GEQIE Framework for Rapid Quantum Image Encoding

TL;DR

GEQIE introduces a generalized, Python-based framework for rapid quantum image encoding built on the Quantum Lattice representation. It formalizes a modular encoding model with position and value maps, and provides a hardware-agnostic workflow via Qiskit transpilation, along with benchmarks using PCC and PSNR under depolarizing noise. The paper contributes an open-source library, a web playground, and a multidimensional Cosmic Web encoding demonstration, showing near-ideal retrieval on simulated data and feasibility for multidimensional analyses. By decoupling data representation from circuit-level detail, GEQIE accelerates cross-domain experimentation and paves the way for hardware-aware studies and potential speedups in quantum image processing for complex data like cosmological snapshots.

Abstract

This work presents a Python framework named after the General Equation of Quantum Image Encoding (GEQIE). The framework creates the image-encoding state using a unitary gate, which can later be transpiled to target quantum backends. The benchmarking results, simulated with different noise levels, demonstrate the correctness of the already implemented encoding methods and the usability of the framework for more sophisticated research tasks based on quantum image encodings. Additionally, we present a showcase example of Cosmic Web dark-matter density snapshot encoding and high-accuracy retrieval (PCC = 0.995) to demonstrate the extendability of the GEQIE framework to multidimensional data and its applicability to other fields of research.

Figures (10)

• Figure 1: The schematic diagram of the GEQIE framework. From the left are visible the Command Line Interface used, e.g., by the web application; the GEQIE package with encoding methods containing init, data, and map associated with \ref{['eq:general_quantum_image_model']} plus the retrieve function; and the interaction with the Qiskit framework that covers automatic transpilation of the circuits.
• Figure 2: GEQIE GUI with available list of quantum encoding methods, possible list of devices to execute the circuit on, and experimental setup in the middle.
• Figure 3: Average value of Pearson's Correlation Coefficient of retrieved vs original image, versus noise level for (a) grayscale and (b) RGB methods.
• Figure 4: Average value of Peak Signal-to-Noise Ratio (PSNR) of retrieved vs original image, versus noise level for (a) grayscale and (b) RGB methods. For perfect retrievals, the MSE used in the PSNR calculation was zero, and the assumed PSNR was infinite; the values are deliberately capped at 60 dB to indicate this.
• Figure 5: Comparison of the original and retrieved images encoded with the FRQI method using GEQIE and executed on the IBM Quantum Platform. The relative metrics of the images are low due to high noise (PCC=0.474, PSNR=30.98 dB).