Quantum computing does not significantly speed up PoW because it is hash based (thus Shor's algorithm doesn't apply). So you must mean that ECDSA signatures could be cracked and double-spent?
https://en.wikipedia.org/wiki/Grover%27s_algorithm:
Grover's algorithm is a quantum algorithm that finds with high probability the unique input to a black box function that produces a particular output value,
using just O(N1/2) evaluations of the function, where N is the size of the function's domain.