qiskit/releasenotes/notes/0.23/clifford_layered_synthesis-...

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Added a new synthesis method of a Clifford circuit into layers, based on a paper by
Bravyi and Maslov (arxiv:2003.09412).
It decomposes the Clifford into 8 layers of gates.
There are two layers of CZ gates, and one layer of CX gates.
For example, a 5-qubit Clifford circuit is decomposed into the following layers:
.. code-block:: text
┌─────┐┌─────┐┌────────┐┌─────┐┌─────┐┌─────┐┌─────┐┌────────┐
q_0: ┤0 ├┤0 ├┤0 ├┤0 ├┤0 ├┤0 ├┤0 ├┤0 ├
│ ││ ││ ││ ││ ││ ││ ││ │
q_1: ┤1 ├┤1 ├┤1 ├┤1 ├┤1 ├┤1 ├┤1 ├┤1 ├
│ ││ ││ ││ ││ ││ ││ ││ │
q_2: ┤2 S2 ├┤2 CZ ├┤2 CX_dg ├┤2 H2 ├┤2 S1 ├┤2 CZ ├┤2 H1 ├┤2 Pauli ├
│ ││ ││ ││ ││ ││ ││ ││ │
q_3: ┤3 ├┤3 ├┤3 ├┤3 ├┤3 ├┤3 ├┤3 ├┤3 ├
│ ││ ││ ││ ││ ││ ││ ││ │
q_4: ┤4 ├┤4 ├┤4 ├┤4 ├┤4 ├┤4 ├┤4 ├┤4 ├
└─────┘└─────┘└────────┘└─────┘└─────┘└─────┘└─────┘└────────┘
This method will allow to decompose a Clifford circuit in 2-qubit depth 7n+2 for
linear nearest neighbor (LNN) connectivity.
Since a CZ circuit can be decomposed in 2-qubit depth 2n by arxiv:1705.09176,
and a CX-CZ circuit can be decomposed in 2-qubit depth 2n by arxiv:2210.16195.
These algorithms will be added in future PRs.