Synthesis of CZ and Clifford circuits for linear nearest neighbor connectivity #9450
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ShellyGarion
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This PR is ready for an initial review (mainly of the API). It only misses the release notes. |
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Thanks @ShellyGarion! The PR looks very good. I only had very minor comments at this point.
qiskit/synthesis/__init__.py
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| from .linear import ( | ||
| synth_cnot_count_full_pmh, | ||
| synth_cnot_depth_line_kms, | ||
| synth_cz_depth_line_mr, | ||
| ) |
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I don't have a strong opinion on this either. Does it make sense that code for CZ synthesis appears under linear? Or would it be better to put it in the synthesis/cz subdirectory?
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I think the best solution is to have another folder of synthesis/linear_phase since the cz synthesis is into cx and phase gates, and relies on the theory of phase polynomials. It's similar to graysynth that should be moved this folder too.
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Moving and renaming graysynth, as well as deprecating https://github.com/Qiskit/qiskit-terra/blob/main/qiskit/transpiler/synthesis/graysynth.py will be done in a separate PR
releasenotes/notes/clifford_cz_lnn_synthesis-4b0328b581749df5.yaml
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…nectivity (Qiskit#9450) * add cz synthesis for LNN * basic cz synthesis test * adjust clifford_decompose_layers to cz synthesis for LNN * add a basic test for layered clifford synthesis for LNN * enhance the tests * fix lint, check function name * Add utils needed for LNN tests * add tests for LNN and depth * Add documentation for cz synthesis * fix misprint * add synth_clifford_depth_lnn * updates following review * rename synth_clifford_depth_lnn * update references * remove a util function that is not needed * update docstring * add release notes * replace int(n/2) by n//2 * reduce the number of 1-qubit gates * fix test * refactor and minor changes following review * update docs * update init file following review --------- Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>
Summary
#9036
Synthesis 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). Note that the synthesized circuit reverts the order of the qubits.
This CZ synthesis method allows to synthesize a Clifford circuit for LNN connectivity in 2-qubit depth of 9n+4 (which is still not optimal), by using the layered Clifford synthesis (clifford_decompose_layers.py) and linear_depth_lnn.py for synthesizing the CX layer in depth 5n.
This PR will be followed by another PR based on a paper of Maslov and Yang (https://arxiv.org/abs/2210.16195), that synthesize the CX-CZ layers in depth 5n for LNN connectivity, and hence reduce the depth of a Clifford circuit to 7n-4 for LNN connectivity.
Details and comments
The algorithm is based on the paper of Maslov and Roetteler https://arxiv.org/abs/1705.09176