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en:quantum_registers

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Quantum registers

Playing with one qubit is fun, but not sufficient to run algorithms. You we'll see that later: we need many more than 1 qubit for interesting purposes.
When more than one qubit are in the game, we use quantum registers containing several.

Let's considers the following experiment: (1) At the left we have a source of qbits (or quantum particles) emitted by a single source in two separate direction. At the right we have two detectors facing the trajectory of qbits.
(2) Each qbit is traveling from the source to the detector in a superposed state between |0> and |1> before being read |0> or |1>.

We could imagine that the behavior with two qbits is the same than one qbit separated from the another. But we have two qbits emitted by the same source, and it changes everything because in this case they are entangled.
That means that the result of the top qbit is linked to the result of the bottom qbit. Their probabilities are linked one to the other.

If we would have two sources with two detectors, each qbit would be in the state seen in the previous chapter:

delim{|}{psi}{}> = alpha delim{|}{0}{}> + beta delim{|}{1}{}>

But since we have a single source emitting two entangled qbits we have amplitudes on all possible result:

delim{|}{psi}{}> = alpha delim{|}{00}{}> + beta delim{|}{01}{}> + gamma delim{|}{10}{}> + delta delim{|}{11}{}>

And because Greek letters does not help to know the corresponding state we use only alpha with the state in little:

delim{|}{psi}{}> = alpha_00 delim{|}{00}{}> + alpha_01 delim{|}{01}{}> + alpha_10 delim{|}{10}{}> + alpha_11 delim{|}{11}{}>

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en/quantum_registers.1610659819.txt.gz · Last modified: 2021/01/16 10:29 (external edit)