Pulse engineering via projection of response functions at infinite nonlinear order

Optimal control in quantum computing is often hindered by complex, high-dimensional landscapes and the need for extensive hyperparameter tuning. The authors seek to develop a more efficient, gradient-free optimization method that can reliably generate high-fidelity control protocols for multi-qubit systems, such as the Quantum Fourier Transform (QFT).

The authors introduce Pulse Engineering via Projection of response functions at infinite nonlinear order (PEPRino). This method extends linear response theory by evaluating the system's response to time-local perturbations at infinite order. By leveraging the algebraic properties of Pauli operators, the authors show that the infinite series of susceptibilities can be resummed into a closed-form expression involving only the first and second-order response functions. This allows for an analytical determination of the optimal parameter update step without requiring a learning rate or other hyperparameters. The method is benchmarked against the Chopped Random Basis (CRAB) algorithm using the Nelder-Mead method for 2-qubit and 3-qubit QFT implementations.

PEPRino demonstrates faster convergence in both iteration steps and computational time compared to the CRAB algorithm. By avoiding the need for hyperparameter tuning, the algorithm simplifies the control process and remains robust across different system sizes. The authors show that while increasing the number of modes in the pulse parameterization improves convergence speed, the method maintains high performance across various configurations. The results suggest that PEPRino is a scalable and user-friendly alternative to traditional gradient-free optimization techniques in quantum control.

As quantum systems scale, the computational cost of optimizing gate operations becomes a significant bottleneck. By removing the reliance on hyperparameter tuning and providing a more direct path to high-fidelity control, PEPRino offers a more efficient tool for experimentalists and researchers working on NISQ devices and beyond, potentially accelerating the development of robust quantum algorithms.