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International Conference on Next-Gen Quantum and Advanced Computing: Algorithms, Security, and Beyond (NQComp)

Performance Analysis of Grover’s Algorithm Under Noise: A Simulation-Driven Study with Error Mitigation and Hybrid Bloom–Grover Search

Souvik Ghosh, Amrita Kundu, Samya Muhuri

Published Mar 5, 2026• 0 citations
Publisher

Abstract

Classical database join operations are a significant performance bottleneck in data-intensive applications, typically requiring quadratic time proportional to the size of the input. Quantum search algorithms, such as Grover’s algorithm, promise asymptotic speedups for unstructured search and can be adapted to accelerate equality-based joins. In this paper, we present a systematic simulation study of a Grover-based quantum join primitive and a hybrid classical-quantum join scheme, comparing them with a baseline classical nested-loop join. Parameterised Grover circuits have been implemented for marked-item search, together with resource estimation (qubit count, circuit depth, and gate counts), using the Qiskit Aer simulator. The classical join is modelled as a nested-loop equality join over two arrays, while the hybrid scheme uses a classical Bloom filter to reduce the candidate space, followed by a Grover search over the remaining items. To approximate near term hardware, we incorporate depolarizing gate noise and readout noise via Aer noise models and investigate two mitigation techniques: readout error calibration and zero noise extrapolation. Our simulations, conducted in a Python environment without GPU acceleration, demonstrate that the Grover based and hybrid joins exhibit the expected sub-quadratic scaling in runtime compared to the classical nested-loop join for problem sizes up to N = 215. We additionally observe that realistic noise significantly degrades the raw success probability of the quantum join, while combining readout mitigation with zero noise extrapolation partially restores accuracy. These results provide a resource-aware and noise-aware baseline for evaluating quantum-accelerated joins on future fault-tolerant or high-fidelity noisy intermediate-scale quantum (NISQ) devices.

DOI
10.1109/nqcomp68334.2026.11497722

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Classical database join operations are a significant performance bottleneck in data-intensive applications, typically requiring quadratic time proportional to the size of the input. Quantum search algorithms, such as Grover’s algorithm, promise asymptotic speedups for unstructured search and can be adapted to accelerate equality-based joins. In this paper, we present a systematic simulation study of a Grover-based quantum join primitive and a hybrid classical-quantum join scheme, comparing them with a baseline classical nested-loop join. Parameterised Grover circuits have been implemented for marked-item search, together with resource estimation (qubit count, circuit depth, and gate counts), using the Qiskit Aer simulator. The classical join is modelled as a nested-loop equality join over two arrays, while the hybrid scheme uses a classical Bloom filter to reduce the candidate space, followed by a Grover search over the remaining items. To approximate near term hardware, we incorporate depolarizing gate noise and readout noise via Aer noise models and investigate two mitigation techniques: readout error calibration and zero noise extrapolation. Our simulations, conducted in a Python environment without GPU acceleration, demonstrate that the Grover based and hybrid joins exhibit the expected sub-quadratic scaling in runtime compared to the classical nested-loop join for problem sizes up to N = 215. We additionally observe that realistic noise significantly degrades the raw success probability of the quantum join, while combining readout mitigation with zero noise extrapolation partially restores accuracy. These results provide a resource-aware and noise-aware baseline for evaluating quantum-accelerated joins on future fault-tolerant or high-fidelity noisy intermediate-scale quantum (NISQ) devices.
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.
Target item searching in large-scale, unstructured text databases is a major computational task for traditional systems and usually requires algorithms whose time complexity is on the order ofO(N)O(N)O(N). Quantum computing presents a strong competitor by using Grover's algorithm, where theoretically the search complexity comes down toO(N)O(\sqrt{N})O(N​), making faster retrieval possible. This research considers the design and assessment of Grover's algorithm as it is used to find a target word in a paragraph. The process entails encoding a group of unique words into a quantum register and implementing a circuit that incorporates a bespoke oracle and a diffusion operator to amplify the probability amplitude of the target state. Performance was evaluated in two situations: an ideal noise-free simulation with Qiskit's AerSimulator and a real-world run on IBM's quantum hardware. Simulation results demonstrated always-high accuracy in identifying the target word. But tests on real quantum machines indicated that the reliability of the algorithm decreases with an increase in qubits. Though circuits of up to five qubits had tolerable accuracy, larger configurations were plagued by noise, gate errors, and decoherence effects. These results highlight both the potential of quantum search algorithms for text processing and the limitations of NISQ today.
Grover’s quantum search algorithm delivers quadratic speedup over classical counterparts for finding an item in unstructured database. But the accuracy of the algorithm degrades as the number of qubits are increased. Noises of various types affect the accuracy of the Grover’s algorithm. The imperfect measurement on the qubit results in measurement errors appears to be one of the factors which limit the scalability of near-term quantum devices/algorithms. This paper is focused on the implementation of measurement error mitigation technique on Grover’s algorithm up to 4-qubits. The measurement error mitigation model for Grover’s algorithm is developed and implemented on the real-time quantum computer. The accuracy of Grover’s algorithm up to 4-qubits with and without measurement errors is evaluated and compared. The results indicate that measurement error mitigation technique mitigates the measurement errors of the Grover’s algorithm and improves its accuracy.
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.
This experimental study introduces a hybrid quantum-classical framework aiming to improve the noise robustness of Shor’s algorithm. By incorporating a novel hybrid logic gate into the modular exponentiation phase, the framework stabilizes qubit interactions and decreases decoherence in a noisy environment simulated by IBM Qiskit. Performance evaluation is accomplished by fidelity and entropy analysis across varied noise levels. Comparative benchmarking with conventional techniques, including Shor’s code, Bacon-Shor code, dynamical decoupling, and zero noise extrapolation, demonstrates that the proposed hybrid gate achieves higher fidelity (0.90) and lower entropy (0.33), while preserving minimal resource overhead. These findings highlight the framework’s effectiveness as a hardware-independent, scalable solution for Noisy Intermediate-Scale Quantum (NISQ) devices. Instead, the study offers an approach toward a scalable, error-resilient model to avoid exaggerating scalability. Despite its promising outcomes, study is presently limited to simulations and a single noise model. Future work will explore implementation on real quantum hardware and extend the framework to incorporate a broader range of noise profiles, contributing to the evolution of fault-tolerant quantum computation.
In my project I would have considered how the old search algorithms that are used when working with large unstructured data set end up taking linear time (O(N)) that in effect is the time that scales with the size of the data. These old ways get gradually sluggish, as everything gets bigger. Then I read about quantum computing, and especially Search Algorithm that was developed by Grover which is capable of quadratic speed-up with a complexity of O(sqrt(N)) of unstructured data. I created a hybrid system which fuses classical and quantum search applied on Flask as the web front end and Qiskit as the quantum one. This will enable me to compare the simple linear algorithm of searching through the list item-by-item with the quantum algorithm of Grover which uses superposition, a marking oracle to identify the desired item, and multiple amplitude amplification diffusion operators. The web page also accepts a student ID, and actually searches both simultaneously and allows me to tweak a depolarizing noise model so as to more closely mimic real quantum hardware. I measured such variables as the number of calls to the oracle, the number of qubits that I require, the quantum run time, and the number of measurements that I receive out of the quantum measurement. As the results indicate, the algorithm developed by Grover reduces the number of operations significantly compared to the classical one, and it must be emphasized that the algorithm remains quite effective even in the case of simulated noise. On the whole, it demonstrates that the classical and quantum components may be an efficient method to deal with the large search in the database.