access channel (MAC) consists of multiple senders simultaneously
transmitting their messages to a single receiver. For the classical-quantum
case (cq-MAC), achievable rates are known assuming that all the messages are
decoded, a common assumption in quantum network design. However, such a
conventional design approach ignores the global network structure, i.e., the
network topology. When a cq-MAC is given as a part of quantum network
communication, this work shows that computation properties can be used to boost
communication speeds with code design dependently on the network topology. We
quantify achievable quantum communication rates of codes with computation
property for a two-sender cq-MAC. When the two-sender cq-MAC is a boson
coherent channel with binary discrete modulation, we show that it achieves the
maximum possible communication rate (the single-user capacity), which cannot be
achieved with conventional design. Further, such a rate can be achieved by
different detection methods: quantum (with and without quantum memory), on-off
photon counting and homodyne (each at different photon power). Finally, we
describe two practical applications, one of which cryptographic.
