Quantum Run-length Encoding: Optimizing Data Compression on Quantum Computers with Exponential Resource Efficiency

Abstract

Quantum computers, leveraging superposition and entanglement, offer significant qubit efficiency for data processing compared to classical systems. However, encoding classical data into quantum states, given the current limitations of quantum hardware, often results in higher runtime complexity than classical methods, thus limiting the perceived quantum advantage. Previous quantum data compression methods, primarily based on Amplitude Encoding and mixed-state systems, result in lossy data recovery and necessitate extensive preprocessing. In this work, we propose Quantum Run-Length Encoding (QRLE), a novel lossless quantum data compression method that integrates Basic Encoding with Run-Length Encoding principles. By encoding repeated data sequences with their run lengths, QRLE achieves efficient and accurate data recovery on quantum computers, while exponentially reducing both qubit costs and runtime complexity compared to existing quantum data storage models. We further explore QRLE’s application in image processing, where it significantly optimizes quantum resource utilization over recent quantum image representation techniques. Experiments conducted on both quantum simulators and IBM’s superconducting quantum computer validate the efficiency of QRLE and confirm its compatibility with current quantum hardware.