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I come from a CS background

I was reading Neven and Farhi's paper ("Classification with Quantum Neural Networks on near Term Processors"), and I am trying to implement the subset parity problem using Qiskit, and solve it using a quantum Neural Network.

There is one thing that doesn't make sense to me though. In the paper, they measure "the Pauli Y gate on the readout qubit" (perhaps this phrasing is wrong, as I have to admit that whenever one does not measure in the computational basis, the whole thing doesn't make sense to me anymore). In one of the questions I already asked on this site, I was told that measuring in a basis other than the computational basis is simply the same as applying a matrix to the qubit and then measuring it in a computational basis.

Through various research, I was able to determine that, for this problem "to measure the Pauli Y gate the readout qubit", I had to apply $HS^{\dagger}$ and then measure in the computational basis in order to obtain the same result. It works, but I don't understand why it has to be this matrix in particular (is there any mathematical proof that shows that this is indeed this matrix ?)

Got it, thank you – Skyris – 2020-05-01T08:18:27.690

Just a question though. Why is the normal measurement a Pauli Z mesurement – Skyris – 2020-05-27T13:27:54.813

The Pauli Z matrix is diagonal in the standard measurement basis. – DaftWullie – 2020-05-27T13:50:47.153