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Quantum computing is a growing field with the potential to revolutionize computation. This thesis explores the foundations of quantum computing with specific focus on the efficacy of the Quantum Fourier Transform (QFT). The fundamentals of quantum computing were described through an explanation of quantum mechanics and the mathematics needed to understand the quantum computing model and its operations. Using IBM’s simulators and quantum processors, the QFT was implemented on a classical data set, and the results were compared to the predicted output values. It was found that the QFT simulator was able to produce results consistent with Discrete Fourier Transform, which affirmed its potential to be a successful method of extracting frequencies from a set of data in the time domain. The quantum processors were able to produce results with small percent error for small qubit systems, but increased in error as the number of qubits within the system grew. Despite this, with the appropriate error correction methods, it was concluded that the QFT is a functional method for transforming a state from the time domain to the frequency domain.
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Dziubelski, Natalia, "Theoretical Foundations of Quantum Computing and the Implementation of the Quantum Fourier Transform" (2023). Senior Projects Spring 2023. 208.
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