Quantum Process Identification: A Method for Characterizing Non-Markovian Quantum Dynamics

TL;DR

This paper introduces quantum process identification (QPI), a systematic experimental method to characterize non-Markovian quantum dynamics by relating them to a time-local process involving an effective environment.

Contribution

The paper presents a novel framework and practical approach for characterizing non-Markovian quantum processes, filling a gap in existing quantum process characterization methods.

Findings

QPI accurately models non-Markovian qubit dynamics.

QPI can identify errors from control drift and material impurities.

Numerical simulations validate QPI's effectiveness.

Abstract

Established methods for characterizing quantum information processes do not capture non-Markovian (history-dependent) behaviors that occur in real systems. These methods model a quantum process as a fixed map on the state space of a predefined system of interest. Such a map averages over the system's environment, which may retain some effect of its past interactions with the system and thus have a history-dependent influence on the system. Although the theory of non-Markovian quantum dynamics is currently an active area of research, a systematic characterization method based on a general representation of non-Markovian dynamics has been lacking. In this article we present a systematic method for experimentally characterizing the dynamics of open quantum systems. Our method, which we call quantum process identification (QPI), is based on a general theoretical framework which relates the (non-Markovian) evolution of a system over an extended period of time to a time-local (Markovian) process involving the system and an effective environment. In practical terms, QPI uses time-resolved tomographic measurements of a quantum system to construct a dynamical model with as many dynamical variables as are necessary to reproduce the evolution of the system. Through numerical simulations, we demonstrate that QPI can be used to characterize qubit operations with non-Markovian errors arising from realistic dynamics including control drift, coherent leakage, and coherent interaction with material impurities.