Quantum Feature Amplification Network (QFAN) as An Autoregressive Quantum Generative Model

Abstract

Simulating calorimeter showers is among the largest computational costs in high-energy physics, and quantum generative models have been proposed as alternatives to classical surrogates. Their progress is hindered by a resource problem. In existing gate-model proposals, the quantum register grows with the image size. Benchmark data sets have thousands of cells and are therefore out of reach. We introduce the Quantum Feature Amplification Network (QFAN), which breaks the link between register size and image size. QFAN splits an image into consecutive blocks of pixels and generates them one block at a time, each produced by the same small circuit conditioned on a fixed-length summary of the pixels already generated. The number of qubits is set by the block size, not by the image dimension. The circuit is used as a sampler. Each block is decoded from a finite set of Born measurement records, so the stochasticity of the generated shower arises from measurement randomness rather than classical noise. A tunable fraction of the records is shared among the pixels within a block to control their correlations. Fast training is performed on a noiseless simulator using analytic gradients, and the resulting model is then deployed on IBM's Heron QPU. Using only three qubits and 12 (18) shared quantum-circuit parameters, QFAN reproduces pixel-intensity spectra, inter-pixel correlations, and total deposited energy for 12- and 25-pixel benchmarks. We quantify the contribution of the quantum component through an ablation study in which individual pipeline elements are removed and the remainder refitted. Replacing the sampled records by their conditional means, which removes only the measurement randomness, collapses the model to a single deterministic image. Leaving the circuit untrained while refitting every classical stage reproduces neither the pixel spectra nor the correlations at either image size.