How Do Qubits and Multiple Qubit Systems Enhance Computing Power?

[Erwin]

At first, good evening.
I want you to know that Eng is not my first language, so you could find many errors while reading my posts.

I was reading something about qubit and multiple qubit systems, which combined can create a powerful processor for a new type of computer.

I'm not sure of how could the correlation between a pair of qubits would do it. Of sure, a single qubit contains a lot of information, it's like a complex number, but how can it be helpful?

Thank you for reading

 

[jerromyjon]

Good evening to you as well! Your use of English is quite good for an alternative language. I believe I understand you well and share your curiosity.

I have an excellent understanding of "classical" computers and have investigated this same question myself recently. As well as I could verify, the value of a q-bit remains a simple bit represented in the quantum "spin" of an atom, for example up=1 or down=0. The difference is in how computations are performed and results are interpreted. From what I understand, the simple description would be that classical computers are deterministic while quantum computers are probabilistic. Where classical computers take a definite number of operations to complete a calculation, a quantum algorithm could find likely solutions with far less operations.

 

[Erwin]

What I found is that a qubit is not only a spin, because it has not only the 0 and 1 states, but also all the states between; for this reason, when we measure it we can, of sure, find only 0 or 1, following probabilistic's laws.
My question is a little bit deeper. I wish to know what happens when I combine two or more qubits: in this case there's more interesting consequence, that is the fundament for quantum computers.

Thank you for your fast answer!

 

[Strilanc]

It's a bit hard to explain what gives quantum computers an advantage, and especially hard to clarify the limitations of those advantage. The advantage is NOT that they are probabilistic.

Ultimately it comes down to the fact that operations are unitary matrices ( instead of permutation matrices or stochastic matrices like classical computers have ). That's why entanglement is a thing, that's why measuring half way through has different outcomes compared to measuring at the end, and that's why it's possible to represent a Fourier transform directly as an operation that can be factored into a short series of simple operations.

 

[jerromyjon]

The advantage is NOT that they are probabilistic.

I actually took the probabilistic nature as a disadvantage. I don't know much but from what I read multiple q-bits are required to assure a sensible result for 1 bit of data, as opposed to the far more efficient checksum error detection method.