Optimizing Quantum Transformation Matrices: A Block Decomposition Approach for Efficient Gate Reduction

This paper introduces an algorithm designed to approximate quantum transformation matrix with a restricted number of gates by using the block decomposition technique. Addressing challenges posed by numerous gates in handling large qubit transformations, the algorithm provides a solution by optimizing gate usage while maintaining computational accuracy. Inspired by the Block Decompose algorithm, our approach processes transformation matrices in a block-wise manner, enabling users to specify the desired gate count for flexibility in resource allocation. Simulations validate the effectiveness of the algorithm in approximating transformations with significantly fewer gates, enhancing quantum computing efficiency for complex calculations.