PALQA: A Novel Parameterized Position-Aware Lossy Quantum Autoencoder using LSB Control Qubit for Efficient Image Compression

TL;DR

The paper addresses the challenge of efficiently compressing quantum-encoded images with quantum autoencoders that generalize beyond tiny images. It introduces PALQA, a parameterized position-aware lossy quantum autoencoder using an LSB control qubit and block-wise transform coefficient encoding via a modified ZSCNEQR circuit. Compared with JPEG and NZ-NEQR-based QAE, PALQA shows improved PSNR with competitive gate counts across several grayscale images, demonstrating better rate-distortion performance. The work provides a pathway toward near-term quantum-classical implementations and highlights the importance of explicit state-position encoding in quantum image compression.

Abstract

With the growing interest in quantum computing, quantum image processing technology has become a vital research field due to its versatile applications and ability to outperform classical computing. A quantum autoencoder approach has been used for compression purposes. However, existing autoencoders are limited to small-scale images, and the mechanisms of state compression remain unclear. There is also a need for efficient quantum autoencoders using standard representation approaches and for studying parameterized position-aware control qubits and their corresponding quality measurement metrics. This work introduces a novel parameterized position-aware lossy quantum autoencoder (PALQA) circuit that utilizes the least significant bit control qubit for image compression. The PALQA circuit employs a transformed coefficient block-based modified state connection approach to efficiently compress images at various resolutions. The method leverages compression opportunities in the state-label connection by applying position-aware least significant control qubit. Compared to JPEG and other enhanced quantum representation-based quantum autoencoders, the PALQA circuit demonstrates superior performance in terms of the number of gates required and PSNR metrics.

Figures (13)

• Figure 1: autoencoder architecture. (a) Architecture of the classical autoencoder (E) encodes $n$ dimensional input data into the lower dimensional of the latent space (L) and the decoder (D) decodes original information from the lower dimension of the latent space. (b) Quantum autoencoder architecture where the encoder(E) takes an $m$ number of qubits state and maps into a lower number latent space(L) qubit and then the decoder (D) reconstructs the image into a $m$ dimensional state.
• Figure 2: A $2\times2$ FRQI quantum image
• Figure 3: An FRQI circuit for representing $|I_{FRQI}\rangle$ image
• Figure 4: An NEQR circuit for pixel values representation
• Figure 5: A NZ-NEQR circuit for pixel values representation where an initial connection (marked as red) and zero-discarded zone (marked as orange). Zero is discarded because the identity gate has no control over the c-not gate.