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I'm having trouble with with the following problem that seems easy but I haven't found any reference discussing it.

It is known that both stabilizer states and Clifford gates admit a tableau representation. There is an easy way to implement the action of the gate on the stabilizer states? Any solution or reference is well accepted.

If this is not the case, what is the simpler algorithm to construct the unitary matrix associated to a generic Clifford gate?

Thanks for any answer in advance :)

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