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# I was wrong...

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On my last post about Quantum, I said that there was a 50/50 chance of the qubit collapsing into a 1 or a 0. Wrong

@flok send me this message

Quote

Dear wall03,

I just came across your post on quantum computing. Even though it is still rather brief, it contains a fundamental misconception. However, I did not see any option to post this comment directly with the blog entry.

In the second quote you mention the ability of quantum computers to work with superpositions, which is a mixture of quantum states. However, when measuring they collapse to a basis state, which means one either measures 0 or 1 but never both. This was stated correctly. The probability for them to yield values 0 or 1 is in general not 50/50, otherwise all computations would be pointless. The probability depends on the exact superposition as is lined out in more detail for example on wikipedia.

If you would like I could also elaborate further, but I think we should try to keep informative contributions factually correct.

Best regards,

flok

I edited the blog post, and all is fixed.

But it isn't!

flok sent me another message

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So a qubit can be set to any superpostion of 0 and 1 initially. This could be for example a state where the probability of measuring either value is 50%. Throughout the computations one can manipulate the value of one qubit by eg. taking a CNOT gate, meaning one qubit is flipped, if the other evaluates to true. Now the mathematics is rather simple, at least if you know some linear algebra and are comfortable in multiplying matrices. The representation of the most commonly used gates can be found again at wikipedia. Depending on the algorithm one uses, which is just a combination of such gates, one can even obtain results where the output is exactly in one of the basis states before measuring.

Regarding the comment on the temperature this has to do with the implementation of current quantum computers. One has to use some physical implementation of the qubit, which could for example be a single electron. Now as you can imagine you require very little energy to disturb a single electron, completely changing its current state. Thus one has to limit the disturbance by operating the qubits in vacuum. However, even the microscopic movements in other particles nearby can cause distractions. Thus one usually has to bring the qubits to some tenth of Kelvin above absolute zero. This allows for them to retain their state for long enough that the computation can complete without them changing their state midway through due to some disturbance. At those temperatures one currently can keep the state for a few seconds or sometimes even minutes. However, when performing the gates one again introduces some interaction which potentially leads to undesired changes in the state, making them very fragile.

If you want to read more I can recommend the following sites/videos/books:

Quantum computation and quantum information / Michael A. Nielsen & Isaac L. Chuang

The latter gives a very in depth explanation of both theory and the current implementations. It is however intended as an entry level text book for scientist emerging into the field of quantum computation and might be demanding if you do not have a background in science.

I would be glad to help if you have any questions in detail or if you need some more inputs for piecing together the blog. I consider this a very interesting subject myself and am sure there is a decent number of people interested in this subject, especially since one often hears that quantum computers will be able to break our encryption. (That claim is certainly true, however there still need to be some major development leaps before there is a capable enough quantum computer.)

Smart guy.

Anyway.

Sorry if you understood something wrong about Quantum.

-wall03

## 1 Comment

I think that you have a fundamental misunderstanding of quantum mechanics.

A qubit is not "at any number between 0 and 1", to paraphrase your original post. When measured, a qubit exists in exactly one state, that is to say that it's probability function "collapsed" (in quotes for a very advanced reason).

When we think of a qubit, it sometimes helps to think of a ball. We can constrain the ball such that it cannot move except to rotate around a single axis. We will assume that the ball is in fact rotating at all times and is never actually motionless.

Without looking at the ball or any of it's starting conditions, all we can say is that the ball is either rotating left or right. We would call this a "superposition" of the two states of the ball, that is: We think of the ball as rotating both to the left and the right at the same time.

However, this is real life and in reality the ball must either be rotating to the left OR to the right, but never both, so when we actually measure (look at) the ball, it's probability functioning "collapses" (again with those pesky quotes) and we see the ball rotating to whichever direction. Hence, the "superposition" of directions on the ball is simply the probability of it spinning in a given direction when we look at it.