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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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From

https://link.springer.com/chapter/10.1007/978-3-030-20726-7_17#:~:text=Roughly%20speaking%2C%20the%20charge%20qubit,I_%5Cmathrm%7Bb%7D.

Roughly speaking, the charge qubit is a box for charge, controlled by an external voltage Vg; the flux qubit is a loop controlled by an external magnetic flux Φext ; and the phase qubit is a Josephson junction biased by a current Ib.

(I was able to download the relevant chapter)

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