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i read about Clifford Data Regression in https://arxiv.org/pdf/2005.10189.pdf.

If I have understood this correctly, then one receives the mitigated expected value of an observable from CDR. For the MaxCut problem this could be the expected cut. But how do I then get the real result in the form of a bit string so that one can split the nodes into two subsets?

The implementation of CDR in mitiq, for example, only returns the mitigated expected value of the observable, but how can I then determine the actual solution from this?

Thanks!

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Almost all error mitigation methods (including CDR) help reduce errors in expectation values and are not suitable to mitigate single-shot experiments.

So, in the context of a quantum variational circuit associated to a MaxCut problem, error mitigation can be used only for better approximating the cost function improving:

  • The variational optimization process. This is however debated (https://arxiv.org/abs/2109.01051).
  • The final estimate of the max number of cuts. This is a non-trivial information about the MaxCut problem.

There is a Mitiq example about this: https://mitiq.readthedocs.io/en/stable/examples/maxcut-demo.html

However, error mitigation methods based on the approximation of expectation values are not directly useful to obtain the optimal bitstring representing the optimal solution of the MaxCut problem. At least there isn't an obvious way of doing it that I am aware of.

Finally, I would also suggest to have a look at techniques for mitigating measurement errors (see e.g., https://arxiv.org/abs/2108.12518). They may help in your case.

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