Synthesis of a stabilizer state for LNN connectivity

[ShellyGarion]

Summary

#9036

Synthesis of a stabilizer state preparation.
Based on the Clifford layered synthesis, it requires only the layers H2 - S1 - CZ1 - H1,
so for linear nearest neighbor (LNN) connectivity it has 2q depth 2n+2.

Details and comments

• synth_stabilizer_layers - a general synthesis of a StabilizerState into layers
• synth_stabilizer_depth_lnn - synthesis of a StabilizerState for LNN connectivity in depth 2n+2

Co-authored by: @alexanderivrii

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[coveralls]

Pull Request Test Coverage Report for Build 4604320027

• 62 of 64 (96.88%) changed or added relevant lines in 3 files are covered.
• 1914 unchanged lines in 127 files lost coverage.
• Overall coverage increased (+0.04%) to 85.398%

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Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit/synthesis/stabilizer/stabilizer_decompose.py	59	61	96.72%

Files with Coverage Reduction	New Missed Lines	%
qiskit/algorithms/amplitude_amplifiers/amplification_problem.py	1	84.72%
qiskit/algorithms/amplitude_amplifiers/amplitude_amplifier.py	1	94.0%
qiskit/algorithms/eigen_solvers/eigen_solver.py	1	97.78%
qiskit/algorithms/evolvers/real_evolver.py	1	92.31%
qiskit/algorithms/phase_estimators/phase_estimation_result.py	1	96.36%
qiskit/algorithms/time_evolvers/variational/var_qite.py	1	94.74%
qiskit/circuit/add_control.py	1	97.2%
qiskit/circuit/library/arithmetic/adders/vbe_ripple_carry_adder.py	1	98.55%
qiskit/circuit/library/standard_gates/p.py	1	98.9%
qiskit/opflow/primitive_ops/pauli_sum_op.py	1	86.63%

Totals
Change from base Build 4332358082:	0.04%
Covered Lines:	67385
Relevant Lines:	78907

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💛 - Coveralls

[alexanderivrii]

Thanks. This looks good and clean. My only suggestion was to implement stabilizer synthesis more directly.

[alexanderivrii]

Sorry for the delay on this. The main comment is that we can avoid doing the full Clifford synthesis (and in particular avoid calling _decompose_hadamard_free), which would make the implementation both faster and more robust.

[alexanderivrii]

LGTM. Thanks for doing all these changes.