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.
Non-Markovian evolution in open quantum systems is often characterized in terms of the backflow of information from environment to system and is thus an important facet in investigating the performance and robustness of quantum information protocols. In this work, we explore non-Markovianity through the breakdown of monotonicity of a metrological figure of merit, called the quantum interferometric power, which is based on the minimal quantum Fisher information obtained by local unitary evolution of one part of the system, and can be interpreted as a quantifier of quantum correlations beyond en…
Correlations of an environment are crucial for the dynamics of non-Markovian quantum systems, which may not be known in advance. In this paper, we propose a gradient algorithm for identifying the correlations in terms of time-varying damping rate functions in a time-convolution-less master equation for spin chains. By measuring time trace observables of the system, the identification procedure can be formulated as an optimization problem. The gradient algorithm is designed based on a calculation of the derivative of an objective function with respect to the damping rate functions, whose effect…
Non-Markovian effects are ubiquitous in physical quantum systems and remain a significant challenge to achieving high-quality control and reliable quantum computation, but due to their inherent complexity, are rarely characterized. Past approaches to quantifying non-Markovianity have concentrated on small, simple systems, and we show that such measures can capture properties that are irrelevant to applications. With this insight, we propose a method for constructing relevant quantifiers of non-Markovian dynamics and illustrate the scheme's computability by characterizing a model quantum dot ar…
We propose to use the quantum Fisher information in characterizing the information flow of open quantum systems. This information-theoretic approach provides a quantitative measure to statistically distinguish Markovian and non-Markovian processes. A basic relation between the QFI flow and non-Markovianity is unveiled for quantum dynamics of open systems. For a class of time-local master equations, the exactly-analytic solution shows that the non-Markovianity is characterized by additive information sub-flows in different non-Markovian channels.
We study quantum information flow in a model comprising of an impurity qubit immersed in a Bose-Einstein condensed reservoir. We demonstrate how information flux between the qubit and the condensate can be manipulated by engineering the ultracold reservoir within experimentally realistic limits. We place a particular emphasis on non-Markovian dynamics, characterized by a reversed flow of information from the background gas to the qubit and identify a controllable crossover between Markovian and non-Markovian dynamics in the parameter space of the model.
Memory-enhanced quantum extreme learning machines for characterizing non-Markovian dynamics
Abdelmalek Essaadi University（阿卜杜勒马利克·埃萨迪大学）；Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；Institute for Cross-Disciplinary Physics and Complex Systems (IFISC) UIB-CSIC（跨学科物理与复杂系统研究所（IFISC）巴伊利亚群岛大学-西班牙国家科研委员会）
We measure and quantify non-Markovian effects in IBM's Quantum Experience. Specifically, we analyze the temporal correlations in a sequence of gates by characterizing the performance of a gate conditioned on the gate that preceded it. With this method, we estimate (i) the size of fluctuations in the performance of a gate, i.e., errors due to non-Markovianity; (ii) the length of the memory; and (iii) the total size of the memory. Our results strongly indicate the presence of non-trivial non-Markovian effects in almost all gates in the universal set. However, based on our findings, we discuss th…
With continuing improvements on the quality of fabricated quantum devices, it becomes increasingly crucial to analyze noisy quantum process in greater details such as characterizing the non-Markovianity in a quantitative manner. In this work, we propose an experimental protocol, termed Spectral Transfer Tensor Maps (SpecTTM), to accurately predict the RHP non-Markovian measure of any Pauli channels without state-preparation and measurement (SPAM) errors. In fact, for Pauli channels, SpecTTM even allows the reconstruction of highly-precised noise power spectrum for qubits. At last, we also disc…
We characterize to what extent it is possible to modify the stationary states of a quantum dynamical semigroup, that describes the irreversible evolution of a two-level system, by means of an auxiliary two-level system. We consider systems that can be initially entangled or uncorrelated. We find that the indirect control of the stationary states is possible, even if there are not initial correlations, under suitable conditions on the dynamical parameters characterizing the evolution of the joint system.
The degree of non-Markovianity allows to characterizing quantum evolutions that depart from a Markovian regime in a similar way as Schmidt number measures the degree of entanglement of pure states. Maximally non-Markovian dynamics are the analogous of maximally entangled states [D. Chruściński and S. Maniscalco, Phys. Rev. Lett. 112, 120404 (2014)]. Here, we demonstrate that there exists a class of maximally non-Markovian quantum evolutions where the associated environment (degrees of freedom not belonging to the system) obeys a Markovian (memoryless) dynamics, which in turn is unperturbed by …
We apply the recently proposed quantum probing protocols with an unknown system-probe coupling to probe the convex coefficients in mixtures of commuting states. By using two reference states instead of one as originally suggested, we are able to probe both lower and upper bounds for the convex coefficient. We perform extensive analysis for the roles of the parameters characterizing the double peaked Gaussian frequency spectrum in the Markovian-to-non-Markovian transition of the polarization dynamics of a single photon. We apply the probing of the convex coefficient to the transition-inducing f…
The non-Markovian decoherence of quantum and classical correlations is analytically obtained when two qubits are asymmetrically subjected to the bit flip channel and phase flip channel. For one class of initial mixed states, quantum correlations quantified by quantum discord decay synchronously with classical correlations. The discovery that the decaying rates of quantum and classical correlations suddenly change at the characteristic time is physically interpreted by the distance from quantum state to the closest classical states. In a large time interval, quantum correlations are greater tha…
In quantum information processing, knowledge of the noise in the system is crucial for high-precision manipulation and tomography of coherent quantum operations. Existing strategies for identifying this noise require the use of additional quantum devices or control pulses. We present a noise-identification method directly based on the system's non-Markovian response of an ensemble measurement to the noise. The noise spectrum is identified by reversing the response relationship in the frequency domain. For illustration, the method is applied to superconducting charge qubits, but it is equally a…
Identification of complicated quantum environments lies in the core of quantum engineering, which systematically constructs an environment model with the aim of accurate control of quantum systems. In this paper, we present an inverse-system method to identify damping rate functions which describe non-Markovian environments in time-convolution-less master equations. To access information on the environment, we couple a finite-level quantum system to the environment and measure time traces of local observables of the system. By using sufficient measurement results, an algorithm is designed, whi…
Non-Markovian effects can speed up the dynamics of quantum systems while the limits of the evolution time can be derived by quantifiers of quantum statistical speed. We introduce a witness for characterizing the non-Markovianity of quantum evolutions through the Hilbert-Schmidt speed (HSS), which is a special type of quantum statistical speed. This witness has the advantage of not requiring diagonalization of evolved density matrix. Its sensitivity is investigated by considering several paradigmatic instances of open quantum systems, such as one qubit subject to phase-covariant noise and Pauli…
Markovian approximation is a widely-employed idea in descriptions of the dynamics of open quantum systems (OQSs). Although it is usually claimed to be a concept inspired by classical Markovianity, the term quantum Markovianity is used inconsistently and often unrigorously in the literature. In this report we compare the descriptions of classical stochastic processes and quantum stochastic processes (as arising in OQSs), and show that there are inherent differences that lead to the non-trivial problem of characterizing quantum non-Markovianity. Rather than proposing a single definition of quant…
I propose a quantum trajectories approach to parametric identification of the effective Hamiltonian for a Markovian open quantum system, and discuss an application motivated by recent experiments in cavity quantum electrodynamics. This example illustrates a strategy for quantum parameter estimation that efficiently utilizes the information carried by correlations between measurements distributed in time.
Non-Markovian processes have recently become a central topic in the study of open quantum systems. We realize experimentally non-Markovian decoherence processes of single photons by combining time delay and evolution in a polarization-maintaining optical fiber. The experiment allows the identification of the process with strongest memory effects as well as the determination of a recently proposed measure for the degree of quantum non-Markovianity based on the exchange of information between the open system and its environment. Our results show that an experimental quantification of memory in q…
Understanding the physical significance and probing the global invariants characterizing quantum topological phases in extended systems is a main challenge in modern physics with major impact in different areas of science. Here, a quantum-information-inspired probing method is proposed where topological phase transitions are revealed by a non-Markovianity quantifier. The idea is illustrated by considering the decoherence dynamics of an external read-out qubit that probes a Su-Schrieffer-Heeger (SSH) chain with either pure dephasing or dissipative coupling. Qubit decoherence features and non-Ma…
Characterizing the memory properties of the environment has become critical for the high-fidelity control of qubits and other advanced quantum systems. However, current non-Markovian tomography techniques are either limited to discrete superoperators, or they employ machine learning methods, neither of which provide physical insight into the dynamics of the quantum system. To circumvent this limitation, we design learning architectures that explicitly encode physical constraints like the properties of completely-positive trace-preserving maps in a differential form. This method preserves the v…
Estimating the parameters that dictate the dynamics of a quantum system is an important task for quantum information processing and quantum metrology, as well as fundamental physics. In this paper we develop a method for parameter estimation for Markovian open quantum systems using a temporal record of measurements on the system. The method is based on system realization theory and is a generalization of our previous work on identification of Hamiltonian parameters [Phys. Rev. Lett. 113, 080401 (2014)].
We develop a notion of dephasing under the action of a quantum Markov semigroup in terms of convergence of operators to a block-diagonal form determined by irreducible invariant subspaces. If the latter are all one-dimensional, we say the dephasing is maximal. With this definition, we show that a key necessary requirement on the Lindblad generator is bistochasticity, and focus on characterizing whether a maximally dephasing evolution may be described in terms of a unitary dilation with only classical noise, as opposed to a genuine non-commutative Hudson-Parthasarathy dilation. To this end, we …
Correlated, non-Markovian noise is present in many solid-state systems employed as hosts for quantum information technologies, significantly complicating the realistic theoretical description of these systems. In this regime, the effects of noise on sequences of quantum gates cannot be described by concatenating isolated quantum operations if the environmental correlation times are on the scale of the typical gate durations. The filter function formalism has been successful in characterizing the decay of coherence under the influence of such classical, non-Markovian environments and here we sh…
Engineering quantum systems offers great opportunities both technologically and scientifically for communication, computation, and simulation. The construction and operation of large scale quantum information devices presents a grand challenge and a major issue is the effective control of coherent dynamics. This is often in the presence of decoherence which further complicates the task of determining the behaviour of the system. Here, we show how to determine open system Markovian dynamics of a quantum system with restricted initialisation and partial output state information.
The quantum adiabatic theorem is fundamental to time dependent quantum systems, but being able to characterize quantitatively an adiabatic evolution in many-body systems can be a challenge. This work demonstrates that the use of appropriate state and particle-density metrics is a viable method to quantitatively determine the degree of adiabaticity in the dynamic of a quantum many-body system. The method applies also to systems at finite temperature, which is important for quantum technologies and quantum thermodynamics related protocols. The importance of accounting for memory effects is discu…
Quantum open system identification via global optimization: Optimally accurate Markovian models of open systems from time-series data
Tulane University（杜兰大学）；DEVCOM Army Research Laboratory（DEVCOM陆军研究实验室）；University of Massachusetts at Boston（马萨诸塞大学波士顿分校）；HSBC Lab（汇丰实验室）；Czech Technical University in Prague（捷克布拉格技术大学）；Athena Research and Innovation Center（雅典娜研究与创新中心）
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of the process matrix acting on a system. This equation is applicable to non-Markovian and/or strong coupling regimes. We propose two distinct applications for this dynamical equation. We first demonstrate identification of quantum Hamiltonians generating dynamics of closed or open systems via performing process tomography. In particular, we argue how one can …
The identification of time-varying \textit{in situ} signals is crucial for characterizing the dynamics of quantum processes occurring in highly isolated environments. Under certain circumstances, they can be identified from time-resolved measurements via Ramsey interferometry experiments, but only with very special probe systems can the signals be explicitly read out, and a theoretical analysis is lacking on whether the measurement data are sufficient for unambiguous identification. In this paper, we formulate this problem as the invertibility of the underlying quantum input-output system, and…
Divisibility of dynamical maps: Schrödinger vs. Heisenberg picture
University of Turku（图尔库大学）；Università degli Studi di Milano（米兰大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Milano（意大利国家核物理研究所米兰分部）；Nicolaus Copernicus University（尼古拉·哥白尼大学）
Quantum Hamiltonian identification is important for characterizing the dynamics of quantum systems, calibrating quantum devices and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) quantum Hamiltonian identification algorithm is developed within the framework of quantum process tomography. In the identification method, different probe states are inputted into quantum systems and the output states are estimated using the quantum state tomography protocol via linear regression estimation. The time-independent system Hamiltonian is reconstructed based on …
The short time dynamics of a quantum Brownian particle in a harmonic potential is studied in the phase space. An exact non-Markovian analytic approach to calculate the time evolution of the Wigner function is presented. The dynamics of the Wigner function of an initially squeezed state is analyzed. It is shown that virtual exchanges of energy between the particle and the reservoir, characterizing the non-Lindblad short time dynamics where system-reservoir correlations are not negligible, show up in the phase space.
Characterizing those quantum channels that correspond to Markovian time evolutions is an open problem in quantum information theory, even different notions of quantum Markovianity exist. One such notion is that of infinitesimal Markovian divisibility for quantum channels introduced in arXiv:math-ph/0611057. Whereas there is a complete characterization for infinitesimal Markovian divisible qubit channels, no necessary or sufficient criteria are known for higher dimensions, except for necessity of non-negativity of the determinant. We describe how to extend the notion of infinitesimal Markovian …
When a quantum system couples strongly to multiple baths then it is generally no longer possible to describe the resulting system dynamics by simply adding the individual effects of each bath. However, capturing such multi-bath system dynamics has up to now required approximations that can obscure some of the non-additive effects. Here we present a numerically-exact and efficient technique for tackling this problem that builds on the time-evolving matrix product operator (TEMPO) representation. We test the method by applying it to a simple model system that exhibits non-additive behaviour: a t…
All physical systems are to some extent open and interacting with their environment. This insight, basic as it may seem, gives rise to the necessity of protecting quantum systems from decoherence in quantum technologies and is at the heart of the emergence of classical properties in quantum physics. The precise decoherence mechanisms, however, are often unknown for a given system. In this work, we make use of an opto-mechanical resonator to obtain key information about spectral densities of its condensed-matter heat bath. In sharp contrast to what is commonly assumed in high-temperature quantu…
We propose a greedy reconstruction algorithm to find the probability distribution of a parameter characterizing an inhomogeneous spin ensemble in Nuclear Magnetic Resonace. The identification is based on the application of a number of constant control processes during a given time for which the final ensemble magnetization vector is measured. From these experimental data, we show that the identifiability of a piecewise constant approximation of the probability distribution is related to the invertibility of a matrix which depends on the different control protocols applied to the system. The al…
