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

TL;DR

This paper introduces a unifying framework using process tensors in matrix-product-operator form to compare and enhance optimal control methods for non-Markovian quantum systems, addressing the challenge of large environment dimensionality.

Contribution

The paper demonstrates that various non-Markovian simulation methods can be unified under process tensors, enabling direct comparison and improved optimal control strategies.

Findings

Process tensors can be expressed as matrix-product-operators.

The framework allows efficient gradient computation via back propagation.

Performance comparison is facilitated through bond dimensions of process tensors.

Abstract

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.