# Quantum Principles of Quantum Computers

I understood many maths of QM and even QFT.. but I can't totally understand how a quantum computer can factorize millions of times faster. In normal turing machine, there is 0 and 1. But in quantum computers, there is 0 and 1 and superpositions of it.. meaning it can be 0.0001 or 0.5253 or 0.874 or anything in between.. meaning billions of combinations in superposition, is this right? But we know that when we measure, there is only one value, so how do they use it to compute? it's something about entangling it with another particle. I have visited dozens of websites about quantum computer, it's not yet clear how it works. Anyone can point me to a good site with very clear explanation or produce some rough ideas yourself. Thanks.

But we know that when we measure, there is only one value, so how do they use it to compute?
I am not well versed in Shor's algorithm (factorization algorithm), but I can tell some things about Grover's algorithm (searching algorithm).
Basically all the quantum algorithms (though they are annoyingly few) use superposition principle to compute. In Grover's algorithm, the database is prepared in some superposed state $| \Psi \rangle$. You apply certain Hamiltonian (and this is how you have to guess/design it) to the database, such that the state $| \Psi \rangle$ evolves nearer to $| \phi \rangle$ (something you are searching for) and the inner product, $\langle \phi| \Psi \rangle$ increases (magnitude-wise). From some theoretical calculations you can find out the number of iterations to maximize the inner product. Then you measure it and get the desired result with high probability (which in some cases is unity!).
If the required $| \phi \rangle$ is not there in database, you get nothing on measurement.

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I see. I'll think of it.

Anyway. Does anyone know how to relate quantum computers with Ballentine Essemble Interpetation since here superposition doesn't occur in real time?