Update _update_edges in DAGDependencyV2

[enavarro51]

Summary

Updates _update_edges

Details and comments

This PR refactors the _update_edges method in DAGdependencyV2, which creates edges based on non-commutativity. This is built on top of #11705 and should be on hold until that PR merges. These changes accomplish the following,

• Previously the method was based on iterating over node indices. This works fine if the dag is created using one of the converters and nodes are never removed. This new version is based on node objects and should allow for removal of nodes and subsequent additions.
• Now all method calls that pass node use the node object and there is no longer any iterating over node_id's. This more closely matches the way DAGCircuit works. This allows for elimination of the _get_node / get_node method which was unique to the dag dependencies.

Here are some additional local test results using circuit_to_dagdependency and circuit_to_dagdependency_v2.

Below "with" or "without" means create_preds_and_succs was set to True or False in V1. (not applicable to V2)

Using 20 qubits and 10,000 gates in a random Clifford circuit,
           V1 with          V1 without     V2 (this PR)
Memory      3.9GB            160MB          152MB
Time      1 min 54 sec     1 min 15 sec     30 sec

Using 100 qubits and 20,000 gates,
           V1 with          V1 without     V2 (this PR)
Memory  (Memory overrun)     176MB          186MB
Time                      6 min 16 sec     2 min 11 sec

[qiskit-bot]

One or more of the the following people are requested to review this:

• @enavarro51
• @Qiskit/terra-core

[coveralls]

Pull Request Test Coverage Report for Build 7976669756

Warning: This coverage report may be inaccurate.

This pull request's base commit is no longer the HEAD commit of its target branch. This means it includes changes from outside the original pull request, including, potentially, unrelated coverage changes.

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Details

• -85 of 293 (70.99%) changed or added relevant lines in 6 files are covered.
• 221 unchanged lines in 31 files lost coverage.
• Overall coverage increased (+0.02%) to 89.22%

---

Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit/visualization/dag_visualization.py	0	3	0.0%
qiskit/dagcircuit/dagdependency_v2.py	171	253	67.59%
<!--	Total:	208	293

Files with Coverage Reduction	New Missed Lines	%
crates/qasm2/src/expr.rs	1	93.81%
qiskit/primitives/base/base_estimator.py	1	97.44%
qiskit/primitives/base/base_sampler.py	1	96.97%
qiskit/primitives/statevector_sampler.py	1	99.1%
qiskit/synthesis/clifford/clifford_decompose_ag.py	1	98.72%
qiskit/synthesis/clifford/clifford_decompose_full.py	1	87.5%
qiskit/synthesis/linear/cnot_synth.py	1	98.0%
qiskit/circuit/duration.py	2	70.27%
qiskit/synthesis/clifford/clifford_decompose_greedy.py	2	98.88%
qiskit/synthesis/linear/linear_depth_lnn.py	2	98.33%
<!--	Total:	221

Totals
Change from base Build 7893751411:	0.02%
Covered Lines:	59116
Relevant Lines:	66259

---

💛 - Coveralls

[alexanderivrii]

With the new GitHub features, we can now easily draw graphs and flowcharts. Just for fun, an illustration of adding a node to DAGDependency.

flowchart LR
    subgraph before
    direction LR
    A["X(0)"] --> C["Y(0)"]
    B["X(0)"] --> C
    C --> F["Z(0)"]
    end
    subgraph after
    direction LR
    A2["X(0)"] --> C2["Y(0)"]
    B2["X(0)"] --> C2
    C2 --> F2["Z(0)"]
    C2 --> H2["Z(0)"]
    end
    subgraph new node
    H["Z(0)"]
    end
    before -->|adding new node to dag dependency| after

[enavarro51]

The 3X improvement is not a function of this PR, but of the 2 PRs combined. It's still somewhat of a mystery to me. The same number of edges are created. I tried a quick and dirty change to dagdependency.py to use DAGOpNode. I thought maybe the _key_cache and find_bit might have some effect, but there was only a minimal difference. Open to suggestions here.

[enavarro51]

I'm closing this since this was an early attempt at optimizing the DAGDependencyV2 conversion process. Most of this was superceded by #11705 and a future PR which will incorporate more rustworkx optimizations.