Unifying methods for optimal control in non-Markovian quantum systems via process tensors

Understand

The large dimensionality of environments is the limiting factor in applying optimal control to open quantum systems beyond Markovian approximations.

• Multiple methods exist to simulate non-Markovian open systems which effectively reduce the environment to a number of active degrees of freedom.
• Here we show that several of these methods can be expressed in terms of a process tensor in the form of a matrix-product-operator, which serves as a unifying framework to show how they can be used in optimal control, and to compare their performance.
• The matrix-product-operator form provides a general scheme for computing gradients using back propagation, and allows the efficiency of the different methods to be compared via the bond dimensions of their respective process tensors.