# Tomographically reconstructed master equations for any open quantum dynamics

## TL;DR

This paper introduces a method to reconstruct memory kernel master equations for open quantum systems using quantum process tomography, enabling efficient simulation of complex dynamics without detailed system-environment information.

## Contribution

The authors derive a transfer tensor method from first principles, allowing memory kernels to be expressed solely in terms of dynamical maps reconstructed via process tomography.

## Key findings

- Reconstruction of memory kernels from dynamical maps is experimentally feasible.
- The method simplifies long-time dynamics simulation for driven or initially correlated systems.
- It offers computational advantages for simulating open quantum systems over traditional approaches.

## Abstract

Memory effects in open quantum dynamics are often incorporated in the equation of motion through a superoperator known as the memory kernel, which encodes how past states affect future dynamics. However, the usual prescription for determining the memory kernel requires information about the underlying system-environment dynamics. Here, by deriving the transfer tensor method from first principles, we show how a memory kernel master equation, for any quantum process, can be entirely expressed in terms of a family of completely positive dynamical maps. These can be reconstructed through quantum process tomography on the system alone, either experimentally or numerically, and the resulting equation of motion is equivalent to a generalised Nakajima-Zwanzig equation. For experimental settings, we give a full prescription for the reconstruction procedure, rendering the memory kernel operational. When simulation of an open system is the goal, we show how our procedure yields a considerable advantage for numerically calculating dynamics, even when the system is arbitrarily periodically (or transiently) driven or initially correlated with its environment. Namely, we show that the long time dynamics can be efficiently obtained from a set of reconstructed maps over a much shorter time.