First time poster and just started with quantum computing for my master thesis, so I'm sorry if the question seems obvious.

I understand that the tomography is used to reconstruct the state and/or process of a quantum circuit, without directly measuring the used qubits but instead using many 'copies' of it. What we then get is the quantum state as a density matrix or the quantum process in e.g. choi matrix representation.

But isn't this process of tomography way too costly to really make use of it? If I understand it correctly, we could use this choi matrix representation to replace our circuit process, but does it improve something? And can we use the state tomography for anything else than verification/error mitigation?

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    $\begingroup$ Short answer: full tomography is very expensive, meaning you can do it for a single, maybe two qubits, but it is also the most informative method. It is mostly used to learn about the type and strength of errors. But there is a zoo of other methods which are "cheaper" but also less informative, like randomised benchmarking, RB tomography, shadow tomography, Pauli tomography, ... $\endgroup$ Feb 12 at 12:08

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