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Approximately how is the cost of a quantum computer related to its number of qubits?
My guess would be more than linear (high confidence) but probably less than exponential (low confidence), but I know almost nothing about these things.
We don't yet know how to build quantum computers of arbitrary size at all, so asking about general scaling laws for cost isn't meaningful yet. There are many problems both theoretical and material that we think in principle are solvable, but we are still in early stages of exploration.