Schmidt Decomposition-Based Methods for Efficient Quantum Image Encoding

2026-06-09

AI Summary

This work addresses the high circuit depth, excessive gate count, and substantial qubit requirements of mainstream quantum image encoding schemes—such as FRQI, QPIE, and NEQR—which hinder their deployment on noisy intermediate-scale quantum (NISQ) devices. To overcome these limitations, the study introduces Schmidt decomposition into quantum image encoding for the first time, leveraging low-rank quantum state approximation to preserve essential image information while drastically reducing circuit complexity. Experimental results demonstrate that the proposed approach achieves near-perfect image reconstruction in FRQI (MSE ≈ 0.27) with a 97% reduction in circuit depth, significantly enhancing feasibility on NISQ hardware and effectively balancing reconstruction accuracy with resource efficiency.

Abstract

In quantum image processing, a fundamental step is encoding classical image data into quantum states. This can be achieved using methods such as Flexible Representation of Quantum Images (FRQI), Quantum Probability Image Encoding (QPIE), and Novel Enhanced Quantum Representation (NEQR). However, on real quantum hardware, these encodings can quickly lead to circuits with many gates, large circuit depth, and high qubit usage, which is a problem for Noisy Intermediate-Scale Quantum (NISQ) devices. In this work, we investigate whether low-rank state approximation, formulated via Schmidt decomposition, can help reduce this complexity. The method keeps only the most significant parts of a quantum state's entanglement structure, making state preparation more efficient while preserving most of the image information. We compare the three encoding techniques in their original form and with low-rank approximation, evaluating metrics such as circuit depth, CNOT count, MSE, and visual quality of reconstructed images. The results reveal meaningful trade-offs between accuracy and resource efficiency, with the FRQI model achieving a 97 percent reduction in circuit depth while maintaining a near-perfect reconstruction (MSE of about 0.27). This demonstrates the potential of low-rank techniques for advancing practical quantum image processing on near-term hardware.

Problem

• quantum image encoding
• NISQ devices
• circuit complexity
• Schmidt decomposition
• low-rank approximation

Innovation

• Schmidt decomposition
• low-rank approximation
• quantum image encoding
• circuit depth reduction
• NISQ