I know the main problem with a quantum computer is that you can't read and write data from it until after it has run though all of its calculations. But would reading and writing quantum data to particles without collapsing their probability fields make this possible?
With constant conditions - No. Because it fails energy/information conservation laws.
But you are able to changle temperature to travel between "macro" and "micro". Write information to macro - freeze - get micro particle with quantum condition.
But the quantum state is so unstable - so developers want to find something more stable but still quantum mechanical.
You can write any quantum state to a (sub-)system as you like. The thing you need is to set an deterministic initial state and use a known unitary operator to let the system evolve to the state you want. But note that this operation itself is effectively performing a quantum computation.
In contrast, you cannot read out the state of the system in the middle of computation. Since the act itself destroy the quantum state, so you cannot know the system state.
You should know that there is no individual state in quantum computation, the whole system itself is a single state. So it doesn't make sense to read or write individual qubit during computation, in most case.