Getting Started

PyZX can be installed as a package using pip:

pip install pyzx

If you wish to use the demo notebooks or benchmark circuits, then the repository can be cloned from Github.

The best way to get started if you have cloned the repository is to run the Getting Started notebook in Jupyter. This page contains the same general information as that notebook.

Let’s start by importing the library:

>>> import pyzx as zx

For all the examples in this documentation we will assume you have imported PyZX in this manner.

Quantum circuits in PyZX are represented by the Circuit class. File in the supported formats (QASM, QC, Quipper) can easily be imported into PyZX:

circuit = zx.Circuit.load("path/to/circuit.extension")

PyZX tries to automatically figure out in which format the circuit is represented. The generate module supplies several ways to generate random circuits:

>>> circuit = zx.generate.CNOT_HAD_PHASE_circuit(qubits=10,depth=20,clifford=True)

If you are running inside a Jupyter notebook, circuits can be easily visualized:

>>> zx.draw(circuit)
_images/clifford.png

The default drawing method is to use the d3 javascript library. When not running in a Jupyter notebook zx.draw returns a matplotlib figure instead.

Most of the functionality of PyZX is based on the ZX-diagrams. These are represented by instances of BaseGraph. To convert a circuit into a ZX-diagram, simply do:

g = circuit.to_graph()

Let us use one of the built-in ZX-diagram simplification routines on this ZX-diagram:

>>> zx.clifford_simp(g)  # simplifies the diagram
>>> g.normalise()  # makes it more presentable
>>> zx.draw(g)
_images/clifford_simp.png

The same circuit, but rewritten into a more compact form. The blue lines represent edges which have a Hadamard gate on them.

A ZX-diagram is represented internally as a graph:

>>> print(g)
Graph(16 vertices, 21 edges)

This simplified ZX-graph no longer looks like a circuit. PyZX supplies some methods for turning a ZX-graph back into a circuit:

>>> c = zx.extract.streaming_extract(g.copy())
>>> zx.draw(c)
_images/clifford_extracted.png

To verify that the simplified circuit is still equal to the original we can convert them to numpy tensors and compare equality directly:

>>> zx.compare_tensors(c,g,preserve_scalar=False)
        True

Note that a Circuit is not much more than just a series of gates:

>>> print(c.gates)
        [S(1), S*(2), Z(3), CZ(1,3), CZ(2,3), S(0), CZ(1,0), CZ(3,0), CNOT(1,0), CNOT(2,0), CNOT(3,0), CNOT(2,3), CNOT(0,3), NOT(2), CX(2,3), HAD(3)]

We can convert circuits into one of several circuit description languages, such as that of QUIPPER:

>>> print(c.to_quipper())
Inputs: 0Qbit, 1Qbit, 2Qbit, 3Qbit
QGate["S"](1) with nocontrol
QGate["S"]*(2) with nocontrol
QGate["Z"](3) with nocontrol
QGate["Z"](3) with controls=[+1] with nocontrol
QGate["Z"](3) with controls=[+2] with nocontrol
QGate["S"](0) with nocontrol
QGate["Z"](0) with controls=[+1] with nocontrol
QGate["Z"](0) with controls=[+3] with nocontrol
QGate["not"](0) with controls=[+1] with nocontrol
QGate["not"](0) with controls=[+2] with nocontrol
QGate["not"](0) with controls=[+3] with nocontrol
QGate["not"](3) with controls=[+2] with nocontrol
QGate["not"](3) with controls=[+0] with nocontrol
QGate["not"](2) with nocontrol
QGate["X"](3) with controls=[+2] with nocontrol
QGate["H"](3) with nocontrol
Outputs: 0Qbit, 1Qbit, 2Qbit, 3Qbit

Optimising random circuits is of course not very useful, so let us do some optimisation on a predefined circuit:

>>> c = zx.Circuit.load('circuits/Fast/mod5_4_before')  # Circuit.load auto-detects the file format
>>> print(c.gates)  #  This circuit is built out of CCZ gates.
[NOT(4), HAD(4), CCZ(c1=0,c2=3,t=4), CCZ(c1=2,c2=3,t=4), HAD(4), CNOT(3,4), HAD(4), CCZ(c1=1,c2=2,t=4), HAD(4), CNOT(2,4), HAD(4), CCZ(c1=0,c2=1,t=4), HAD(4), CNOT(1,4), CNOT(0,4)]
>>> c = c.to_basic_gates()  #  Convert it to the Clifford+T gate set.
>>> print(c.gates)
[NOT(4), HAD(4), CNOT(3,4), T*(4), CNOT(0,4), T(4), CNOT(3,4), T*(4), CNOT(0,4), T(3), T(4), HAD(4), CNOT(0,3), T(0), T*(3), CNOT(0,3), HAD(4), CNOT(3,4), T*(4), CNOT(2,4), T(4), CNOT(3,4), T*(4), CNOT(2,4), T(3), T(4), HAD(4), CNOT(2,3), T(2), T*(3), CNOT(2,3), HAD(4), HAD(4), CNOT(3,4), HAD(4), CNOT(2,4), T*(4), CNOT(1,4), T(4), CNOT(2,4), T*(4), CNOT(1,4), T(2), T(4), HAD(4), CNOT(1,2), T(1), T*(2), CNOT(1,2), HAD(4), HAD(4), CNOT(2,4), HAD(4), CNOT(1,4), T*(4), CNOT(0,4), T(4), CNOT(1,4), T*(4), CNOT(0,4), T(1), T(4), HAD(4), CNOT(0,1), T(0), T*(1), CNOT(0,1), HAD(4), HAD(4), CNOT(1,4), CNOT(0,4)]
>>> print(c.stats())
Circuit mod5_4_before on 5 qubits with 71 gates.
        28 is the T-count
        43 Cliffords among which
        28 2-qubit gates and 14 Hadamard gates.
>>> g = c.to_graph()
>>> print(g)
Graph(109 vertices, 132 edges)
>>> zx.simplify.full_reduce(g)  # Simplify the ZX-graph
>>> print(g)
Graph(31 vertices, 38 edges)
>>> c2 = zx.extract.streaming_extract(g).to_basic_gates()  # Turn graph back into circuit
>>> print(c2.stats())
Circuit  on 5 qubits with 42 gates.
        8 is the T-count
        34 Cliffords among which
        24 2-qubit gates and 10 Hadamard gates.
>>> c3 = zx.optimize.full_optimize(c2)  #  Do some further optimization on the circuit
>>> print(c3.stats())
Circuit  on 5 qubits with 27 gates.
        8 is the T-count
        19 Cliffords among which
        14 2-qubit gates and 2 Hadamard gates.

The circuit file-formats supported by Circuit.load are curently qasm, qc or quipper. PyZX can also be run from the command-line for some easy circuit-to-circuit manipulation. In order to optimise a circuit you can run the command:

python -m pyzx opt input_circuit.qasm

For more information regarding the command-line tools, run python -m pyzx --help.

This concludes this tutorial. For more information about the simplification procedures see List of simplifications. Information regarding the circuit extraction can be found in Circuit extraction and matrices over Z2. The different representations of the graphs and circuits is detailed in Importing and exporting quantum circuits and ZX-diagrams. The low level graph api is explained in graph.