Quantum Circuits for Amplitude Reweighting

초록

We propose an amplitude reweighting framework that amplifies candidate states in proportion to the Hamming weight of their feature encodings, so that candidates satisfying more constraints receive proportionally larger amplitudes. The framework combines a weight state constructed via single-qubit rotations with a Hadamard product operation realized via parallel CNOT gates and post-selection. We analyze the post-selection overhead inherent in the Hadamard product implementation and introduce a relaxation parameter and a compensation weighting scheme to consider classical post-processing strategies available under this overhead. Simulations on two Max-Cut instances using Qiskit confirm that the proposed amplitude reweighting increases the detection rate of optimal solutions, and that the compensation weighting scheme restores the target distribution under relaxed post-selection.

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