Why are quantum computers scalable?
With the subjects of spontaneous collapse models and decoherence in mind, it seems to me that the scalability of quantum computers is something which is not only physically difficult to achieve but also theoretically.
When a measurement is made, a quantum state, whose probability amplitude is a Gaussian function, becomes an eigenstate, whose probability is definite. This change from quantum state to eigenstate on measurement happens also to qubits which change to classical bits in terms of information.
Measurement, decoherence & quantum Darwinism
From the work of Zurek one starts to see the environment as a valid observer and indeed one that makes measurments. Within this view, how can we have scalable quantum computers if many-qubit systems create more and more decoherence and as such, from my current understanding, inevitably reduce such a system of qubits to a system of eigenstates.
Is there an upper bound to quantum computing?
If the train of thought I am following is correct than shouldn't there be an upper bound to the number of qubits we can have without them (all, the whole system) being reduced to eigenstates, classical states.
I get the feeling that what I am saying is incorrect and I am fundamentally misunderstanding something. I'd really appreciate it if you could tell me why my argument is wrong and point me in the direction of understanding why quantum computers are theoretically scalable.
An example with ion trap quantum computers
Within this set up, the information is encoded within the energy levels of ions with a shared trap. Given that the ions are all within the shared trap then interactions are bound to occur given scaling within such a shared trap, or at least that's what my intuition says. Do we overcome this by having multiple traps working say in tandem?