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First of all, quantum algorithms are written in a mathematical way.
This kind of representation, with texts and symbols, is quite appropriate in a theoretical point of view,
but it doesn't allow an easy implementation if you want to program a simulation on a classical machine.
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extract from a Richard Jozsa's course
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Another way to represent quantum algorithms is often used: a hybrid of graphics and mathematical symbols.
But such representations are sometimes not very accurate, like the ellipse that show interferences in this particular image.
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extract from "Quantum computer, twelve years after Shor", Valerio Scarani
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In a more elementary point of view, qubits are usually represented by a 2-dimensional vector.
This is very simple and easy to understand. The drawback is, that for a non-expert, it is difficult to remember that each coefficient
corresponds in fact to the modulus of the complex magnitude.
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extract from a Frédéric Magniez's course
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To compromise for the previous problem, the qubit can be represented as a sphere, the Bloch's sphere,
which shows the complex magnitudes with 2 angles.
Unfortunately, such representations don't exist for higher dimensions.
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preview from any initiation about quantum computing
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Some attempts were made to use colors.
Either with the blend of 2 colors...
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extract from an article of Scientific American, Nov 2002
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... or with very different colors...
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images from various articles futura-sciences, sup-info, aso.
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Lastly 2 colors - Green and Red - are sometimes used to represent the two base-vectors |0> et |1>.
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image obtained from a course at Sherbrooke University.
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