  Connecting multiple processors via quantum interconnect technologies could
help to overcome issues of scalability in single-processor quantum computers.
Transmission via these interconnects can be performed more efficiently using
quantum multiplexing, where information is encoded in high-dimensional photonic
degrees of freedom. We explore the effects of multiplexing on logical error
rates in surface codes and hypergraph product codes. We show that, although
multiplexing makes loss errors more damaging, assigning qubits to photons in an
intelligent manner can minimize these effects, and the ability to encode
higher-distance codes in a smaller number of photons can result in overall
lower logical error rates. This multiplexing technique can also be adapted to
quantum communication and multimode quantum memory with high-dimensional qudit
systems.
