Quantum signal processing (single qubit)

Quantum signal processing (QSP) interleaves a fixed one-parameter signal rotation with tunable processing phase rotations and characterizes exactly which SU(2)-valued polynomial transforms of the signal are achievable.

This is the umbrella module for the single-qubit QSP development. It splits by polynomial basis and re-exports both halves:

• LeanPool.LeanQuantumAlg.Primitives.QSP.Chebyshev — the Chebyshev-basis forms: the reflection-derived O-convention (qsp_reflection_iff) and the Wx-convention / XZX form (qsp_wx_iff), characterized by IsQSPPair.
• LeanPool.LeanQuantumAlg.Primitives.QSP.Fourier — the Fourier-basis (trigonometric) forms: the YZY (qsp_yzy_iff) and YZZYZ / W-Z-W (qsp_yzzyz_iff) quantum-neural-network forms, characterized by IsYZYPair/IsYZPair through the Laurent encoding lEval.

The two families are genuinely different transforms with different inputs (Chebyshev polynomials in x ∈ [-1,1] vs. Laurent/Fourier polynomials in e^{ix/2}); a cross-convention bridge (x = cos θ) is left as future work.

Main results (registered targets)

• LeanPool.LeanQuantumAlg.ReflectionBasedQuantumSignalProcessing.main, LeanPool.LeanQuantumAlg.ReflectionBasedQuantumSignalProcessing.main_wx — Chebyshev basis.
• LeanPool.LeanQuantumAlg.qsp_yzy_iff, LeanPool.LeanQuantumAlg.qsp_yzzyz_iff — Fourier basis.