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What are the differences among charge qubit, flux qubit and phase qubit?

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The main difference is that each one has its own wikipedia page ...

Now about the concepts they share : they are all some implementation of the superconducting quantum computing scheme and they are all based on the non-linearity of the Josephson relations.

Other superconducting Qubit exist, like the transmon Qubit, the fluxonium, and all are representative of the recent interest in circuit quantum electro-dynamics (circuit-QED).

Now if you make a longer question you will get a longer answer ... and if you ask a precise question you will get a precise answer ...

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