Grover's algorithm is one of the most significant quantum algorithms, enabling the search for a marked element in an unsorted database quadratically faster than classical search algorithms. We utilize Groves's algorithm to detect the edges of a digital image faster than any classical edge detection methods. The high success probability of our method in detecting image edges, compared to most existing quantum edge detection methods, makes it a more suitable candidate for use in the presence of noise on current quantum devices. We implemented our model for the $2\times 2$ blocks of the image using a two-qubit Qiskit circuit with the QASM simulator and the noisy IBM Sydney(fake) device, making it suitable for most of the current NISQ devices.
Journal reference
2025 IEEE International Conference on Quantum Computing and Engineering(QCE)
Grover's algorithm is one of the most significant quantum algorithms, enabling the search for a marked element in an unsorted database quadratically faster than classical search algorithms. We utilize Groves's algorithm to detect the edges of a digital image faster than any classical edge detection methods. The high success probability of our method in detecting image edges, compared to most existing quantum edge detection methods, makes it a more suitable candidate for use in the presence of noise on current quantum devices. We implemented our model for the 2×2 blocks of the image using a two-qubit Qiskit circuit with the QASM simulator and the noisy IBM Sydney(fake) device, making it suitable for most of the current NISQ devices.
Quantum computing offers the potential to enhance computational efficiency beyond classical methods, but practical implementation remains challenging due to the limitations of Noisy Intermediate-Scale Quantum (NISQ) hardware, namely, restricted qubit counts, limited connectivity, and the presence of noise and decoherence. This study presents a novel approach to edge detection by leveraging a recently developed Quantum Fuzzy Inference Engine, implemented on a NISQ device. We introduce an optimized quantum circuit for its implementation, reducing qubit requirements and gate depth to improve execution on NISQ hardware. To overcome constraints related to large-scale image processing, a hybrid quantum–classical lookup table approach is employed. Edge detection performance is evaluated on the Berkeley Segmentation Data Set and Benchmarks 500 dataset under different conditions, including classical execution, ideal quantum simulation, noisy quantum simulation, and NISQ hardware calculation. Results demonstrate that the quantum fuzzy logic-based edge detection achieves outcomes comparable to classical methods by using fewer operations, marking a step toward practical quantum-enhanced image processing.
Quantum computing represents the leading edge of computational technology, leveraging the principles of quantum mechanics to execute targeted computations much faster than classical computers. In contrast to classical bits, which are limited to representing either 0 or 1, qubits, or quantum bits, exhibit the extraordinary property of superposition. This distinctive characteristic enables qubits to simultaneously occupy multiple states, empowering quantum computers to explore numerous potential solutions to a problem concurrently. This feature makes quantum computing particularly potent for specific tasks. Recent research endeavors have been sparked by the potential of advanced quantum computing technology, leading to the creation of simulations of quantum computers using classical hardware. Grover's quantum search algorithm serves as a notable illustration of quantum computing application, enabling quantum computers to conduct a database search within an unsorted array with a quadratic speedup in time efficiency compared to classical computers. This document presents the quantum Grover search algorithm and its application through 5-qubit quantum circuits, as well as a design framework to simplify the creation of an oracle for a greater number of qubits.
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.
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.
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 computing is a quickly growing field of research thanks to recent hardware advances. The quantum mechanical properties of quantum computers allow them to solve certain families of problems faster than classical computers. A quantum algorithm solving such a problem is Grover's algorithm, which finds an element in an unordered set faster than any classical search algorithm. In this paper an implementation of a 4-qubit Grover's algorithm for the IBM Q computer ibmqx5 is presented. Executing the implementation on an ibmqx5 simulator yield results in line with the theoretically optimal results. The accuracy of the ibmqx5 simulation results compared to the ibmqx5 execution results suggests that current hardware is not yet suitable,due to required complexity of the circuits for a 4-qubit Grover implementation.