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

TL;DR

The paper tackles efficient quantum-assisted classical image compression by removing coordinate qubits in quantum image representations. It introduces MPM-QIR, a variational quantum circuit that learns pixel ordering implicitly by aligning its measurement-probability distribution $P_{quantum}( heta)$ with normalized image intensities, enabling compression to scale with circuit complexity rather than explicit addresses. A novel bidirectional, full-width convolutional ansatz enables long-range entanglement at shallow depth, improving reconstruction quality with fewer parameters. On MNIST, Fashion-MNIST, and CIFAR-10, the method achieves PSNRs above $30\,\mathrm{dB}$ at PCRs as low as around $0.69$–$0.84$, outperforming QCNN and QAE baselines and demonstrating VQCs as effective generative models for classical image compression. The work supports two-stage classical-quantum pipelines and suggests extensions to modalities beyond 2D imagery.

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.

Figures (5)

• Figure 1: Overview of the MPM-QIR training pipeline. A target grayscale image is first normalized into the range $[0, 1]$ to produce the normalized image $I_{\text{norm}}$. The VQC is initialized with the $|0\rangle^{\otimes n}$ state and executed to generate a measurement image fluctuation distribution $|P\rangle$. The output probabilities are then rescaled through a shifting operation, where parameters $\mu$ and $\sigma$ are computed from $I_{norm}$. The reconstructed image is compared with $I_{\text{norm}}$ using the MSE loss, and the VQC parameters are iteratively updated via the Adam optimizer to minimize the reconstruction error.
• Figure 2: Schematic of the proposed bidirectional VQC architecture.A single layer consists of a Forward Convolution pass (blue) followed by a complementary Backward Convolution pass (orange). The entire layer can be repeated ($n$ times) to increase depth.
• Figure 3: Gate-level decomposition of the unitary blocks. This figure illustrates the basic structure of the quantum convolution operation used in our model. The forward convolution (left) applies parameterized rotation gates $R_y(\theta_0)$, $R_y(\theta_1)$, $R_z(\theta_2)$ and controlled-NOT (CNOT) operation to entangle neighboring qubits and extract local correlations. The backward convolution (right) performs the inverse entanglement operation using a reversed CNOT pattern and an $R_x(\theta_3)$ rotation, allowing information to propagate backward across qubit pairs. Together, these two blocks form a bidirectional quantum convolutional layer capable of encoding both forward and backward feature dependencies in the quantum state.
• Figure 4: Reconstruction performance on CIFAR-10 dataset. (A) Average PSNR (dB) of reconstructed images under different compression ratios for the proposed model (Ours), QCNN, and QAE. Our model consistently achieves higher reconstruction fidelity across all parameter compression levels. (B) Visual reconstruction examples from our model, along with their corresponding PSNR and SSIM scores.
• Figure 5: Convergence of training loss for different models. The mean squared error (MSE) loss is plotted as a function of training steps for the proposed model (Ours), QCNN and QAE. All models show smooth convergence, but the proposed approach achieves both faster loss reduction and a lower final MSE, indicating more stable and efficient optimization.