Quantum Circuit Optimization Techniques Using Iterative Pre-Conditioned Gradient Descent

This paper introduces new optimization techniques which are optimizing QFT(Qunatum Fourier Transformation) circuit, Momentum-Based Iterative Pre-Conditioned Gradient Descent and Nesterov Accelerated Momentum IPCGD to obtain faster and closer approximations in complex problems of optimization. Traditional algorithms, such as normal Gradient Descent, Adam, normal IPCGD (Iteratively Pre-Conditioned Gradient Descent), often suffer from slow progress, oscillations about the solution, and challenges in dealing with noise, especially in complicated or unstable regimes. These proposed techniques use momentum to smooth the updates and predict future steps to arrive at the desired solution in as many as 50 percent fewer iterations compared to standard methods. Experimentation has shown these methods to be outstanding for tasks like quantum circuit optimization with faster convergence and better accuracy. This research addresses some of the key challenges in optimization, improving both efficiency and stability, making it suitable for using in noisy and dynamic settings.