  Quantum networks (QNs) relying on free-space optical (FSO) quantum channels
can support quantum applications in environments wherein establishing an
optical fiber infrastructure is challenging and costly. However, FSO-based QNs
require a clear line-of-sight (LoS) between users, which is challenging due to
blockages and natural obstacles. In this paper, a reconfigurable intelligent
surface (RIS)-assisted FSO-based QN is proposed as a cost-efficient framework
providing a virtual LoS between users for entanglement distribution. A novel
modeling of the quantum noise and losses experienced by quantum states over FSO
channels defined by atmospheric losses, turbulence, and pointing errors is
derived. Then, the joint optimization of entanglement distribution and RIS
placement problem is formulated, under heterogeneous entanglement rate and
fidelity constraints. This problem is solved using a simulated annealing
metaheuristic algorithm. Simulation results show that the proposed framework
effectively meets the minimum fidelity requirements of all users' quantum
applications. This is in stark contrast to baseline algorithms that lead to a
drop of at least 83% in users' end-to-end fidelities. The proposed framework
also achieves a 64% enhancement in the fairness level between users compared to
baseline rate maximizing frameworks. Finally, the weather conditions, e.g.,
rain, are observed to have a more significant effect than pointing errors and
turbulence.
