Many existing static analysis algorithms suffer from cubic bottlenecks because of the need to compute a dynamic transitive closure (DTC). For the first time, this article studies the quantum speedups on searching subtasks in DTC-based static analysis algorithms using quantum search (e.g., Grover’s algorithm). We first introduce our oracle implementation in Grover’s algorithm for DTC-based static analysis and illustrate our quantum search subroutine. Then, we take two typical DTC-based analysis algorithms: context-free-language reachability and set constraint-based analysis, and show that our quantum approach can reduce the time complexity of these two algorithms to truly subcubic ( \(O(N^2\sqrt {N}{\it polylog}(N))\) ), yielding better results than the upper bound ( O ( N 3 /log N )) of existing classical algorithms. Finally, we conducted a classical simulation of Grover’s search to validate our theoretical approach, due to the current quantum hardware limitation of lacking a practical, large-scale, noise-free quantum machine. We evaluated the correctness and efficiency of our approach using IBM Qiskit on nine open-source projects and randomly generated edge-labeled graphs/constraints. The results demonstrate the effectiveness of our approach and shed light on the promising direction of applying quantum algorithms to address the general challenges in static analysis.
Many existing static analysis algorithms suffer from cubic bottlenecks because of the need to compute a dynamic transitive closure (DTC). For the first time, this article studies the quantum speedups on searching subtasks in DTC-based static analysis algorithms using quantum search (e.g., Grover’s algorithm). We first introduce our oracle implementation in Grover’s algorithm for DTC-based static analysis and illustrate our quantum search subroutine. Then, we take two typical DTC-based analysis algorithms: context-free-language reachability and set constraint-based analysis, and show that our quantum approach can reduce the time complexity of these two algorithms to truly subcubic ( (O(N^2\sqrt {N}{\it polylog}(N))) ), yielding better results than the upper bound ( O ( N 3 /log N )) of existing classical algorithms. Finally, we conducted a classical simulation of Grover’s search to validate our theoretical approach, due to the current quantum hardware limitation of lacking a practical, large-scale, noise-free quantum machine. We evaluated the correctness and efficiency of our approach using IBM Qiskit on nine open-source projects and randomly generated edge-labeled graphs/constraints. The results demonstrate the effectiveness of our approach and shed light on the promising direction of applying quantum algorithms to address the general challenges in static analysis.
Abstract Quantum computing can solve some classes of problems faster than classical computing. Among the greatest quantum algorithms to showcase this benefit is Grover's search algorithm, which has a quadratic speed-up for unstructured search problems. In this study, we present an implementation of Grover’s algorithm on a large-scale dataset comprising approximately 131,072 (217) names. We contrast its efficiency with the classical linear search based on time complexity, scalability, and the likelihood of success. The experiment was conducted using Qiskit on a quantum simulator, where several query scenarios were implemented to verify the algorithm's efficiency and accuracy. Our findings highlight the theoretical advantage of Grover’s algorithm in situations involving large data sets, while also discussing real-world limitations such as gate noise, qubit number, and circuit depth as we move towards actual quantum hardware. This study serves as a step toward evaluating the real-world relevance of quantum search algorithms and provides information on current challenges and future directions in quantum information retrieval.
Quantum computing is on the cusp of transforming the way we tackle complex problems, and the Grover search algorithm exemplifying its potential to revolutionize the search for unstructured large datasets, offering remarkable speedups over classical methods. Here, we report results for the implementation and characterization of a three-qubit Grover search algorithm using the state-of-the-art scalable quantum computing technology of superconducting quantum architectures. To delve into the algorithm's scalability and performance metrics, our investigation spans the execution of the algorithm across all eight conceivable single-result oracles, alongside nine two-result oracles, employing IBM Quantum's 127-qubit quantum computers. Moreover, we conduct five quantum state tomography experiments to precisely gauge the behavior and efficiency of our implemented algorithm under diverse conditions - ranging from noisy, noise-free environments to the complexities of real-world quantum hardware. By connecting theoretical concepts with real-world experiments, this study not only shed light on the potential of Noisy Intermediate-Scale Quantum Computers in facilitating large-scale database searches but also offer valuable insights into the practical application of the Grover search algorithm in real-world quantum computing applications.
Background: The future computations need parallelism, and a way to achieve the same is through quantum-based specific properties. Quantum computation supports exponential operation to be performed in parallel over a single execution step and hence achieves computational speedup. Objective: One of the quantum-based algorithms allows to search the key element over an index based unstructured database and succeeds to obtain the speedup. In the whole context of article writing, our approach reviews the significance of quantum computing, the basics required for quantum computation and their quantum logic-based circuit operations. Method: The article focuses on Grover’s search algorithm and its variations, and then illustrates the relevant amplitude amplification & phase matching techniques in accordance with the advantages and limitation to the specific perspective. Results: We made the comparative analysis between the amplitude amplification-based static & dynamic Grover’s searching and phase estimation technique. Along with this, we justified the possibilities of the empirical results and observed facts over Grover’s variant approaches. Conclusion: Finally, we conclude the analytical comparison between quantum-based searching techniques along with the applicability of Grover’s algorithm in practical computational science.
Grover’s algorithm is one of the primary algorithms offered as evidence that quantum computers can provide an advantage over classical computers. It involves an “oracle” (external quantum subroutine), which must be specified for a given application and whose internal structure is not part of the formal scaling of the quadratic quantum speedup guaranteed by the algorithm. Grover’s algorithm also requires exponentially many calls to the quantum oracle (approximately 2 n calls where n is the number of qubits) to succeed, raising the question of its implementation on both noisy and error-corrected quantum computers. In this work, we construct a quantum-inspired algorithm executable on a classical computer that performs Grover’s task in a linear number of calls to (simulations of) the oracle—an exponentially smaller number than Grover’s algorithm—and demonstrate this algorithm explicitly for Boolean satisfiability problems. The complexity of our algorithm depends on the cost to simulate the oracle once, which may or may not be exponential, depending on its internal structure. Indeed, Grover’s algorithm does not have an quantum speedup as soon as one is given access to the “source code” of the oracle, which may reveal an internal structure of the problem. Our findings illustrate this point explicitly, as our algorithm exploits the structure of the quantum circuit used to program the quantum computer to speed up the search. There are still problems where Grover’s algorithm would provide an asymptotic speedup if it could be run accurately for large enough sizes. Our quantum-inspired algorithm provides lower bounds, in terms of the quantum-circuit complexity, for the quantum hardware to beat classical approaches for these problems. These estimates, combined with the unfavorable scaling of the success probability of Grover’s algorithm, which in the presence of noise decays as the exponential of the exponential of the number of qubits, makes a practical speedup unrealistic even under extremely optimistic assumptions of the evolution of both hardware quality and availability. Published by the American Physical Society 2024
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 quantum search algorithm provides a proven quadratic speedup over classical linear search for unstructured databases. While its theoretical advantage is well established, experimental validation on real noisy intermediate-scale quantum (NISQ) hardware remains limited by noise, decoherence, and hardware constraints. In this work, we present an experimental comparison between classical linear search and Grover's quantum search algorithm executed on IBM Quantum real superconducting hardware using Qiskit Runtime. A four-qubit implementation corresponding to a 16-element search space is evaluated across multiple experimental runs. The results demonstrate consistent amplitude amplification, achieving an average success probability of 54.25% and an amplification factor of 8.68× over random guessing. Although classical execution remains faster in wall-clock time due to quantum hardware overhead, the experiment empirically validates the algorithmic advantage of Grover's search and quantifies the performance gap between ideal and real quantum processors in the NISQ era.