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[DAGCircuit Oxidation] Port `DAGCircuit` to Rust (#12550)

* Port DAGCircuit to Rust

This commit migrates the entirety of the `DAGCircuit` class to Rust. It
fully replaces the Python version of the class. The primary advantage
of this migration is moving from a Python space rustworkx directed graph
representation to a Rust space petgraph (the upstream library for
rustworkx) directed graph. Moving the graph data structure to rust
enables us to directly interact with the DAG directly from transpiler
passes in Rust in the future. This will enable a significant speed-up in
those transpiler passes. Additionally, this should also improve the
memory footprint as the DAGCircuit no longer stores `DAGNode`
instances, and instead stores a lighter enum NodeType, which simply
contains a `PackedInstruction` or the wire objects directly.

Internally, the new Rust-based `DAGCircuit` uses a `petgraph::StableGraph`
with node weights of type `NodeType` and edge weights of type `Wire`. The
NodeType enum contains variants for `QubitIn`, `QubitOut`, `ClbitIn`,
`ClbitOut`, and `Operation`, which should save us from all of the
`isinstance` checking previously needed when working with `DAGNode` Python
instances. The `Wire` enum contains variants `Qubit`, `Clbit`, and `Var`.

As the full Qiskit data model is not rust-native at this point while
all the class code in the `DAGCircuit` exists in Rust now, there are
still sections that rely on Python or actively run Python code via Rust
to function. These typically involve anything that uses `condition`,
control flow, classical vars, calibrations, bit/register manipulation,
etc. In the future as we either migrate this functionality to Rust or
deprecate and remove it this can be updated in place to avoid the use
of Python.

API access from Python-space remains in terms of `DAGNode` instances to
maintain API compatibility with the Python implementation. However,
internally, we convert to and deal in terms of NodeType. When the user
... (continued)

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10529252305 gh-readonly-queue/main/pr-12550-a4bf87bf66df53a6984bd2fd82c19125339cc431 [DAGCircuit Oxidation] Port `DAGCircuit` to Rust (#12550) * Port DAGCircuit to Rust This commit migrates the entirety of the `DAGCircuit` class to Rust. It fully replaces the Python version of the class. The primary advantage of this migration i... push web-flow github
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