I'm reading about error correction mainly in the Qiskit Measurement error mitigation chapter contains what it seems and easy way to "clean up" the noise obtained in the IBM (or NISQ) devices. One thing that I feel is missing is what is the logic behind the method?

The example in the ebook is clear, but I would like to know what it is that way. I started looking in the literature and found, as expected, different approaches to do so. What is (or resembles most) the method presented in Qiskit? Can someone provide literature?

  • 1
    $\begingroup$ This paper titled "Mitigating measurement errors in multi-qubit experiments" by Sergey Bravyi et al. might help: arxiv.org/pdf/2006.14044.pdf The link you provided seem to correspond to the unbiased error mitigation section in the paper (section II) $\endgroup$
    – KAJ226
    Jun 3 at 13:16

Measurement error, as the name says, is the error that is added to the qubits when you try to measure them. In this paper Mitigating measurement errors in multi-qubit experiments you can find different methods for measurement error mitigation.

The logic behind these methods is to measure a circuit prepared in a certain known state and see the results. For example, if you prepare a circuit in of one qubit in state 0, execute it with 100 shots and the results are 0: 95, 1:5, you can see that your measurement turned 5 of the 0s in 1s. Using this information, you can correct the errors in other circuits, like the link you provided explains.

All of the methods follow a similar structure: you create some simple circuits in the basis states, you run them and you create a matrix using the results. Using this matrix, you can mitigate the measurement errors of other circuits ran in the same backend.

The main difference between the methods used to create the mitigation matrix is the assumptions they make. The method presented in the textbook creates the matrix executing one circuit for each basis state, which requires $2^n$ circuits, with n being the number of qubits. When n becomes too large for this to be a convenient method, you can use some of the other techniques proposed in the paper, like tensored mitigation and CTMP. These techniques are also implemented in qiskit.


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