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I've been reading a lot about quantum mechanics and arrived at entanglement. I understand these things and I understand how to perform computation on qbits if they are represented as vectors and the transformations as matrices.

However I have not seen any physics about how to construct a quantum gate or why it's possible to alter a qbit. Since even the most delicate measurement makes it colapse, the intuition I have is that it'd be impossible to alter it without making it collapse, but apparently it's possible.

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The specific details about how to apply quantum gates depend on the system you are looking at. For example, in a photonic system, you could apply some gates by beam splitters, polarizers, mirrors, waveplates and $\cdots$ . Or in spin systems you can tune the Hamiltonian of the system by changing the electric and magnetic fields(e.g. with a laser) and with that effectively apply a quantum gate on your spin system.

Also, it's true that performing a measurement would collapse the system; however, these gates typically do not consist a measurement. If the experimenter is sloppy with their experiment there will be decoherence though.

Chapter 7 of Nielsen and Chuang includes some physical realizations like NMR or ion traps. Also, I'm sure there are plenty of courses that cover these materials, e.g. you can look at David Cory's Explorations in Quantum Information course.

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