A Comparative Analysis of Classical and Quantum Algorithms through the Environmental Impact Lens

Author(s)	Mr. Nemi Chirag Botadara
Country	India
Abstract	This paper evaluates eight computational algorithms across sorting, searching, and factoring tasks to analyze how their operation counts impact environmental sustainability. Classical algorithms (Bubble Sort, Insertion Sort, Merge Sort, Timsort, Quicksort, Linear Search) are compared against quantum algorithms (Grover's Search, Shor's Factoring) using algorithmic time complexity as a proxy for processing energy consumption. The analysis establishes a distinct efficiency hierarchy determined by problem scale and mathematical scaling behavior. For quadratic speedups like Grover's Search, a high problem-size threshold exists before quantum algorithms become more energy-efficient than classical alternatives. For exponential speedups like Shor's Algorithm, the quantum framework crosses this threshold almost immediately due to the impossibly large operation counts required by classical alternatives at cryptographic scales. These findings demonstrate that achieving sustainable quantum computing requires targeted deployment at exponential problem domains.
Keywords	Quantum Computing, Grover's Algorithm, Shor's Algorithm, Classical Algorithms, Environmental Sustainability, Energy Efficiency, Algorithmic Complexity, NISQ
Field	Computer
Published In	Volume 8, Issue 3, May-June 2026
Published On	2026-06-13
DOI	https://doi.org/10.36948/ijfmr.2026.v08i03.81384

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