Grover's algorithm can search an unordered list of length $N$ in time $\sqrt{N}$ on a quantum computer. Applied to cryptography, this means that it can recover n-bit keys and find preimages for n-bit hashes with a cost of $2^{n/2}$.
But the basic version of Grover's algorithm is sequential. Each iteration uses the output of the previous iteration as input. I don't see an obvious way to parallelize the algorithm. Reducing the number of iterations significantly reduces the success probability more than linearly.
If the algorithm is inherently sequential, building a bigger computer won't speed up the attack, limiting its impact. $2^{80}$ sequential cipher invocations looks pretty hard to achieve to me. On the other hand, $2^{80}$ parallel cipher invocations is already on the edge of feasibility today using classical computers.
Assume an attacker using a quantum computer is limited to $T$ timesteps with $T<\sqrt{N}$, so they can't run Grover's algorithm with the optimum number of sequential steps. What's the cost for finding a preimage/recovering a key? What is the average cost per-break if they have multiple targets?