The superposition state of qubits in quantum computers enables a more efficient data representation than conventional binary methods in classical computers. Grover’s algorithm amplifies the amplitude of a target state within a superposed set of states having equal amplitudes. However, except for a 2-qubit system, the amplitudes of the nontarget states and left residual amplitudes induced by the algorithm do not reduce to zero. Therefore, a new method was devised to overcome this drawback. We select new target state among the nontarget states by applying Grover’s algorithm and obtain two distinct states with different amplitudes. Consequently, by excluding duplicate cases, this method enables the representation of [Formula: see text] data points. This technique is referred to as superdense data representation (SDR). Specifically, SDR is a new data representation method for quantum computers using superposition and entanglement. This offers several advantages for encoding data. For instance, 8-qubit data can be effectively represented in 4-qubit, thereby reducing the resources required to store the information. Additionally, SDR allows the representation of more complex data, such as Unicode, without increasing calculation or storage costs. UTF-8 encoding method can be implemented using only eight qubits. By extending SDR, Asian languages that require more than two bytes of data can also be expressed using eight qubits.
The superposition state of qubits in quantum computers enables a more efficient data representation than conventional binary methods in classical computers. Grover’s algorithm amplifies the amplitude of a target state within a superposed set of states having equal amplitudes. However, except for a 2-qubit system, the amplitudes of the nontarget states and left residual amplitudes induced by the algorithm do not reduce to zero. Therefore, a new method was devised to overcome this drawback. We select new target state among the nontarget states by applying Grover’s algorithm and obtain two distinct states with different amplitudes. Consequently, by excluding duplicate cases, this method enables the representation of [Formula: see text] data points. This technique is referred to as superdense data representation (SDR). Specifically, SDR is a new data representation method for quantum computers using superposition and entanglement. This offers several advantages for encoding data. For instance, 8-qubit data can be effectively represented in 4-qubit, thereby reducing the resources required to store the information. Additionally, SDR allows the representation of more complex data, such as Unicode, without increasing calculation or storage costs. UTF-8 encoding method can be implemented using only eight qubits. By extending SDR, Asian languages that require more than two bytes of data can also be expressed using eight qubits.
Grover's algorithm, which was discovered in 1996, is faster than any classical algorithm can ever be. Quantum systems are in a superposition of states and can examine multiple data simultaneously. This work conducted a comprehensive analysis to understand how Grover's algorithm works. Grover's search provides quadratic speed in comparison to the classical one; it explores target data in the unstructured database. Grover search starts with the superposition of all Qubits, which results in the same amplitude for all data points. To achieve superposition, the Hadamard gate was applied to all Qubits. Further, a black box function named Oracle is applied to mark the desired state. In the next phase, amplitude amplification is done, which enhances the probability of the desired data point. Thus, Grover's search yields results with an O (√ N) complexity, while its counterpart classical algorithm searches the desired data point with an O (N) complexity. Experiments have been performed on the Qiskit simulator using 2 and 3 qubits for the detailed analysis of Grover's search.
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.
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.
Grover’s algorithm harnesses the power of quantum computing to swiftly locate specific elements in an unstructured database, outperforming classical computers in tasks like database searching. This algorithm capitalizes on the unique ability of qubits to be in both 0 and 1 states simultaneously (superposition), allowing it to scan the entire search space at once. It then boosts the probability of the target element, making it more prominent. While the foundational concepts of Grover’s algorithm are well-documented, practical implementation using quantum operators, especially for large search spaces, remains less explored beyond basic examples with a small number of qubits. Existing general synthesis techniques often involve numerous operators or are time-consuming. Our proposed methods specifically address the amplitude-amplification component of Grover’s algorithm for any size of search space. These methods detail the required types and quantities of qubits and operators, emphasizing minimal usage and efficient assembly. Developed and evaluated in Python, our methods consistently identified target elements with over 95% accuracy and achieved configurations comparably compact as those in the existing literature but at a faster pace. We anticipate that these methods facilitate practical implementations of Grover’s algorithm across various domains.
The K-SAT problem is a fundamental challenge in computational theory, widely used in artificial intelligence, cryptography, and optimization. Classical algorithms struggle with exponential time complexity, making them inefficient for large-scale instances. In this research, we propose an efficient quantum computing approach based on Grover’s algorithm to enhance the search process for satisfiable solutions in K-SAT problems. Our implementation leverages quantum superposition and amplitude amplification to explore multiple possible solutions simultaneously, reducing the search complexity from O (2ⁿ) in classical methods to O(√2ⁿ) in quantum computing. We design a quantum oracle that encodes the K-SAT clauses and integrates it into Grover’s iterative search framework. The performance is evaluated through Qiskit simulations, demonstrating a significant improvement in search efficiency compared to classical brute-force techniques. The results highlight the potential of quantum algorithms in solving complex combinatorial problems with enhanced speed and accuracy. This study contributes to the development of quantum-accelerated optimization methods, paving the way for real-world applications in machine learning, cryptanalysis, and large-scale data processing.
Grover's search algorithm is one of the most significant quantum algorithms, which can obtain quadratic speedup of the extensive search problems. Since Grover's search algorithm cannot be implemented on a real quantum computer at present, its quantum simulation is regarded as an effective method to study the search performance. When simulating the Grover's algorithm, the storage space required is exponential, which makes it difficult to simulate the high-qubit Grover's algorithm. To this end, we deeply study the storage problem of probability amplitude, which is the core of the Grover simulation algorithm. We propose a novel memory-efficient method via amplitudes compression, and validate the effectiveness of the method by theoretical analysis and simulation experimentation. The results demonstrate that our compressed simulation search algorithm can help to save nearly 87.5% of the storage space than the uncompressed one. Thus under the same hardware conditions, our method can dramatically reduce the required computing nodes, and at the same time, it can simulate at least 3 qubits more than the uncompressed one. Particularly, our memory-efficient simulation method can also be used to simulate other quantum algorithms to effectively reduce the storage costs required in simulation.