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.
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.
The rapid growth of data-intensive applications and cloud computing has significantly increased the energy consumption of modern computing infrastructures, particularly data centers, raising critical sustainability and environmental concerns. Green computing seeks to address these challenges by improving energy efficiency and reducing carbon footprints without sacrificing performance. Quantum computing has emerged as a promising paradigm due to its ability to exploit quantum mechanical principles such as superposition and entanglement to achieve computational speedups beyond classical limits. This paper examines the role of quantum computing in advancing green computing technologies by analyzing its algorithmic capabilities, application domains, and hardware-related energy implications. Key quantum algorithms, including Shor’s algorithm, Grover’s search, the Quantum Approximate Optimization Algorithm (QAOA), and quantum simulation methods, are reviewed with respect to their potential to reduce execution time and energy consumption for computationally intensive tasks such as cryptography, optimization, and system modeling. The study further explores sustainability-oriented applications, including energy systems optimization, materials discovery for renewable technologies, and quantum machine learning for resource forecasting and management. Comparative analysis indicates that quantum approaches may offer substantial energy-efficiency advantages over classical methods as hardware matures. However, significant challenges remain, including qubit decoherence, error correction overhead, cryogenic cooling requirements, and scalability limitations. The paper concludes that continued advances in hybrid quantum–classical architectures and fault-tolerant hardware are essential for realizing quantum computing’s potential contribution to sustainable and energy-efficient computing.
Quantum algorithms offer substantial advantages for selected computational tasks, but asymptotic speedup alone does not determine engineering utility. This article examines classical and quantum algorithms through a complexity-theoretic lens, compares integer factorisation and unstructured search as representative cases, and derives a structured framework for evaluating engineering feasibility. Shor's algorithm achieves polynomial-time factorisation over the best known classical methods, and Grover's algorithm achieves a quadratic reduction in query complexity for unstructured search. Both results depend on theoretical models with idealised noise, coherence, and oracle assumptions. A realistic engineering assessment requires accounting for complete workflow cost, noise constraints, hardware overhead, and application-specific requirements. The framework developed here provides a structured reporting checklist intended to support rigorous comparisons in applied science and engineering contexts.
The advent of large-scale quantum computers poses an existential threat to the cryptographic algorithms that underpin modern digital security. Shor's algorithm enables quantum computers to factor large integers and compute discrete logarithms in polynomial time, rendering RSA, Elliptic Curve Cryptography (ECC), and Diffie-Hellman key exchange fundamentally insecure. Meanwhile, Grover's algorithm provides a quadratic speedup for brute-force search, effectively halving the security strength of symmetric ciphers and hash functions. This paper presents a comprehensive investigation into the impact of quantum computing on both asymmetric and symmetric cryptographic algorithms. We analyze the computational resources required by quantum attacks on current standards, evaluate the timeline of quantum threats based on hardware roadmaps from leading quantum computing companies, and conduct a systematic performance comparison of NIST-standardized post-quantum cryptographic (PQC) algorithms. Our experimental evaluation covers key generation time, encapsulation/decapsulation latency, signature generation/verification speed, key sizes, and bandwidth overhead across lattice-based, code-based, hash-based, and multivariate cryptographic schemes. Results indicate that lattice-based schemes, particularly CRYSTALS-Kyber and CRYSTALS-Dilithium, offer the most favorable balance of security and performance for practical deployment. We also propose a phased migration framework for transitioning existing cryptographic infrastructure to quantum-resistant alternatives, addressing compatibility, performance, and operational challenges.
The power of quantum mechanics, that is too complex for conventional computers, can be solved by an innovative model of computing known as quantum computing. Quantum algorithms can provide exponential speedups for some types of problems, such as many difficult mathematical ones. In this paper, we review some of the most important quantum algorithms for hard mathematical problems. When factoring large numbers, Shor's algorithm is orders of magnitude faster than any other known classical algorithm. The Grover's algorithm, which searches unsorted databases much more quickly than conventional algorithms, is then discussed.
Quantum computing offers transformative computational power by harnessing phenomena such as superposition and entanglement. Yet, this potential simultaneously poses severe risks to classical cryptographic systems. In this paper, we explore how quantum algorithms, most notably Shor’s algorithm for integer factorization and Grover’s algorithm for unstructured search, could break widely deployed cryptographic schemes. We present a rigorous mathematical analysis of these quantum algorithms, compare their complexity with classical methods, and examine their impact on public-key and symmetric cryptography. Finally, we discuss potential countermeasures, including post-quantum cryptographic solutions, to safeguard data in the quantum era.
For decades, classical computers have been governed by predictable rules. But as we approach the physical limits of computation, a new paradigm is emerging. Quantum computing operates on the strange and powerful laws of quantum mechanics—superposition, entanglement, and interference—to tackle problems far beyond the reach of any classical machine. The true potential of this field was unlocked by two landmark discoveries: Shor’s algorithm, a revolutionary method for integer factorization that threatens to upend modern cryptography, and Grover’s algorithm, a versatile tool that offers a quadratic speedup for unstructured search problems. This paper serves as a guide to these foundational algorithms, detailing their inner workings and their profound impact. We also explore post-quantum cryptography, hybrid frameworks, and quantum machine learning—illustrating the evolving role of quantum algorithms in shaping the future of science and technology.