Physics-Informed Neural Networks for Gate Design using Quantum Optimal Control

TL;DR

This paper introduces physics-informed neural networks (PINNs) to tackle quantum optimal control for gate design, embedding quantum dynamics directly into the learning objective. It develops two PINN frameworks—a Schrödinger-based closed-system model and a Lindblad-based open-system model—to predict smooth, high-fidelity two-qubit gate pulses under noise. The authors demonstrate high gate fidelities (near 0.999) across multiple target gates and show that sinusoidal activation with variance-scaled initialization improves training and pulse quality, while open-system results reveal sensitivity to decoherence. They validate consistency with standard solvers and discuss future directions toward transferability and hardware-aware constraints, highlighting potential advantages over traditional methods like GRAPE and CRAB. The work suggests a path toward low-cost, flexible gate design that can adapt to different quantum architectures and noise environments.

Abstract

Implementing quantum gates on quantum computers can require the application of carefully shaped pulses for high-fidelity operations. We explore the use of physics-informed neural networks (PINNs) for quantum optimal control to assess their usefulness in predicting such pulses. Our PINN is a feedforward neural network that utilizes an unsupervised learning approach, whose loss function includes terms that enforce the equations that govern the evolution of a quantum system, measure how close the learned unitary is to the target unitary operation, and ensure state normalization. We use a sinusoidal activation function and adopt variance-type weight initialization, tailored to our activation function. By analyzing the model's performance with important machine learning metrics, we demonstrate that the choice of our architecture is well-suited for this type of problem. We ensure that our network avoids the vanishing and exploding gradients with our relevant choices. We build two different PINNs, one based on the Schrödinger equation and another one based on the Lindblad equation. Our PINNs are able to discover high-fidelity two-qubit gate pulses for a variety of quantum operations, demonstrating its flexibility and robustness. We build two different PINNs, one based on the Schrödinger equation and another one based on the Lindblad equation. Our PINNs are able to discover high-fidelity two-qubit gate pulses for a variety of quantum operations, demonstrating its flexibility and robustness.

Figures (6)

• Figure 1: PINN overview and Neural Network architecture.
• Figure 2: Visualization of activation distributions, gradient distributions, and activation spectrum across all the layers using the Schrödinger model trained with $U_{\mathrm{targ}} = \text{CNOT}$ and $\omega_0 = 1$, following the analysis of Ref. sitzmann2020implicit.
• Figure 3: Top: Different Activation Functions. Bottom: Fidelity vs Epochs for different activation functions for the Schrödinger model trained on $U_{CNOT}$.
• Figure 4: Control amplitudes for models trained with custom initialization for different $\omega_0$ vs a model trained with weight initialization using PyTorch’s default initialization for nn.Linear (first four graphs from the top). Maximum epochs were set to 4000. Decoherence rates influence on final gate fidelities (last graph).
• Figure 5: Training Loss for models trained on $U_{CNOT}$ Gate over 5000 epochs for runs of Schrödinger PINN and Lindblad PINN (with different rates of the collapse operators).