The authors define the QA-KS(φ) gate family embedding Toffoli with Hadamard sandwich and CP kickback, provide its exact 8x8 unitary, and demonstrate orthogonality to CCX on q0=1 inputs while agreeing on q0=0.
Elementary gates for quantum computation,
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Quantum-Adaptive KS($\varphi$): A Parameterized Three-Qubit Gate Family Embedding Toffoli with Measurement-Free Phase Kickback and Intrinsic Error Non-Amplification
The authors define the QA-KS(φ) gate family embedding Toffoli with Hadamard sandwich and CP kickback, provide its exact 8x8 unitary, and demonstrate orthogonality to CCX on q0=1 inputs while agreeing on q0=0.