# Gradient-based optimal control of open quantum systems using quantum trajectories and automatic differentiation

## TL;DR

This paper introduces a gradient-based optimal control method for open quantum systems that uses quantum trajectories and automatic differentiation, significantly reducing computational costs and enabling complex multi-target optimizations.

## Contribution

The paper presents a novel, efficient optimization technique combining quantum trajectories with automatic differentiation for open quantum systems, improving scalability and flexibility.

## Key findings

- Reduces computational complexity compared to density matrix methods.
- Achieves high fidelity state transfer despite dissipation.
- Optimizes multiple targets like gate speed and measurement fidelity.

## Abstract

We present a gradient-based optimal-control technique for open quantum systems that utilizes quantum trajectories to simulate the quantum dynamics during optimization. Using trajectories allows for optimizing open systems with less computational cost than the regular density matrix approaches in most realistic optimization problems. We introduce an improved-sampling algorithm which minimizes the number of trajectories needed per optimization iteration. Together with employing stochastic gradient descent techniques, this reduces the complexity of optimizing many realistic open quantum systems to the complexity encountered with closed systems. Our optimizer harnesses automatic differentiation to provide flexibility in optimization and to suit the different constraints and diverse parameter regimes of real-life experiments. We utilize the optimizer in a variety of applications to demonstrate how the use of quantum trajectories significantly reduces the computation complexity while achieving a multitude of simultaneous optimization targets. Demonstrated targets include high state-transfer fidelities despite dissipation, faster gate times and maximization of qubit-readout fidelity while maintaining the quantum non-demolition nature of the measurement and allowing for subsequent fast resonator reset.