ZX-Graphs

PyZX represents quantum circuits as ZX-graphs. These graphs have 4 different types of vertices: boundaries, Z-spiders, X-spiders and H-boxes. Boundary vertices represent an input or an output to the circuit and carry no further information. Z- and X-spider are the usual bread and butter of ZX-diagrams. H-boxes are used in ZH-diagrams as a generalisation of the Hadamard gate. Non-boundary vertices carry additional information in the form of a phase. This is a fraction q representing a phase pi*q.

As a simple example, we could have a ZX-gaph with 3 vertices. The first being a boundary acting as input, the last being a boundary acting as output. If the middle one is a Z-node with phase a that is connected to both the input and output, then this graph represents a Z[pi*a]-phase gate.

Edges in a PyZX graph come in two flavors. The first is the default edge type which represents a regular connection. The second is a Hadamard-edge. This represents a connection between nodes with a Hadamard gate applied between them, and in the drawing functions of PyZX is represented by a blue edge.

Accessing and setting vertex and edge type

The type of a vertex v in a graph g can be retrieved by g.type(v). This returns an integer representing the type. These integers are stored in pyzx.utils.VertexType and is one of the following:

  • VertexType.BOUNDARY

  • VertexType.Z

  • VertexType.X

  • VertexType.H_BOX

To get the type of all the vertices at once you call g.types(). This returns a dictionary-like object that maps vertices to their types. So for instance one can do the following:

ty = g.types()
if ty[vertex] == VertexType.BOUNDARY:
        #It is a boundary

Similarly, the type of an edge is stored as one of the integers EdgeType.SIMPLE or EdgeType.HADAMARD, where EdgeType can be found as pyzx.utils.EdgeType. The edge type of a given edge can be retrieved by g.edge_type(edge).

Backends

ZX-graphs can be represented internally in different ways. The only fully functioning backend right now is pyzx.graph.graph_s.GraphS, which is written entirely in Python. A partial implementation using the python-igraph package is also available as pyzx.graph.graph_ig.GraphIG. A new backend can be constructed by subclassing pyzx.graph.base.BaseGraph.