Optimisation of non-Markovian systems using tensor networks

Abstract

Structured environments that do not admit simple time-local descriptions display a wealth of features which are otherwise absent from unstructured environments. Here we use optimal control to learn how to perform quantum operations in systems under the influence of non-Markovian decoherence. Despite recent advancements, non-Markovian environments are difficult to simulate and complex to understand, which inhibits the ability to perform optimal control. We present an efficient method to find optimal controls for quantum systems coupled to non-Markovian environments, by using the process tensor to compute the gradient of an objective function.

We consider the case of a driven two level system coupled to a bosonic environment. We use optimal control to identify control protocols to perform state transfer on our system. We demonstrate how there is a trade-off between process duration and fidelity, and how longer processes can have higher fidelity by exploiting non-Markovian effects. We contrast this to the case of Hamiltonian dynamics where the quantum speed limit characterises the shortest time possible to perform state transfer. We describe how optimal control can be used to characterise the performance-speed trade-off. We propose a non-trivial mechanism for how the optimiser is suppressing decoherence while exploiting non-Markovian effects. We give an overview of how these results could be generalised to quantum gates.