A novel quantum circuit for the quantum Fourier transform

The Quantum Fourier Transform (QFT) is a fundamental component of many quantum computing algorithms. In this paper, we present an alternative method for factoring this transformation. Inspired by this approach, we introduce a new quantum circuit for implementing the QFT. We show that this circuit is more efficient than the conventional design. Furthermore, using this circuit, we develop alternative versions of the HHL algorithm and Shor's algorithm, which also demonstrate improved performance compared to their standard implementations.