<p>Seismic data processing is fundamentally challenged by the presence of complex noise that obfuscates subsurface structures and compromises interpretation fidelity, particularly in scenarios involving thin-bed tuning effects, fault edge preservation, and amplitude-versus-offset (AVO) anomaly characterization. Traditional denoising techniques, including frequency-wavenumber (F-K) filtering, wavelet transforms, and deep learning approaches, often suffer from either insufficient adaptability or the loss of critical geological features such as subtle stratigraphic pinch-outs and channel boundaries. Inspired by quantum mechanical principles, this paper proposes a novel, unified denoising framework termed Quantum-Information-Geometric Denoising (QIGD). The method reconceptualizes seismic traces as quantum systems, where local signal attributes derived via Synchrosqueezing Transform (SST) form a potential field within a discretized Schrödinger equation. The Hamiltonian operator, constructed from this potential and a kinetic energy term, is diagonalized to yield a set of data-adaptive orthogonal basis functions. The core innovation lies in augmenting this quantum model with principles from information geometry and topological data analysis. A geometric Hamiltonian term, derived from the Fisher information metric on the statistical manifold of seismic signals, preserves local statistical structures and stratigraphic textures. A topological term, based on persistent homology, safeguards multi-scale geometrical features—including fault planes and channel edges—against over-smoothing. The seismic section is projected onto this joint eigenbasis, and a multivariate thresholding function, dependent on quantum energy levels, geometric curvature, and topological persistence, is applied for sparse reconstruction. Synthetic and field data experiments demonstrate that QIGD significantly outperforms quantum adaptive basis (QAB) denoising, in terms of signal-to-noise ratio enhancement and structural similarity index preservation, particularly in scenarios with low SNR and complex noise interference. Quantitative analysis of fault displacement errors and amplitude preservation ratios confirms that QIGD maintains geological fidelity superior to competing methods. This work establishes a groundbreaking interdisciplinary paradigm at the confluence of geophysics, quantum theory, and differential geometry for advanced seismic signal processing.</p>