I'm new to quantum computing, and computing in general, but it seems like quantum computing networks are really lagging behind what we have achieved with classical networks. I know that there are limitations, such as the need for quantum repeaters, as quantum information can not be cloned, but I have also seen that designs for such repeaters have been created. I was wondering why, if these limitations can be surpassed, has no global quantum computing network been created?
Quantum communication is a field where theory is far beyond experiment. Entanglement theory lies at the heart of computational complexity and entanglement is what really separates quantum mechanics from classical physics. To create a highly entangled state and keep it free from noise is the main problem of building a quantum computer and also of building a quantum network. Given that most quantum networks are represented by a graph state which is also a resource for universal quantum computation your question is equal to "Why cannot we build a decent fault tolerant quantum computer while we can build classical computers with billions of bits?" The problem is error correction again and it is far easier to error correct qubits in a quantum computer where you have all qubits lying close to each other when compared to a highly entangled graph state where you need to keep entanglement in the presence of thermal noise while sending the individual qubits over long distances.