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

TL;DR

This paper introduces physics-informed neural networks (PINNs) tailored for quantum optimal control to design high-fidelity quantum gate pulses, demonstrating their effectiveness with Schrödinger and Lindblad equations.

Contribution

The paper develops and tests PINNs for quantum gate design, integrating quantum dynamics equations into neural network training for the first time.

Findings

PINNs successfully generate high-fidelity two-qubit gate pulses.

The approach is flexible across different quantum operations.

The model avoids vanishing and exploding gradients effectively.

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 Schr\"odinger 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 Schr\"odinger 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.