qiskit/releasenotes/notes/0.24/clifford_cz_lnn_synthesis-4...

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Add a new synthesis algorithm :class:`.synth_cz_depth_line_mr` of a CZ circuit
for linear nearest neighbor (LNN) connectivity in 2-qubit depth of 2n+2
using CX and phase gates (S, Sdg or Z). The synthesized circuit reverts
the order of the qubits. The synthesis algorithm is based on the paper of Maslov and Roetteler
(https://arxiv.org/abs/1705.09176).
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Add a new synthesis algorithm :class:`.synth_clifford_depth_lnn` of a Clifford circuit
for LNN connectivity in 2-qubit depth of 9n+4 (which is still not optimal),
using the layered Clifford synthesis (:class:`.synth_clifford_layers`),
:class:`.synth_cnot_depth_line_kms` to synthesize the CX layer in depth 5n,
and :class:`.synth_cz_depth_line_mr` to synthesize each of the CZ layers in depth 2n+2.
This PR will be followed by another PR based on the recent paper of Maslov and Yang
(https://arxiv.org/abs/2210.16195), that synthesizes the CX-CZ layers in depth 5n
for LNN connectivity and performs further optimization, and hence reduces the depth
of a Clifford circuit to 7n-4 for LNN connectivity.