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.
Highlights
The experimental characterization of dynamical processes is fundamental to physics
In all of the simulation studies above, our quantum process identification (QPI) method was able to accurately capture and reproduce the observable behavior of the qubit over very long time scales, with trace distance errors on the order of 10−2. While this level of error would not be impressive for tomography of the state at any one time, the fact that this accuracy is maintained over more than a thousand time steps implies that the process itself is characterized to an accuracy on the order of 10−5
We have developed a new method for the characterization of quantum dynamical processes, called quantum process identification
Summary
In the burgeoning field of quantum information science, the characterization of quantum processes in a general, systematic way has become important. In quantum key distribution, characterization of the information-preserving properties of the quantum channel between communicating parties is crucial to establishing the security of the generated key [1]. In the circuit model of quantum computing, a computation is represented as a sequence of primitive quantum logic operations or “gates”, each of which is implemented via a controlled quantum process. Characterization of these processes essential to assessing and improving their performance [2,3,4,5]. The process is expressed as a quantum channel —a linear, completely positive, trace-preserving (CPTP) map on the system state space—that can be estimated from the experimental results
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