Quantum DCT Amplitude Encoding for RGB Image Reconstruction: Shot-Budget Characterisation and a Unified Multi-Channel Formulation

We present a systematic empirical study of quantum amplitude encoding applied to the reconstruction of a full-colour photographic image via Discrete Cosine Transform (DCT) coefficients. A 256x256 RGB photograph is compressed by retaining the K lowest-frequency DCT coefficients per channel in zigzag scan order, whose magnitudes are loaded into an n-qubit quantum state using Qiskit's StatePreparation gate. We conduct a comprehensive sweep of n from 4 to 16 qubits at shot counts from 200,000 to 16,000,000, recording PSNR and SSIM at every combination. A principal finding is the PSNR dome: image quality peaks at intermediate n and falls as n increases further. We derive an optimality condition n* approximately log2(S/50). A unified RGB formulation encoding all three colour channels as a single 18-qubit amplitude state (K=262,144) is introduced, achieving PSNR=29.07 dB at 8M shots. All experiments run on the Qiskit Aer sampling simulator.