Local fidelity #9504
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Local fidelity #9504
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Changelog: New Feature
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test/python/algorithms/state_fidelities/test_compute_uncompute.py
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Co-authored-by: Julien Gacon <[email protected]>
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releasenotes/notes/computeuncompute-local-fidelity-501fe175762b7593.yaml
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| .. math:: | ||
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| \hat{O} = \frac{1}{N}\sum_{i=1}^N|0_i\rangle\langle 0_i|, | ||
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This is not formatted correctly:
I think you have to add an additional linebreak before the .. math -- but if that doesn't work then you could also put this info in the class docstring 🙂
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Thanks, adding the extra line break worked 👍
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* local fidelity * lint * Update qiskit/algorithms/state_fidelities/compute_uncompute.py Co-authored-by: Julien Gacon <[email protected]> * implement suggestions * doc fix * private variable renamed * reno * try doc fix --------- Co-authored-by: Julien Gacon <[email protected]> Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>
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* local fidelity * lint * Update qiskit/algorithms/state_fidelities/compute_uncompute.py Co-authored-by: Julien Gacon <[email protected]> * implement suggestions * doc fix * private variable renamed * reno * try doc fix --------- Co-authored-by: Julien Gacon <[email protected]> Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>
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* local fidelity * lint * Update qiskit/algorithms/state_fidelities/compute_uncompute.py Co-authored-by: Julien Gacon <[email protected]> * implement suggestions * doc fix * private variable renamed * reno * try doc fix --------- Co-authored-by: Julien Gacon <[email protected]> Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>
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Summary
Adds a flag
average_localto theComputeUncomputestate fidelity class that allows to compute the local fidelity, which is defined by averaging over single-qubit projectors. It has been shown that global observables, such as the global projector used in the standard fidelity, lead to cost-function induced barren plateaus that can be mitigated by employing a local cost-function instead [1].While this local fidelity cannot replace the global fidelity in all use cases, it coincides with the global version in the case that the fidelity is 1. This is especially useful in algorithms where the fidelity is maximised variationally, such as for example in p-VQD.
Details and Comments
I added a unit test for the case where the fidelity is 1. Open for suggestions for further unit tests if anyone has an idea of an example that would make sense.
References
[1] Cerezo, M., Sone, A., Volkoff, T. et al. Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nat Commun 12, 1791 (2021). https://doi.org/10.1038/s41467-021-21728-w