Open Graph

graphix.opengraph module

This module defines classes for defining MBQC patterns as Open Graphs.

class graphix.opengraph.OpenGraph(graph: nx.Graph[int], input_nodes: Sequence[int], output_nodes: Sequence[int], measurements: Mapping[int, _M_co])

An unmutable dataclass providing a representation of open graph states.

graph

The underlying resource-state graph. Nodes represent qubits and edges represent the application of \(CZ\) gate on the linked nodes.

Type:

networkx.Graph[int]

input_nodes

An ordered sequence of node labels corresponding to the open graph inputs.

Type:

Sequence[int]

output_nodes

An ordered sequence of node labels corresponding to the open graph outputs.

Type:

Sequence[int]

measurements

A mapping between the non-output nodes of the open graph (key) and their corresponding measurement label (value). Measurement labels can be specified as Measurement, Plane or Axis instances.

Type:

Mapping[int, _M_co]

Notes

The inputs and outputs of OpenGraph instances in Graphix are defined as ordered sequences of node labels. This contrasts the usual definition of open graphs in the literature, where inputs and outputs are unordered sets of nodes labels. This restriction facilitates the interplay with Pattern objects, where the order of input and output nodes represents a choice of Hilbert space basis.

Example

>>> import networkx as nx
>>> from graphix.fundamentals import Plane
>>> from graphix.opengraph import OpenGraph
>>> from graphix.measurements import Measurement
>>>
>>> graph = nx.Graph([(0, 1), (1, 2)])
>>> measurements = {i: Measurement(0.5 * i, Plane.XY) for i in range(2)}
>>> input_nodes = [0]
>>> output_nodes = [2]
>>> og = OpenGraph(graph, input_nodes, output_nodes, measurements)