Quantum computing is emerging as a transformative tool for communication systems, offering the potential to overcome long-standing physical limitations. In free-space optical networks, orbital angular momentum (OAM) multiplexing promises massive capacity gains, but its practical use is fundamentally constrained by multiphysics degradations such as atmospheric turbulence, volumetric Mie scattering, and stochastic quantum noise. These effects induce nonlinear modal crosstalk and severe beam distortions, against which classical approaches -- most notably convolutional neural networks (CNNs) -- provide only partial and non-scalable compensation. To address this gap, we report the first use of variational quantum neural networks (QNNs) for adaptive OAM beam compensation in realistic channels. By embedding parameterized entangling layers into a supervised regression pipeline, our QNN achieves end-to-end reconstruction of distorted Laguerre-Gaussian beams with topological charges l ∈ {1,4,8,12}. Using experimentally validated channel parameters, QNNs achieve mean squared error as low as 4.0 × 10, SSIM above 0.99, and bit-error rates suppressed by > 99.9% (0.0125% BER). To ensure scalability, we introduce the quasi-quantum neural network (QqNN), a classical surrogate that emulates quantum dynamics via tensorial projections, achieving near-optimal performance (0.0375% BER) at reduced complexity. This hybrid framework positions QNNs as a quantum-resilient paradigm for OAM decoding and establishes QqNNs as the first scalable surrogate for near-term deployment.