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Quantum Information Processing

Impact of hardware connectivity on Grover’s algorithm in NISQ era

Mohit Joshi, Manoj Kumar Mishra, S. Karthikeyan

Published Apr 19, 2025• 2 citations
Publisher
DOI
10.1007/s11128-025-04733-6

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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.
The Noisy Intermediate-Scale Quantum (NISQ) era poses a challenge for developers: hardware providers expose capabilities through heterogeneous interfaces with proprietary metrics varying widely across providers, hindering informed backend selection. Static characterization metrics - coherence times T1/T2, gate error rates - exhibit limitations: they fail to capture dynamic variability across successive executions, overlook the impact of transpilation, and lack architectural comparability across physically distinct technologies. We propose a Figure of Merit (FoM) based on Grover's algorithm as an algorithmic stress test evaluating quantum backend performance holistically. The metric combines success probability on target states with penalties for non-uniform amplification and leakage to non-marked states, yielding a unified score across hardware architectures. Implemented via the Qonscious framework - a conditional execution platform using polymorphic adapters, it executes agnostically on IBM, IonQ backends, and simulators. Main contributions: (1) proposal and validation of GroverFigureOfMerit, incorporating uniformity and leakage penalties (adapted from GRADE) with emphasis on noise, transpilation, and topological constraints; (2) systematic analysis of heterogeneity across nine quantum providers motivating agnostic metrics; and (3) experimental demonstration via ideal simulators and real-processor noise models, confirming sensitivity to noise, topology, and transpilation overhead. Results confirm the metric distinguishes backend performance under a unified score, capturing intrinsic algorithmic limits. Validation on physical QPUs is identified as a natural next step.