non-Markovian Quantum Dynamics Research Articles

Recovering Complete Positivity of Non-Markovian Quantum Dynamics with Choi-Proximity Regularization

Recovering Complete Positivity of Non-Markovian Quantum Dynamics with Choi-Proximity Regularization

Non-Markovian quantum dynamics from symmetric measurements

Non-Markovian quantum dynamics from symmetric measurements

Non-Markovian dynamics of time-fractional open quantum systems

The Time-Fractional Schrödinger Equation (TFSE) is suitable to describe the non-Markovian dynamics of a quantum system exposed to an environment, which is instructive for understanding and characterizing the time behavior of actual physical systems. Three popular TFSEs, namely Naber’s TFSE I, Naber’s TFSE II, and XGF’s TFSE, have been introduced in the form of ∂β∂tβ with β∈0,1. However, they suffer from the drawbacks. In their respective descriptions, the total probability for finding a particle in the entire space equals one only when β=1, implying that time-fractional quantum mechanics violates quantum mechanical probability conservation. By applying the three TFSEs to a basic single-qubit open system model, we discover that in describing the non-Markovian evolution of the system, the three TFSEs are limited by their own applicable ranges of β. This indicates that the three TFSEs cannot effectively describe the non-Markovian quantum dynamics. To address these issues, we introduce a well-performed TFSE by constructing a new analytic continuation of time without iβ combined with the conformable fractional derivative. In its description, for one thing, the total probability for finding the system in any single-qubit state equals one when β∈0,1. For another, the system evolves correctly in the non-Markovian manner at all values of β. Furthermore, we study the performances of the four TFSEs applying to a two-qubit open system model and show that our TFSE still possesses the above two advantages compared with the other three TFSEs.

Exact Non-Markovian Quantum Dynamics on the NISQ Device Using Kraus Operators.

The theory of open quantum systems has many applications ranging from simulating quantum dynamics in condensed phases to better understanding quantum-enabled technologies. At the center of theoretical chemistry are the developments of methodologies and computational tools for simulating charge and excitation energy transfer in solutions, biomolecules, and molecular aggregates. As a variety of these processes display non-Markovian behavior, classical computer simulation can be challenging due to exponential scaling with existing methods. With quantum computers holding the promise of efficient quantum simulations, in this paper, we present a new quantum algorithm based on Kraus operators that capture the exact non-Markovian effect at a finite temperature. The implementation of the Kraus operators on the quantum machine uses a combination of singular value decomposition (SVD) and optimal Walsh operators that result in shallow circuits. We demonstrate the feasibility of the algorithm by simulating the spin-boson dynamics and the exciton transfer in the Fenna-Matthews-Olson (FMO) complex. The NISQ results show very good agreement with the exact ones.

Path integral quantum algorithm for simulating non-Markovian quantum dynamics in open quantum systems

Path integral quantum algorithm for simulating non-Markovian quantum dynamics in open quantum systems

Survey of the hierarchical equations of motion in tensor-train format for non-Markovian quantum dynamics

Survey of the hierarchical equations of motion in tensor-train format for non-Markovian quantum dynamics

Non-Markovian open quantum dynamics in squeezed environments: Coherent-state unraveling

Non-Markovian open quantum dynamics in squeezed environments: Coherent-state unraveling

Topological Subordination in Quantum Mechanics

An example of non-Markovian quantum dynamics is considered in the framework of a geometrical (topological) subordination approach. The specific property of the model is that it coincides exactly with the fractional diffusion equation, which describes the geometric Brownian motion on combs. Both classical diffusion and quantum dynamics are described using the dilatation operator xddx. Two examples of geometrical subordinators are considered. The first one is the Gaussian function, which is due to the comb geometry. For the quantum consideration with a specific choice of the initial conditions, it corresponds to the integral representation of the Mittag–Leffler function by means of the subordination integral. The second subordinator is the Dirac delta function, which results from the memory kernels that define the fractional time derivatives in the fractional diffusion equation.

Many-body quantum non-Markovianity

We port the concept of non-Markovian quantum dynamics to the many-particle realm, by a suitable decomposition of the many-particle Hilbert space. We show how the specific structure of many-particle states determines the observability of non-Markovianity by single- or many-particle observables, and discuss a realization in a readily implementable few-particle setup.

Chiral SQUID-metamaterial waveguide for circuit-QED

Superconducting metamaterials, which are designed and fabricated with structured fundamental circuit elements, have motivated recent developments of exploring unconventional quantum phenomena in circuit quantum electrodynamics (circuit-QEDs). We propose a method to engineer 1D Josephson metamaterial as a chiral waveguide by considering a programmed spatiotemporal modulation on its effective impedance. The modulation currents are in the form of travelling waves which phase velocities are much slower than the propagation speed of microwave photons. Due to the Brillouin-scattering process, non-trivial spectrum regimes where photons can propagate unidirectionally emerge. Considering superconducting qubits coupling with this metamaterial waveguide, we analyze both Markovian and non-Markovian quantum dynamics, and find that superconducting qubits can dissipate photons unidirectionally. Moreover, we show that our proposal can be extended a cascaded quantum network with multiple nodes, where chiral photon transport between remote qubits can be realized. Our work might open the possibilities to exploit SQUID metamaterials for realizing unidirectional photon transport in circuit-QED platforms.

Probing non-Markovian quantum dynamics with data-driven analysis: Beyond “black-box” machine-learning models

A precise understanding of the influence of a quantum system's environment on its dynamics, which is at the heart of the theory of open quantum systems, is crucial for further progress in the development of controllable large-scale quantum systems. However, existing approaches to account for complex system-environment interaction in the presence of memory effects are either based on heuristic and oversimplified principles or give rise to computational difficulties. In practice, one can leverage on available experimental data and replace first-principles simulations with a data-driven analysis that is often much simpler. Inspired by recent advances in data analysis and machine learning, we propose a data-driven approach to the analysis of the non-Markovian dynamics of open quantum systems. Our method allows, on the one hand, capturing the most important characteristics of open quantum systems such as the effective dimension of the environment and the spectrum of the joint system-environment quantum dynamics, and, on the other hand, reconstructing a predictive model of non-Markovian quantum dynamics, and denoising the measured quantum trajectories. We demonstrate the performance of the proposed approach with various models of open quantum systems, including a qubit coupled with a finite environment, a spin-boson model, and the damped Jaynes-Cummings model.

Piecewise ensemble averaging stochastic Liouville equations for simulating non-Markovian quantum dynamics

Here we present a novel stochastic Liouville equation with piecewisely correlated noises, in which the inter-piece correlation is rigorously incorporated by a convolution integral involving functional derivatives. Due to the feature of piecewise correlation, we can perform piecewise ensemble average and serve the average of the preceding interval as the initial condition of the subsequent propagation. This strategy avoids the long-time stochastic average and the statistical errors are saturated at long times. By doing so, we circumvent the intrinsic difficulty of the stochastic simulations caused by the fast increase in the variance of the quantum Brownian motion. Therefore, as demonstrated by the numerical examples, the proposed method enables us to simulate the long-time quantum dissipative dynamics with long memories in the non-perturbative regime.

Quantifying Non-Markovianity in Open Quantum Dynamics

Characterization of non-Markovian open quantum dynamics is both of theoretical and practical relevance. In a seminal work [Phys. Rev. Lett. 120, 040405 (2018)], a necessary and sufficient quantum Markov condition is proposed, with a clear operational interpretation and correspondence with the classical limit. Here we propose two non-Markovianity measures for general open quantum dynamics, which are fully reconciled with the Markovian limit and can be efficiently calculated based on the multi-time quantum measurements of the system. A heuristic algorithm for reconstructing the underlying open quantum dynamics is proposed, whose complexity is directly related to the proposed non-Markovianity measures. The non-Markovianity measures and the reconstruction algorithm are demonstrated with numerical examples, together with a careful reexamination of the non-Markovianity in quantum dephasing dynamics.

Reconstructing non-Markovian open quantum evolution from multiple time measurements

For a quantum system undergoing non-Markovian open quantum dynamics, we demonstrate a tomography algorithm based on multi-time measurements of the system, which reconstructs a minimal environment coupled to the system, such that the system plus environment undergoes unitary evolution and that the reduced dynamics of the system is identical to the observed dynamics of it. The reconstructed open quantum evolution model can be used to predict any future dynamics of the system when it is further assumed to be time-independent. We define the memory size and memory complexity for the non-Markovian open quantum dynamics which characterize the complexity of the reconstruction.

Non-Markovian Quantum Dynamics in Strongly Coupled Multimode Cavities Conditioned on Continuous Measurement

A new theory is introduced that describes the conditioned state of a system with continuous measurement undergoing non-Markovian open quantum systems dynamics, opening new perspectives both on a fundamental and practical level.

Global correlation and local information flows in controllable non-Markovian open quantum dynamics

In a fully-controllable experiment platform for studying non-Markovian open quantum dynamics, we show that the non-Markovianity could be investigated from the global and local aspects. By mixing random unitary dynamics, we demonstrate non-Markovian and Markovian open quantum dynamics. From the global point of view, by tuning the base frequency we demonstrate the transition from the Markovianity to the non-Markovianity as measured by the quantum mutual information (QMI). In a Markovian open quantum process, the QMI decays monotonically, while it may rise temporarily in a non-Markovian process. However, under some circumstances, it is not sufficient to globally investigate the non-Markovianity of the open quantum dynamics. As an essential supplement, we further utilize the quantum Fisher information (QFI) flow to locally characterize the non-Markovianity in different channels. We demonstrate that the QMI in combination with the QFI flow are capable of measuring the non-Markovianity for a multi-channel open quantum dynamics.

Non-Markovian Quantum Dynamics in a Squeezed Reservoir.

We study non-Markovian dynamics of an open quantum system system interacting with a nonstationary squeezed bosonic reservoir. We derive exact and approximate descriptions for the open system dynamics. Focusing on the spin boson model, we compare exact dynamics with Redfield theory and a quantum optical master equation for both short and long time dynamics and in non-Markovian and Markov regimes. The squeezing of the bath results in asymptotic oscillations in the stationary state, which are captured faithfully by the Redfield master equation in the case of weak coupling. Furthermore, we find that the bath squeezing direction modifies the effective system–environment coupling strength and, thus, the strength of the dissipation.

Non-Markovian dynamics of open quantum system with memory

In this paper, non-Markovian generalization of master equation for open quantum system is proposed. Non-Markovian dynamics of two-level quantum system with memory and interaction with environment is described. To describe this system, the Gorini–Kossakowski–Sudarshan equation for open quantum states is generalized by taking into account power-law fading memory. The non-Markovian quantum processes with power-law memory are described by using integration and differentiation of non-integer orders. Complete positivity and bi-positivity in non-Markovian quantum dynamics with memory are described. An example of two-level quantum systems with power-law memory is suggested. Exact solution of the non-Markovian master equations of two-level open quantum systems with memory is derived.

Dynamical learning of non-Markovian quantum dynamics

We study the non-Markovian dynamics of an open quantum system with machine learning. The observable physical quantities and their evolutions are generated by using the neural network. After the pre-training is completed, we fix the weights in the subsequent processes thus do not need the further gradient feedback. We find that the dynamical properties of physical quantities obtained by the dynamical learning are better than those obtained by the learning of Hamiltonian and time evolution operator. The dynamical learning can be applied to other quantum many-body systems, non-equilibrium statistics and random processes.

Operational applications of the diamond norm and related measures in quantifying the non-physicality of quantum maps

Although quantum channels underlie the dynamics of quantum states, maps which are not physical channels — that is, not completely positive — can often be encountered in settings such as entanglement detection, non-Markovian quantum dynamics, or error mitigation. We introduce an operational approach to the quantitative study of the non-physicality of linear maps based on different ways to approximate a given linear map with quantum channels. Our first measure directly quantifies the cost of simulating a given map using physically implementable quantum channels, shifting the difficulty in simulating unphysical dynamics onto the task of simulating linear combinations of quantum states. Our second measure benchmarks the quantitative advantages that a non-completely-positive map can provide in discrimination-based quantum games. Notably, we show that for any trace-preserving map, the quantities both reduce to a fundamental distance measure: the diamond norm, thus endowing this norm with new operational meanings in the characterisation of linear maps. We discuss applications of our results to structural physical approximations of positive maps, quantification of non-Markovianity, and bounding the cost of error mitigation.