MPM-QIR: Measurement-Probability Matching for Quantum Image Representation and Compression via Variational Quantum Circuit

TL;DR

This paper introduces MPM-QIR, a variational quantum circuit framework that efficiently compresses classical images by matching measurement probabilities with pixel intensities, achieving high quality at low compression ratios.

Contribution

It proposes a novel VQC-based image compression method that implicitly learns positional info and captures global correlations with fewer parameters, outperforming benchmarks.

Findings

Achieves PSNR ≥ 30 dB at low PCR on multiple datasets.

Demonstrates parameter efficiency and effective global correlation capture.

Validates VQCs as generative models for classical image compression.

Abstract

We present MPM-QIR, a variational-quantum-circuit (VQC) framework for classical image compression and representation whose core objective is to achieve equal or better reconstruction quality at a lower Parameter Compression Ratio (PCR). The method aligns a generative VQC's measurement-probability distribution with normalized pixel intensities and learns positional information implicitly via an ordered mapping to the flattened pixel array, thus eliminating explicit coordinate qubits and tying compression efficiency directly to circuit (ansatz) complexity. A bidirectional convolutional architecture induces long-range entanglement at shallow depth, capturing global image correlations with fewer parameters. Under a unified protocol, the approach attains PSNR $\geq$ 30 dB with lower PCR across benchmarks: MNIST 31.80 dB / SSIM 0.81 at PCR 0.69, Fashion-MNIST 31.30 dB / 0.91 at PCR 0.83, and CIFAR-10 31.56 dB / 0.97 at PCR 0.84. Overall, this compression-first design improves parameter efficiency, validates VQCs as direct and effective generative models for classical image compression, and is amenable to two-stage pipelines with classical codecs and to extensions beyond 2D imagery.