[burgholzer]

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Description

Add the GPI single-qubit synthesis basis: equatorial rotations R(π, φ) and R(π/2, φ) with unrestricted azimuth on every target site. The compiler emits at most three pulses for constant and runtime single-qubit unitaries and preserves global phase. The basis is exposed as GPI in C++ and Python and gpi in pass options. Qiskit export retains native GPI/GPI2 names and phase conventions.

Direct runtime fusion normalizes large rotation angles before adding the pulse phase offsets. This preserves the unitary for inputs such as RZ(0.3), RX(theta), RZ(0.7) with theta = 1e16.

Validation: 913 native compiler, decomposition, synthesis, and optimization tests plus 63 Python Qiskit-target tests pass. The large-angle regression fails before the normalization fix and passes afterward. Generated stubs, repository lint, and whole-file C++ lint pass. Independent Ponytail review has no remaining findings. CI for the updated head is pending.

AI assistance covered implementation, cleanup, independent review, regression tests, validation, and this description. Human acceptance remains.

Checklist

• The pull request only contains commits that are focused and relevant to this change.
• I have added appropriate tests that cover the new/changed functionality.
• I have updated the documentation to reflect these changes.
• The changes follow the project's style guidelines and introduce no new warnings.
• The changes are fully tested and pass the CI checks.
• I have reviewed my own code changes.

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[codecov]

Codecov Report

❌ Patch coverage is 95.83333% with 2 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
...lib/Dialect/QCO/Transforms/Decomposition/Euler.cpp	94.2%	2 Missing ⚠️

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