Assuming a 1024qb quantum computer, how long to brute force 1024bit RSA, 256bit AES and 512bit SHA512
Adding more qubits does not increase the computation speed. A quantum computer with 4 qubits does not factorize faster than one with 2. The qubits are the &quot;memory&quot; of the quantum computer. More qubits mean you can factor bigger numbers. If I remember correctly, you need a superposition of $\Theta(N^2)$ terms, which means $\Theta(\log(N^2))$ qubits to factor N.
The running time of Shor's algorithm is $O((\log N)^3)$ to factorize $N$. What is important to remember is that Shor's algorithm can only factorize (by solving the discrete log problem). See wikipedia's entry on Shor's algorithm.
As for Grover's algorithm, it provides quadratic advantage over classical computers for &quot;black-box&quot; queries. So a quantum computer could perform a brute-force attack in $O(\sqrt{N})$ trials whereas a classical computer would need $O(N)$ trials. Again, increasing the number of qubits does not lower the running time, but increases the &quot;memory&quot; of the quantum computer. In order to run Grover's algorithm to brute-force a key, you need a superposition of all keys, which requires $\log K$ qubits where $K$ is the number of possible keys.