Recent advances in quantum computing systems attract tremendous attention. Commercial companies, such as IBM, Amazon, and IonQ, have started to provide access to noisy intermediate-scale quantum computers. Researchers and entrepreneurs attempt to deploy their applications that aim to achieve a quantum speedup. Grover’s algorithm and quantum phase estimation are the foundations of many applications with the potential for such a speedup. While these algorithms, in theory, obtain marvelous performance, deploying them on existing quantum devices is a challenging task. For example, quantum phase estimation requires extra qubits and a large number of controlled operations, which are impractical due to low-qubit and noisy hardware. To fully utilize the limited onboard qubits, we develop a distributed application with a key-value data structure based on Grover’s algorithm called IQuCS . Consider a database with duplicates. By encoding each element to a binary type with a unique key and forming a key-value pair, we can count the number of occurrences of each element in the database based on quantum computing. We have optimized the operation process by filtering data points to make it more efficient. To determine the effect of this optimization, we evaluate it with datasets of different sizes and with different numbers of duplicates. With the assistance of classical computers, IQuCS can reduce the problem set for each query. Due to this reduction, IQuCS requires fewer qubits. Through the iterative management, IQuCS achieves a reduction of qubit virtualized consumption, up to 66.2%, with reasonable accuracy.
Recent advances in quantum computing systems attract tremendous attention. Commercial companies, such as IBM, Amazon, and IonQ, have started to provide access to noisy intermediate-scale quantum computers. Researchers and entrepreneurs attempt to deploy their applications that aim to achieve a quantum speedup. Grover’s algorithm and quantum phase estimation are the foundations of many applications with the potential for such a speedup. While these algorithms, in theory, obtain marvelous performance, deploying them on existing quantum devices is a challenging task. For example, quantum phase estimation requires extra qubits and a large number of controlled operations, which are impractical due to low-qubit and noisy hardware. To fully utilize the limited onboard qubits, we develop a distributed application with a key-value data structure based on Grover’s algorithm called IQuCS . Consider a database with duplicates. By encoding each element to a binary type with a unique key and forming a key-value pair, we can count the number of occurrences of each element in the database based on quantum computing. We have optimized the operation process by filtering data points to make it more efficient. To determine the effect of this optimization, we evaluate it with datasets of different sizes and with different numbers of duplicates. With the assistance of classical computers, IQuCS can reduce the problem set for each query. Due to this reduction, IQuCS requires fewer qubits. Through the iterative management, IQuCS achieves a reduction of qubit virtualized consumption, up to 66.2%, with reasonable accuracy.
Recent advances in quantum computing systems attract tremendous attention. Commercial companies, such as IBM, Amazon, and IonQ, have started to provide access to noisy intermediate-scale quantum computers. Researchers and entrepreneurs attempt to deploy their applications that aim to achieve a quantum speedup. Grover’s algorithm and quantum phase estimation are the foundations of many applications with the potential for such a speedup. While these algorithms, in theory, obtain marvelous performance, deploying them on existing quantum devices is a challenging task. For example, quantum phase estimation requires extra qubits and a large number of controlled operations, which are impractical due to low-qubit and noisy hardware. To fully utilize the limited onboard qubits, we propose IQuCS, which aims at index searching and counting in a quantum-classical hybrid system. IQuCS is based on Grover’s algorithm. From the problem size perspective, it analyzes results and tries to filter out unlikely data points iteratively. A reduced data set is fed to the quantum computer in the next iteration. With a reduction in the problem size, IQuCS requires fewer qubits iteratively, which provides the potential for a shared computing environment. We implement IQuCS with Qiskit and conduct intensive experiments. The results demonstrate that it reduces qubits consumption by up to 66.2%.
Over the past decade, the rapid advancement of deep learning and big data applications has been driven by vast datasets and high-performance computing systems. However, as we approach the physical limits of semiconductor fabrication in the post-Moore's Law era, questions arise about the future of these applications. In parallel, quantum computing has made significant progress with the potential to break limits. Major companies like IBM, Google, and Microsoft provide access to noisy intermediate-scale quantum (NISQ) computers. Despite the theoretical promise of Shor's and Grover's algorithms, practical implementation on current quantum devices faces challenges, such as demanding additional resources and a high number of controlled operations. To tackle these challenges and optimize the utilization of limited onboard qubits, we introduce ReSaQuS, a resource-efficient index-value searching system within a quantum-classical hybrid framework. Building on Grover's algorithm, ReSaQuS employs an automatically managed iterative search approach. This method analyzes problem size, filters fewer probable data points, and progressively reduces the dataset with decreasing qubit requirements. Implemented using Qiskit and evaluated through extensive experiments, ReSaQuS has demonstrated a substantial reduction, up to 86.36\% in cumulative qubit consumption and 72.72\% in active periods, reinforcing its potential in optimizing quantum computing application deployment.
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.
Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grover's search algorithm finds the target element in an unsorted database with quadratic speedup than classical search and has been proved to be optimal in terms of the number of queries to the database. The challenge, however, is that Grover's search algorithm leads to high numbers of quantum gates, which make it infeasible for the Noise-Intermediate-Scale-Quantum (NISQ) computers. In this paper, we propose a novel hardware efficient quantum search algorithm to overcome this challenge. Our key idea is to replace the global diffusion operation with low-cost local diffusions. Our analysis shows that our algorithm has similar oracle complexity to the original Grover's search algorithm while significantly reduces the circuit depth and gate count. The circuit cost reduction leads to a remarkable improvement in the system success rates, paving the way for quantum search on NISQ machines.
Quantum search is one of the most important algorithmic developments in quantum computing because it demonstrates how quantum principles can improve the efficiency of solving unstructured search problems. Grover’s algorithm provides a quadratic speed-up over classical linear search by reducing query complexity from O(N) to O(√N), where N represents the size of the search space. This review examines the principles, performance, and applications of Grover’s algorithm, with emphasis on its theoretical foundation and practical relevance. The discussion covers the roles of superposition, quantum interference, oracle operations, diffusion operators, and amplitude amplification in increasing the probability of measuring a desired solution. The manuscript also reviews the computational performance of quantum search in comparison with classical search methods and considers its relevance to database searching, combinatorial optimisation, cryptography, machine learning, bioinformatics, quantum chemistry, and materials science. The review highlights that Grover’s algorithm is not limited to database retrieval, as many computationally intensive problems can be reformulated as search or optimisation tasks. However, practical implementation remains constrained by current quantum hardware limitations, including decoherence, quantum noise, limited qubit availability, circuit depth, and the difficulty of designing efficient oracles. Despite these challenges, continuing progress in quantum hardware, error correction, cloud-based quantum platforms, and hybrid quantum-classical architectures suggests that quantum search will remain an important area of research. Overall, Grover’s algorithm represents a foundational quantum algorithm with significant theoretical value and potential long-term application in computational domains involving large and unstructured search spaces.
Grover's algorithm stands as a cornerstone of quantum computing, offering a theoretical quadratic speedup for unstructured search problems. This allows for finding a target item in an unsorted database of N entries in approximately the square root of N steps, a significant improvement over classical algorithms which require a number of operations on the order of N in the worst case. This speedup becomes particularly compelling for very large datasets, where classical exhaustive search becomes computationally intractable. The algorithm achieves this by leveraging fundamental quantum mechanical principles, primarily superposition and interference. It operates by preparing qubits in a uniform superposition of all possible states, then iteratively applying a quantum oracle to mark the desired state by flipping its phase, followed by a diffusion operator that amplifies the probability of the marked state. Despite its theoretical promise, real-world implementation faces substantial challenges stemming from Noisy Intermediate-Scale Quantum (NISQ) hardware, which is characterized by high error rates and short coherence times. Consequently, achieving a true, scalable quantum advantage remains a future endeavor, contingent on significant hardware advancements. Nevertheless, Grover's algorithm holds significant potential across diverse fields, including enhancing brute-force attacks on cryptographic systems, accelerating solutions for optimization problems, and speeding up search processes in machine learning and unstructured database queries.