$O(N^3)$ Pauli-flow finding algorithm

.gitignore

@@ -167,3 +167,4 @@ docs/source/benchmarks
 docs/source/gallery
 graphix/_version.py
 docs/source/sg_execution_times.rst
+/.benchmarks/

CHANGELOG.md

@@ -8,7 +8,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 ## Unreleased
 
 ### Added
-
+- New module `graphix.find_pauliflow` with the $O(N^3)$ Pauli-flow finding algorithm introduced in Mitosek and Backens, 2024 (arXiv:2410.23439).
 ### Fixed
 
 ### Changed

graphix/generator.py

@@ -4,9 +4,9 @@
 
 from typing import TYPE_CHECKING
 
+import graphix.gflow
 from graphix.command import E, M, N, X, Z
 from graphix.fundamentals import Plane
-from graphix.gflow import find_flow, find_gflow, find_odd_neighbor, find_pauliflow, get_layers
 from graphix.pattern import Pattern
 
 if TYPE_CHECKING:
@@ -78,24 +78,24 @@ def generate_from_graph(
     meas_planes = dict.fromkeys(measuring_nodes, Plane.XY) if not meas_planes else dict(meas_planes)
 
     # search for flow first
-    f, l_k = find_flow(graph, inputs_set, outputs_set, meas_planes=meas_planes)
+    f, l_k = graphix.gflow.find_flow(graph, inputs_set, outputs_set, meas_planes=meas_planes)
     if f is not None:
         # flow found
         pattern = _flow2pattern(graph, angles, inputs, f, l_k)
         pattern.reorder_output_nodes(outputs)
         return pattern
 
     # no flow found - we try gflow
-    g, l_k = find_gflow(graph, inputs_set, outputs_set, meas_planes=meas_planes)
-    if g is not None:
+    g, l_k = graphix.gflow.find_gflow(graph, inputs_set, outputs_set, meas_planes=meas_planes)
+    if g is not None and l_k is not None:
         # gflow found
         pattern = _gflow2pattern(graph, angles, inputs, meas_planes, g, l_k)
         pattern.reorder_output_nodes(outputs)
         return pattern
 
     # no flow or gflow found - we try pflow
-    p, l_k = find_pauliflow(graph, inputs_set, outputs_set, meas_planes=meas_planes, meas_angles=angles)
-    if p is not None:
+    p, l_k = graphix.gflow.find_pauliflow(graph, inputs_set, outputs_set, meas_planes=meas_planes, meas_angles=angles)
+    if p is not None and l_k is not None:
         # pflow found
         pattern = _pflow2pattern(graph, angles, inputs, meas_planes, p, l_k)
         pattern.reorder_output_nodes(outputs)
@@ -112,7 +112,7 @@ def _flow2pattern(
     l_k: Mapping[int, int],
 ) -> Pattern:
     """Construct a measurement pattern from a causal flow according to the theorem 1 of [NJP 9, 250 (2007)]."""
-    depth, layers = get_layers(l_k)
+    depth, layers = graphix.gflow.get_layers(l_k)
     pattern = Pattern(input_nodes=inputs)
     for i in set(graph.nodes) - set(inputs):
         pattern.add(N(node=i))
@@ -143,7 +143,7 @@ def _gflow2pattern(
     l_k: Mapping[int, int],
 ) -> Pattern:
     """Construct a measurement pattern from a generalized flow according to the theorem 2 of [NJP 9, 250 (2007)]."""
-    depth, layers = get_layers(l_k)
+    depth, layers = graphix.gflow.get_layers(l_k)
     pattern = Pattern(input_nodes=inputs)
     for i in set(graph.nodes) - set(inputs):
         pattern.add(N(node=i))
@@ -152,7 +152,7 @@ def _gflow2pattern(
     for i in range(depth, 0, -1):  # i from depth, depth-1, ... 1
         for j in layers[i]:
             pattern.add(M(node=j, plane=meas_planes[j], angle=angles[j]))
-            odd_neighbors = find_odd_neighbor(graph, g[j])
+            odd_neighbors = graphix.gflow.find_odd_neighbor(graph, g[j])
             for k in odd_neighbors - {j}:
                 pattern.add(Z(node=k, domain={j}))
             for k in g[j] - {j}:
@@ -169,7 +169,7 @@ def _pflow2pattern(
     l_k: Mapping[int, int],
 ) -> Pattern:
     """Construct a measurement pattern from a Pauli flow according to the theorem 4 of [NJP 9, 250 (2007)]."""
-    depth, layers = get_layers(l_k)
+    depth, layers = graphix.gflow.get_layers(l_k)
     pattern = Pattern(input_nodes=inputs)
     for i in set(graph.nodes) - set(inputs):
         pattern.add(N(node=i))
@@ -178,7 +178,7 @@ def _pflow2pattern(
     for i in range(depth, 0, -1):  # i from depth, depth-1, ... 1
         for j in layers[i]:
             pattern.add(M(node=j, plane=meas_planes[j], angle=angles[j]))
-            odd_neighbors = find_odd_neighbor(graph, p[j])
+            odd_neighbors = graphix.gflow.find_odd_neighbor(graph, p[j])
             future_nodes: set[int] = set.union(
                 *(nodes for (layer, nodes) in layers.items() if layer < i)
             )  # {k | k > j}, with "j" last corrected node and ">" the Pauli flow ordering