Development of Neural Network-Based Optimal Control Pulse Generator for Quantum Logic Gates Using the GRAPE Algorithm in NMR Quantum Computer

In this paper, we introduce a neural network to generate optimal control pulses for general single-qubit quantum logic gates, within a Nuclear Magnetic Resonance (NMR) quantum computer. By utilizing a neural network, we can efficiently implement any single-qubit quantum logic gates within a reasonable time scale. The network is trained by control pulses generated by the GRAPE algorithm, all starting from the same initial point. After implementing the network, we tested it using numerical simulations. Also, we present the results of applying Neural Network-generated pulses to a three-qubit benchtop NMR system and compare them with simulation outcomes. These numerical and experimental results showcase the precision of the Neural Network-generated pulses in executing the desired dynamics. Ultimately, by developing the neural network using the GRAPE algorithm, we discover the function that maps any single-qubit gate to its corresponding pulse shape. This model enables the real-time generation of arbitrary single-qubit pulses. When combined with the GRAPE-generated pulse for the CNOT gate, it creates a comprehensive and effective set of universal gates. This set can efficiently implement any algorithm in noisy intermediate-scale quantum computers (NISQ era), thereby enhancing the capabilities of quantum optimal control in this domain. Additionally, this approach can be extended to other quantum computer platforms with similar Hamiltonians.