Quantum Computing through Computational Imaging: Representations, Measurement, and Inference

Abstract

An algebraic correspondence between an imaging model and a quantum state does not specify a computational method: input access, measurement and decoding determine what can be returned. This exposition develops four distinctions for computational-imaging and engineering readers. It separates amplitude encodings of input values from encodings of complete candidate labelings, explaining why amplitude storage does not provide full-array readout. Complex-field interference motivates unknown-phase inference: complementary measurements resolve ambiguities that local Fisher information alone does not detect. Reshaping joint amplitudes into a matrix connects singular-value decomposition to pure-state entanglement, while distinguishing Schmidt rank from conditions for efficient classical simulation. In a four-pixel segmentation, an objective becomes a cost operator and a sampling circuit. One layer of the quantum approximate optimization algorithm (QAOA) lowers mean energy from $1.675$ to $0.686$ relative to uniform sampling, yet makes a nonoptimal labeling more probable than the optimum 0.484 versus 0.365. Archived IBM and IQM measurements illustrate a separate six-variable local boundary decision. Low-rank state reconstruction and selected quantum algorithms connect these distinctions to an end-to-end resource account. The derivations and reproducible numerical references assume complex linear algebra and probability, without prior quantum mechanics. The accompanying Seeing Amplitudes browser laboratory supports interactive exploration; the article remains self-contained and connects each representation to the estimate or decision it permits and the resources that output requires.