[LatteLazy]

Isn't the whole point of QC that a classical computer needs to do 2^64th calculations to try 64 bits of data in a function BUT a QC just needs 64 QBits, because each Qbit can be both 0 and 1 simultaneously? This effectively turns a time problem (2^64th operations) into a memory one (64 qbits and 1 operation over all of them, maybe repeat 10 times for error detection).

[mikewarot]

Qubits are NEVER both 0 and 1 simultaneously... they might be either at any given moment. Qubits are a vector in 3 dimensions of unit length, best illustrated with the Bloch Sphere[1] In this sphere Up, where Z=1 is written as |0> because of history.

One of the most common Quantum Logic Gates[2], the Hadamard gate performs a rotation of a diagonal axis half way between X and Z. This gate is used many, many times in Grover's algorithm

There are many such rotations in quantum computing. Error correction can only ensure that a state is at either end of an axis, not at the correct point anywhere on the sphere.

[1] https://en.wikipedia.org/wiki/Bloch_sphere

[2] https://en.wikipedia.org/wiki/Quantum_logic_gate#Hadamard_ga...