[Bug]: `RecursionError` in causal-flow finding algorithm

[matulni]

Causal-flow finding algorithm is implemented in a recursive fashion following the presentation in the original publication (see references in the source code). Linear open graphs with $\sim$ 1000 nodes raise a RecursionError exception on a MacBook Air M4, 24 GB running OS 15.7.3.

The following code snippet allows to reproduce the issue:

import networkx as nx
from graphix.fundamentals import Plane
from graphix.opengraph import OpenGraph


def create_line_og(n_nodes: int) -> OpenGraph[Plane]:
    if n_nodes < 2:
        raise ValueError("n_nodes must be larger than 1.")

    graph: nx.Graph[int] = nx.Graph([(i, i + 1) for i in range(n_nodes - 1)])
    input_nodes = [0]
    output_nodes = [n_nodes - 1]
    measurements = dict.fromkeys(range(n_nodes - 1), Plane.XY)
    return OpenGraph(graph, input_nodes, output_nodes, measurements)


n_nodes = 990
while True:
    og = create_line_og(n_nodes)
    try:
        og.extract_causal_flow()
    except RecursionError:
        break
    n_nodes += 1

print(f"Recursion limit hit at {n_nodes}")

Note that a flow correction function can be found for these graphs with the cubic Pauli-flow finding algorithm.

Since the recursion in the causal-flow finding algorithm is terminal, it should be possible to rewrite the algorithm in an iterative fashion without needing to represent the stack in a custom data structure.