Schrödinger bridges to open quantum systems

Quantum systems are inherently stochastic.

At the quantum level, randomness is introduced not only through the act of measurement, but also due to the uncontrollable interaction with the surrounding environment.

Indeed, the precise manipulation of quantum dynamics presents a challenge for emerging quantum technologies, such as computing, simulation, and quantum sensing.

On the other hand, optimal transportation and Brownian/Schrödinger bridges are of central importance in applications requiring regulation and estimation of classical stochastic processes.

These include unsupervised machine learning, motion planning in robotics or protein docking and single-cell genomics in biology. In this project, we set out to extend these classical theories into the quantum domain. Specifically, we will develop original methods to regulate and estimate the dynamics of open quantum systems.

The research will lead to powerful optimization tools for state steering quantum control of noisy quantum dynamics, and will also provide novel insights into the thermodynamics of stochastic quantum processes.

Furthermore, the project will deliver new methods to characterize the dynamics of complex quantum systems that better fit experimental observations, thus making a groundbreaking contribution to the theory of open quantum systems.

Overall, this research will bridge the gap between mathematics and the next generation of quantum technologies, which will have broad implications, from quantum thermodynamics to quantum sensing or coherent control.