Quantum process identification: a method for characterizing non-markovian quantum dynamics

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.

Hamiltonian assignment for open quantum systems

“…The extension of our results to a greater diversity of open quantum systems remains an open research direction. For example, it will be of great interest to understand how our current work can be enhanced by incorporating existing techniques such as Bayesian learning [5], and quantum process identification [16]. Note that for current superconducting devices, the measurement infidelity is ∼1%, meaning that either these rates must fall by around two orders of magnitude or the assignment must be improved with other sources of information.…”

Spectral quantum tomography

“…One must estimate the function g(k) defined in Eq. (13). This reconstruction process requires running 2 n ×N ×(K +1) different experiments and repeating each experiment N samples times.…”

“…In this section we consider how spectral tomography behaves under error models that violate the assumptions that go into Eq. (13).…”

“…where W † T prep T meas W is not the identity matrix due SPAM errors, implying that g(k) can depend on E and have a non-exponential dependence on k. Thus, in the special case of a non-diagonalizable matrix T , the signal g(k) would not have the dependence on the eigenvalues as in Eq. (13).…”

“…This technique has been advocated in [8] in the context of randomized benchmarking and has also been used in [12] for processing data in the algorithm of quantum phase estimation. It has also been used, under the phrase 'linear systems identification', in [13] to predict the time evolution of quantum systems. While the matrix pencil technique leads to explicitly useful estimates of eigenvalues and their amplitudes, we note that the same underlying idea is used in the method of "delayed vectors" which has been proposed in [14] to assess the dimensionality of a quantum system from its dynamics.…”