Histopathologic cancer detection is challenging due to tissue variability, staining differences, and subtle visual distinctions between disease classes. We propose two quantum algorithms for this task: a configurable dual-gradient CSWAP circuit (DG-CSWAP) that computes multi-directional edge responses in a single execution via per-pixel local Ry encoding, and a hardware-efficient destructive swap circuit (DG-DST) natively matched to quantum processing unit (QPU) gate sets at substantially lower circuit complexity. We prove algebraic equivalence between DG-CSWAP and DG-DST, enabling a two-circuit QPU validation strategy. A three-stage NISQ mitigation pipeline, including readout error correction, bias subtraction, and slope regression, reduces single-pixel hardware MSE by ~8x. Validated on five quantum processors via Amazon Braket, the method achieves inter-platform Pearson r ~ 0.93-0.94 across all local-simulator pairs. Compared to a prior Quantum Fourier Transform (QFT) based amplitude-encoding baseline requiring 12-qubit global state preparation and a three-model ensemble (85.55% on PatchCamelyon), the proposed method uses shot-based measurements, executes on real quantum hardware, and achieves 79.80% accuracy with a single ResNet-50. A Lite configuration delivers a 17x preprocessing speedup at a 2.59% accuracy cost. To the best of our knowledge, this is the first quantum hardware implementation study with noise mitigation for histopathologic image classification.

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