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%.
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%.
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.
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 search is a renowned quantum search algorithm that leverages quantum superposition to find a marked item with quadratic speedup. However, when implemented on Noisy Intermediate-scale Quantum (NISQ) hardware, the required repeated iterations of the oracle and diffusion operators increase exponentially with the number of qubits, resulting in significant noise accumulation. To address this, we propose a hybrid quantum-classical architecture that replaces quantum iterations with updates from a classical optimizer. This optimizer minimizes the expectation value of an oracle Hamiltonian with respect to a parameterized quantum state representing the target bit string. Our parameterized quantum circuit is much shallower than Grover search circuit, and we found that it outperforms Grover search on noisy simulators and NISQ hardware. When the number of qubits is greater than 5, our approach still maintains usable success probability, while the success probability of Grover search is at the same level as random guessing.
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.
State-of-the-art noisy intermediate-scale quantum devices (NISQ), although imperfect, enable computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, present quantum computations are restricted to exploring specific simplified protocols, whereas the implementation of full-scale quantum algorithms aimed at solving concrete large scale problems arising in data analysis and numerical modelling remains a challenge. Here we introduce and implement a hybrid quantum algorithm for solving linear systems of equations with exponential speedup, utilizing quantum phase estimation, one of the exemplary core protocols for quantum computing. We introduce theoretically classes of linear systems that are suitable for current generation quantum machines and solve experimentally a 217-dimensional problem on superconducting IBMQ devices, a record for linear system solution on quantum computers. The considered large-scale algorithm shows superiority over conventional solutions, demonstrates advantages of quantum data processing via phase estimation and holds high promise for meeting practically relevant challenges.
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.