QUANTUM COMPUTING CHALLENGES: EXPLORING DECOHERENCE THROUGH THE LENS OF SHOR'S ALGORITHM

Abstract

Quantum computing, with its transformative potential in solving complex problems, faces a critical challenge: coupling with the environment and the consequent decoherence of quantum systems. This article examines the state of the art on the subject, providing a theoretical basis for understanding how environmental interactions impact quantum algorithms. Quantum coherence, a fundamental element of quantum mechanics, allows quantum states to exist in superposition. However, interaction with the environment triggers decoherence, resulting in the loss of this coherence and affecting the accuracy of the results of quantum algorithms. The study investigates the mechanisms of environmental coupling, such as interactions with photons, fluctuations in magnetic fields, and other external factors. Additionally, the impact of decoherence on notable algorithms, such as Shor's algorithm, is explored, analyzing its implications for the efficiency in determining results. Contemporary mitigation strategies, including quantum error correction techniques applied to this algorithm, are also discussed. The results highlight that decoherence represents a significant obstacle to the practical application of quantum computing in scientific, organizational and social problems. In parallel, a promising set of tools to mitigate or avoid the effects of decoherence is being developed, advancing the viability of quantum computers as applicable technologies.