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IEEE International Conference on Acoustics Speech and Signal Processing

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

Jiale Zhang, Xilong Che, Shi Jin, Kaifan Pan, Shun Peng, Juncheng Hu

Published Mar 12, 2025• 0 citations
Publisher

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.

DOI
10.1109/icassp49660.2025.10889351

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Abstract We examine information loss, resource costs, and run time from practical application of quantum data compression. Compressing quantum data to fewer qubits enables efficient use of resources, as well as applications for quantum communication and denoising. In this context, we provide a description of the quantum and classical components of the hybrid quantum autoencoder algorithm, implemented using IBMs Qiskit language. Utilizing our own data sets, we encode bitmap images as quantum superposition states, which correspond to linearly independent vectors with density matrices of discrete values. We successfully compress this data with near-lossless compression using simulation, and then run our algorithm on an IBMQ quantum chip. We describe conditions and run times for training and compressing our data on quantum devices, and relate trainability to specific characteristics and performance metrics of our parametric quantum circuits.
High-resolution images are being generated due to the rapid development of image sensors. Various image processing algorithms require images of reduced sizes, given the computational constraints. Hence, preprocessing the images to reduce their size is crucial for many applications. This letter proposes a novel approach to compress images using quantum computing. A comparative study on different standard data encoding techniques used in quantum computing is undertaken. We propose four quantum compression techniques by extending the unitary operations of amplitude embedding for compressing images. The proposed methods provide exponential scaling as amplitude embedding is used, where2n2^{n}2nclassical data values are encoded intonnnqubits. Compression performance, visual evaluation, and objective evaluation are carried out to assess the proposed compression techniques. Our experimental results show that the crucial patterns in images are retained in the compressed images even at 75% compression. The compressed images can be used for postprocessing tasks using classical or quantum computing algorithms.
This paper proposes a novel data compression technique leveraging the unique properties of quantum entanglement. The core idea involves encoding data into the correlated phase space of entangled qubits, achieving lossless compression. The algorithm utilizes controlled phase manipulation for both encoding and decoding, capitalizing on the inherent correlations between entangled particles. Unlike traditional entropy-based compression methods, this approach directly exploits quantum mechanical phenomena. We demonstrate a theoretical framework and outline a compression algorithm with the potential for significant improvements in compression ratios. The key mathematical representation of the compression process is defined as follows: Let x=(x1,x2,...,xN)x = (x_1, x_2, ..., x_N)x=(x1​,x2​,...,xN​) be the original data sequence, where each xix_ixi​ is a binary value (0 or 1). The compression algorithm maps this sequence to an entangled state (∣ψ1⟩,∣ψ2⟩,...,∣ψN⟩)(|\psi_1\rangle, |\psi_2\rangle, ..., |\psi_N\rangle)(∣ψ1​⟩,∣ψ2​⟩,...,∣ψN​⟩), where ∣ψi⟩|\psi_i\rangle∣ψi​⟩ represents the state of the *i*-th qubit in the entangled pair. The compression ratio *R* is defined as: R=NNencodedR = \frac{N}{N_{encoded}}R=Nencoded​N​ where *N* is the length of the original data sequence and *Nencoded* is the number of qubits used to represent the data. The encoding process is described by: ∣ψi⟩=αi∣0⟩+βi∣1⟩|\psi_i\rangle = \alpha_i |0\rangle + \beta_i |1\rangle∣ψi​⟩=αi​∣0⟩+βi​∣1⟩ where αi\alpha_iαi​ and βi\beta_iβi​ are complex amplitudes determined by the data bit xix_ixi​. The decoding process reverses this operation, reconstructing the original data from the measured state of the qubits. The fidelity of the reconstruction is crucial, and the algorithm incorporates techniques to minimize errors due to measurement noise. The overall compression algorithm can be summarized as follows:
This paper investigates a novel approach to data compression inspired by the principles of quantum entanglement. Traditional data compression techniques often struggle to efficiently represent complex data patterns, particularly in scenarios with high redundancy. We propose an algorithm that utilizes the concept of entangled qubits to represent data, exploiting the strong correlations between these qubits to achieve potentially higher compression ratios. The core idea involves encoding data into a set of entangled qubits, where the state of one qubit directly influences the state of the others. This inherently creates a compact representation, reducing the overall data size. The algorithm is designed to be computationally efficient, aiming to mimic the core advantages of quantum mechanics without requiring full quantum computing resources. We explore the theoretical foundations of this approach, detailing the mathematical framework for qubit representation and the encoding/decoding processes. The paper highlights the potential advantages and challenges associated with this quantum-inspired method, suggesting future research directions and refinements.
Quantum image computing has attracted attention due to its vast storage and faster processing of image data than classical computers. Although classical computing power has grown substantially in the last decade, its abilities have plateaued, struggling to meet the needs of huge datasets. Quantum computers, on the other hand, take advantage of unique qualities like quantum parallelism, superposition, and entanglement to provide faster solutions to complicated problems. Managing huge image data in classical systems necessitates significant memory and hardware resources, which makes quantum computing a possible alternative. Several approaches have arisen for encoding and compressing classical images in the quantum processor. However, one of the most significant limitations is the complexity of quantum state preparation, which translates pixel coordinates to corresponding quantum circuits. Current approaches for representing large-scale images require a huge number of quantum resources including qubit, and qubit connection, which presents significant hurdles. Therefore, this article aims to overview the pixel intensity and state preparation circuit that needs fewer connections, i.e., quantum gates to represent quantum image data, and then explore and design effective compression and processing methods for medium and high-resolution images. This work specializes in emerging quantum models’ potential for enhancing image representation and compression capabilities. It also conducts a comprehensive study of quantum image representation and compression techniques, categorizing existing methods by grayscale and color image types and evaluating their methods, strengths, and limitations. It focuses on crucial difficulties, such as high qubit requirements and complex state preparation, that limit scalability for huge images. This paper also assesses each model’s compression efficacy, which will help future research focus on efficient circuit designs with lower complexity for medium to high-resolution images. It is an essential reference for advancing quantum image processing research since it provides a systematic framework for evaluating quantum image compression and representation algorithms.
This paper proposes a novel approach to temporal data compression leveraging the principles of quantum entanglement. The core idea is to encode correlated data points within a temporal stream into entangled qubits, thereby achieving lossless compression. The method exploits the non-local correlations inherent in entanglement, enabling a more efficient representation of sequential data compared to classical compression techniques. We demonstrate a theoretical framework outlining the compression process, utilizing mathematical notation to define the key concepts and performance metrics. The potential for significantly higher compression ratios is explored, driven by the instantaneous relationship between entangled qubits. This research represents a fundamentally new approach, merging the strengths of quantum mechanics with the demands of temporal data compression. The proposed method offers a promising direction for future research and development in data storage and transmission.