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qml.transforms.rowcol

rowcol(tape, connectivity=None)[source]

CNOT routing algorithm RowCol.

This transform maps a CNOT circuit to a new CNOT circuit under constrained connectivity. The algorithm was introduced by Wu et al. and is detailed on its compilation page, where additional examples can be found as well.

Parameters:

  • tape (QNode or QuantumScript or Callable) – Input circuit containing only CNOT gates. Will internally be translated to the parity_matrix() IR.

  • connectivity (nx.Graph) – Connectivity graph to route into. If None (the default), full connectivity is assumed.

Returns:

the transformed circuit as described in qml.transform.

Return type:

qnode (QNode) or quantum function (Callable) or tuple[List[QuantumScript], function]

Raises:

TypeError – if the input quantum circuit is not a CNOT circuit.

Example

Let us start by defining a connectivity graph

(0) - (3) - (4)
       |
      (2)
       |
      (1)

and define it in code as a networkx.Graph (networkx documentation).

>>> import networkx as nx
>>> G = nx.Graph([(0, 3), (1, 2), (2, 3), (3, 4)])

Further we define the following circuit:

>>> print(qml.draw(qfunc, wire_order=range(5))())
0: ─╭●──────────╭●─╭X─╭●───────┤
1: ─╰X─╭●───────│──│──│──╭X────┤
2: ────╰X─╭●────│──│──╰X─│──╭●─┤
3: ───────╰X─╭●─│──╰●────╰●─│──┤
4: ──────────╰X─╰X──────────╰X─┤

We now run the algorithm:

>>> new_qfunc = qml.transforms.rowcol(qfunc)
>>> print(qml.draw(new_qfunc, wire_order=range(5))()) 
0: ──────────╭X─╭X─╭●─╭●─╭●─╭X─┤
1: ────╭●─╭X─│──│──│──│──│──│──┤
2: ─╭X─╰X─╰●─│──╰●─│──│──╰X─╰●─┤
3: ─╰●───────╰●────│──╰X───────┤
4: ────────────────╰X──────────┤

We can confirm that this circuit indeed implements the original circuit:

>>> import numpy as np
>>> U1 = qml.matrix(new_qfunc, wire_order=range(5))() 
>>> U2 = qml.matrix(qfunc, wire_order=range(5))() 
>>> np.allclose(U1, U2) 
True

The same is true for the parity_matrix() of both circuits.

Please see the compilation page on RowCol for more details and step-by-step explanations of the algorithm.

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