QDRM: a quantum diffusion framework for the reconstruction of degraded Brahmi script

Abstract Restoring ancient manuscript characters is difficult owing to severe erosion, stroke fragmentation and nonuniform degradation; classical restoration models often oversmooth thin strokes or hallucinate paleographically invalid structures. We propose the Quantum Diffusion Restoration Model (QDRM), a hybrid quantum–classical framework for degraded Brahmi characters, combining a flexible representation of quantum images-matrix product states (FRQI–MPS) contextual representation evaluated through a scalable classical surrogate, a forward diffusion process of completely positive trace-preserving depolarizing channels providing severity-matched supervision, a timestep- and degradation-conditioned parameterized quantum circuit for reverse restoration initialized from the degraded observation, with Hamiltonian-energy and structural regularization preserving stroke topology. On a public paired dataset of 5100 Brahmi characters from 170 classes, QDRM improves the degraded input by 2.50 dB peak signal-to-noise ratio and raises recognizability from 33% to 80% against a 94.6% clean ceiling at moderate severity. The quantum-derived 108-parameter latent-transition design outperforms an unconstrained higher-capacity latent model by about 2.3 dB and a strictly parameter-matched, architecture-isomorphic classical realization reproduces its performance on every metric. The gain stems from the inductive bias of the quantum formulation, which the 9-qubit circuit executes at parity with its classical counterpart. Results hold across K = 3 degradation realizations, five held-out degradation protocols and, after leave-one-out fine-tuning, 19 authentic rock-inscription characters. Real-device execution on ibm_kingston (8 images, depth 88, 2048 shots) retains restoration quality (utility retention 1.19, observable deviation 0.04). The complete pipeline is released.