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

TL;DR

The paper tackles efficient, real-time generation of optimal control pulses for arbitrary single-qubit gates in an NMR quantum computer by training a neural network on GRAPE-optimized pulses started from a common initial point. The network receives the target gate $U$ (flattened as real and imaginary components of a $2\times2$ unitary) and outputs a phase-only pulse that implements the desired operation, achieving high fidelities $F>0.9$ for most of $15{,}000$ test cases and accelerating generation by roughly $3$ orders of magnitude compared with standard GRAPE. Numerical results are complemented by benchtop NMR experiments (1 T) validating the approach on a three-qubit system, with PPS tomography and spectral measurements showing close agreement to simulations despite open-system effects. The work advances quantum optimal control in the NISQ era by enabling near real-time synthesis of arbitrary single-qubit gates and sets the stage for extending to two-qubit gates and larger platforms.

Abstract

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.

Figures (14)

• Figure 1: The subspace of the GRAPE-generated pulse shapes when the algorithm starts from the same point. In each subspace, pulses are similar to one another and correspond to a common starting point.
• Figure 2: Cosine similarity analysis of 16 samples generated using the GRAPE algorithm for a specific logic gate, each with a different starting point.The horizontal (x) and vertical (y) axes represent the indices of sample pulses. Value of the similarity between the pulses x and y is shown on the x-y cells. The diagonal entries all equal 1, as the cosine similarity between a pulse and itself is always 1.
• Figure 3: Cosine similarity analysis of 17,000 samples generated using the GRAPE algorithm for the random logic gates, each with a same starting point.The horizontal (x) and vertical (y) axes represent the indices of sample pulses. Value of the similarity between the pulses x and y is shown on the x-y cells.
• Figure 4: The neural network receives a $U$ (2×2 unitary matrix), representing the gate to be applied to the target qubit (for example, qubit 1). It flattens and concatenates the real and imaginary components into a one-dimensional input array with 8 elements. The network then interprets the overall evolution as $U_1 \otimes I_2 \otimes I_3$ and generates the pulse required to implement the desired gate, which is transmitted to the output. Upon applying the pulse, the operator $U_f$ is executed on the system.
• Figure 5: Neural Network Architecture Overview. This diagram presents the structured flow of the neural network, beginning with the feature input and advancing through sequential layers that include fully connected layers, dropout modules, and activation functions (ReLU and Tanh). The final stage culminates in a regression output, illustrating how the network processes and transforms input data to generate predictions.