Implementation and Performance Evaluation of Quantum Computing Based on Practical Experiments

In recent years, the technology of quantum computing has been continuously improving, with organizations such as IBM, Google, and NASA establishing quantum computers and applying them in fields like artificial intelligence. However, while quantum computing currently may still be limited by factors such as measurement techniques, which can lead to significant errors, this study designs three core quantum circuits and provides theoretical proofs that these core quantum circuits are equivalent. Furthermore, these core quantum circuits are applied to matrix transposition calculations, and the computation time and accuracy required for each core quantum circuit are evaluated based on the truth values. In the experimental setup, this study implements the research using the IBM Quantum Platform, conducting empirical tests in an environment with up to 127 qubits to explore computation time and accuracy when calculating matrices of different sizes.