I have a decent knowledge of quantum mechanics, undergraduate level, but would like a description of how a quantum computer works and why it is important that superpositions of states, ie coherence, exists.
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A bit exists as a $1$ and $0$ but a qubit can exist as both $1$ and $0$ at the same time, an array of these qubits would then exist in all possible states at the same time. This allows a quantum computer to compute faster since it calculates all possibilities simultaneously, however the downside is that the answers it gives is probabilistic which means it can be wrong depending on several factors unlike a conventional computer. – Horus Mar 14 '16 at 08:57
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There are some interesting videos on quantum computing by a number of quite serious youtube channels. This is a good place to start: https://www.youtube.com/watch?v=g_IaVepNDT4 – Jaywalker Mar 14 '16 at 09:36
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There are about a gazillion tutorial papers. Two that I like are Stanley Gudder's http://www.du.edu/nsm/departments/mathematics/media/documents/preprints/m0310.pdf and Abbas Edalat's lecture notes. They used to be at his homepage http://www.doc.ic.ac.uk/~ae/ but I can't find them there. So I uploaded a copy to http://www.forkosh.com/qc4.ps.gz which I got from his homepage some time ago. You may or may not find either or both of these to your taste. Like I said, there are gazillions of such tutorials. Nobody's gonna write another one specially for you right here and now. – Mar 14 '16 at 09:55
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A quantum computer uses the state of quantum system to store the information and in a "de coherence condition" all the possible state can be used as sites for keeping the 'binary' info say I1> and I0>;that's why it can work faster.In a two level quantum system the superposed states like 11, 10, 00,01 ; all the four states can be used for calculation. – drvrm Mar 14 '16 at 10:07
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3Possible duplicate of How Does a Quantum Computer Work? – glS Mar 14 '16 at 12:07
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Explanations like @Horus and drvrm gave in their comments are the ones you can find all over the web, and can be summarized to something like: qubits -> hence superposition -> (skip everything in between) -> hence simultaneous answer to everything. I don't think it's at all obvious (to non-QM-experts) how a quantum computer "calculates all possibilities simultaneously", since as soon as you actually read those qubits, you will collapse the wave-function and effectively get a "definitive" eigenstate - a bunch of "plain old bits". – vgru Mar 14 '16 at 19:51
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The simple answer: It doesn't work at all, because there is no quantum computer at the moment. The only viable candidate D-Wave might be the first somewhat quantum computer, but is far from doing anything useful.
So you might want to ask "How would a quantum computer work" and the answer to that is that this question is way too broad. There are many different models of quantum computation which use quantum mechanics in very different ways - the models I can think of just now would be
- Circuit based QC (similar to reversible boolean circuits).
- Measurement based QC (build up correlations in a lattice of e.g. spins and then do the computation by measuring the lattice sites).
- Quantum annealing and especially adiabatic quantum computation (the computation result is the ground state of a Hamiltonian and you change the Hamiltonian of a known system adiabatically, i.e. leaving the system in the ground state).
- Topological QC (using systems with anyons, i.e. two-dimensional systems, for computation. This results in robustness to errors).
Apart from that, there are a multitude of proposed implementations in many different systems, but I believe you are not so interested in that. In any case, have a look at Nielsen & Chuang to get an introduction to the physics and computer science part of quantum computation.
There is actually some debate about what actually makes a quantum computation work other than that it is definitely due to being able to use entanglement and superpostions. To get an idea, you should have a look at an algorithm that outperforms classical algorithms such as Grover's search (see the book for an introduction).
Martin
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I disagree with you. Quantum computers do exist, though they are currently too primitive and small scale to be of any use practically (unless you count the human brain). – Horus Mar 16 '16 at 04:52
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It's not at all clear that the human brain is a quantum computer (signals are electric pulses). Certainly, it is not a universal quantum computer. As for the small scale quantum computers: None of them currently has the amount of control necessary to be a multi-purpose instrument, most of them do not yet allow for error-correction, which is crucial for a real quantum computer. I believe the recently published ion-trap experiments might be one of the first instances of a real computer. Anyway, I guess we disagree on what to call a "computer". For me, I need some sort of universality. – Martin Mar 16 '16 at 08:52