Qiskit / qiskit-addon-obp / 14601043384

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Add Lindblad Noise Support (#58)

* add noise stuff

* renamed apply_ple method, moved some logic around slightly

* removed PauliEvolution class`

* pushing test notebook, it shows a small discrepancy now

* disable map

* lint: apply formatting to minimize diff to main

* fix: clean up unrelated code changes

* fix: track qargs and operator under PLE evolution

* refactor: directly use PauliLindbladError object

* refactor: clean up the PLEInstruction

* refactor: clean up apply_ple_to

* docs: for the apply_ple_to function

* docs: for the PLEInstruction

* test: some basic unittests for apply_ple_to

* test: an end-to-end backpropagation test with a PLE

* ci: ignore coverage around temporary PLEInstruction class

In the long run, I expect this class to be removed in favor of either a
solution directly part of the Qiskit SDK or in the utils addon.

* fix: bump minimum qiskit-ibm-runtime version

* docs: add reno

* refactor: remove unnecessary __eq__ implementation

* refactor: remove `index` from `PauliLindbladErrorInstruction`

It should be possible to track this through other means. If this is
truly needed, we can add support for it later.

* docs: fix typesetting

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Co-authored-by: Bryce-Fuller <bryce.fuller@ibm.com>
Co-authored-by: Swarnadeep Majumder <Swarnadeep.Majumder@ibm.com>
Co-authored-by: Max Rossmannek <oss@zurich.ibm.com>

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