A. Isar, A. Sandulescu, W. Scheid
By using the Lindblad theory for open quantum systems, an analytical expression of the tunneling probability through an inverted parabola is obtained. This penetration probability depends on the environment coefficients. It is shown that the tunneling probability increases with the dissipation and the temperature of the thermal bath.
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It is by now well understood that quantum dissipative processes can be harnessed and turned into a resource for quantum-information processing tasks. In this paper we demonstrate yet another way in which this is true by providing a dissipation-assisted protocol for the simulation of general Markovian dynamics. More precisely, we show how a suitable coherent coupling of a quantum system to a set of Markovian dissipating qubits allows one to enact an effective Liouvillian generator of any Lindbladian form. This effective dynamical generator arises from high-order virtual-dissipative processes an…
We present a robust method for quantum process tomography, which yields a set of Lindblad operators that optimally fit the measured density operators at a sequence of time points. The benefits of this method are illustrated using a set of liquid-state Nuclear Magnetic Resonance (NMR) measurements on a molecule containing two coupled hydrogen nuclei, which are sufficient to fully determine its relaxation superoperator. It was found that the complete positivity constraint, which is necessary for the existence of the Lindblad operators, was also essential for obtaining a robust fit to the measure…
Dissipative Dynamics and Symmetry Breaking in Bosonic Sachdev-Ye-Kitaev Lindbladian
本文研究玻色型SYK模型与Lindbladian环境耦合下的耗散动力学，利用Schwinger-Keldysh路径积分揭示对称性破缺与相变，发现耗散可抑制倒置势不稳定性并产生新稳态相。
We consider an open bipartite quantum system with dissipative Lindblad type dynamics. In order to study the entanglement of the stationary states, we develop a perturbative approach and apply it to the physically significant case when a purely dissipative perturbation is added to the unperturbed generator which by itself would produce reversible unitary dynamics.
Quantum Dissipative Search via Lindbladians
本文通过 Lindblad 主方程分析纯耗散量子随机游走在无结构搜索空间中的收敛性，证明 OQRW 并不优于经典搜索，并利用低实现成本的耗散基态制备算法揭示相干性对二次加速的关键作用。
Kadanoff-Baym equations for interacting systems with dissipative Lindbladian dynamics
本文提出一种针对耗散NEGF理论的二次量子化方法，通过重新表述Keldysh思想以适应Lindbladian动力学并扩展Kadanoff-Baym方程，实现了关联和耗散的实时模拟，用于探索材料的瞬态和稳态电子、输运及光学性质变化。
We investigate dissipative extensions of the Su-Schrieffer-Heeger model with regard to different approaches of modeling dissipation. In doing so, we use two distinct frameworks to describe the gain and loss of particles, one uses Lindblad operators within the scope of Lindblad master equations, the other uses complex potentials as an effective description of dissipation. The reservoirs are chosen in such a way that the non-Hermitian complex potentials are $\mathcal{PT}$-symmetric. From the effective theory we extract a state which has similar properties as the non-equilibrium steady state foll…
Gorini-Kossakowski-Sudarshan-Lindblad equation in different bases: application to driven-dissipative two- and multilevel systems
研究驱动耗散量子系统，通过考虑不同基下的戈里尼-科萨克夫斯基-苏达山-林德布拉德方程，计算量子比特和量子多体系统动力学，指出基的恰当选择对理论和实践的重要性。
Three inter-related topics are discussed here. One, the Lindblad dynamics of quantum dissipative systems; two, quantum entanglement in composite systems and its quantification based on the Tsallis entropy; and three, robustness of entanglement under dissipation. After a brief review of the Lindblad theory of quantum dissipative systems and the idea of quantum entanglement in composite quantum systems illustrated by describing the three particle systems, the behavior of entanglement under the influence of dissipative processes is discussed. These issues are of importance in the discussion of qu…
We investigate the critical behavior, both in space and time, of the wetting interface within the coexistence region around the first-order phase transition of a fully-connected quantum Ising model in slab geometry. For that, we employ the Lindblad master equation formalism in which temperature is inherited by the coupling to a dissipative bath, rather than being a functional parameter as in the conventional Cahn's free energy. Lindblad's approach gives not only access to the dissipative dynamics and steady-state configuration of the quantum wetting interface throughout the whole phase diagram…
We prove that a harmonic oscillator driven by Lindblad dynamics where the typical drive and loss channels are two-photon processes instead of single-photon ones, converges to a protected subspace spanned by two coherent states of opposite amplitude. We then characterize the slow dynamics induced by a perturbative single-photon loss on this protected subspace, by performing adiabatic elimination in the Lindbladian dynamics.
We present a general approach to derive Lindblad master equations for a subsystem whose dynamics is coupled to dissipative bosonic modes. The derivation relies on a Schrieffer-Wolff transformation which allows to eliminate the bosonic degrees of freedom after self-consistently determining their state as a function of the coupled quantum system. We apply this formalism to the dissipative Dicke model and derive a Lindblad master equation for the atomic spins, which includes the coherent and dissipative interactions mediated by the bosonic mode. This master equation accurately predicts the Dicke …
The Monte Carlo wave function method or the quantum trajectory/jump approach is a powerful tool to study dissipative dynamics governed by the Markovian master equation, in particular for high-dimensional systems and when it is difficult to simulate directly. In this paper, we extend this method to the non-Markovian case described by the generalized Lindblad master equation. Two examples to illustrate the method are presented and discussed. The results show that the method can correctly reproduce the dissipative dynamics for the system. The difference between this method and the traditional Mar…
Dissipative dynamics of quantum systems can be classified topologically based on the correspondence between the Lindbladian in the Gorini-Kossakowski-Sudarshan-Lindblad equation and the non-Hermitian Hamiltonian in the Schrödinger equation. While general non-Hermitian Hamiltonians are classified into 38 symmetry classes, previous studies have shown that the Lindbladians are classified into 10 symmetry classes due to a physical constraint. In this work, however, we unveil a topological classification of Lindbladians based on shifted sublattice symmetry (SLS), which can increase the number of sy…
Thermal wave packets are used to analyze transmission probabilities and characteristic times through a parabolic repeller within the dissipative Bohmian mechanics. Thermal arrival, dwelling, transmission and reflection times are defined and calculated by using a Maxwell-Boltzmann distribution for the initial velocities of the incident particles. The dissipation is considered within the Caldirola-Kanai and Kostin approaches where a linear and nonlinear framework is used, respectively. The initial parameters are chosen to have only a dissipative tunnelling dynamics at zero temperature; at any no…
On the linear friction many-body equation for dissipative spontaneous wavefunction collapse
本文构造了用二次量子化质量密度和流表示的普适耗散Lindblad主方程，在线性摩擦假设下给出严格约束，并推导分析了Diósi-Penrose和连续自发局域化模型的耗散扩展。
A single quantum dissipative oscillator described by the Lindblad equation serves as a model for a nanosystem. This model is solved exactly by using the ambiguity function. The solution shows the features of decoherence (spatial extent of quantum behavior), correlation (spatial scale over which the system localizes to its physical dimensions), and mixing (mixed- state spatial correlation). A new relation between these length scales is obtained here. By varying the parameters contained in the Lindblad equation, it is shown that decoherence and correlation can be controlled. We indicate possible…
The so-called Lindblad equation, a typical master equation describing the dissipative quantum dynamics, is shown to be solvable for finite-level systems in a compact form without resort to writing it down as a set of equations among matrix elements. The solution is then naturally given in an operator form, known as the Kraus representation. Following a few simple examples, the general applicability of the method is clarified.
A quantum algorithm to simulate Lindblad master equations
本文提出一种基于二阶乘积公式和随机编译的量子算法，用于模拟 Lindblad 主方程，无需辅助量子比特即可实现耗散过程并降低门复杂度，同时扩展至时间依赖情形并给出新的 diamond 范数误差界。
Dissipative preparation of Laughlin-like states
提出基于局域损耗和泵浦通道的纯耗散协议，用于制备填充因子1/3的类Laughlin态，证明其为Lindbladian精确稳态且可从任意初态达到，并展示绝热泵浦操控。
The properties of some complex many body systems can be modeled by introducing in the dissipative dynamics of each single component a set of kinetic constraints that depend on the state of the neighbor systems. Here, we characterize this kind of dynamics for two quantum systems whose independent dissipative evolutions are defined by a Lindblad equation. The constraints are introduced through a set of projectors that restrict the action of each single dissipative Lindblad channel to the state of the other system. Conditions that guaranty a classical interpretation of the kinetic constraints are…
A pair of coupled quantum dissipative oscillators, serving as a model for a nanosystem, is here described by the Lindblad equation. Its dynamic evolution is shown to exhibit the features of decoherence (spatial extent of quantum behavior), correlation (spatial scale over which the system localizes to its physical dimensions), and entanglement (a special quantum feature making its appearance first in such bipartite systems) as a function of the coupling constants of the Lindblad equation. One interesting feature emerging out of this calculation is that the entanglement may exhibit revivals in t…
Parallelizing Dissipative Quantum Algorithms
本文提出并行化耗散量子算法中跳跃算子的方案，利用几何局域性使电路深度指数级降低，实验显示100量子比特一维系统查询深度减少53倍，提升了近期量子计算的实用性。
We formulate the general approach based on the Lindblad equation to calculate the full counting statistics of work and heat produced by driven quantum systems weakly coupled with a Markovian thermal bath. The approach can be applied to a wide class of dissipative quantum systems driven by an arbitrary force protocol. We show the validity of general fluctuation relations and consider several generic examples. The possibilities of using calorimetric measurements to test the presence of coherence and entanglement in the open quantum systems are discussed.
Quantum viscosity mechanism of the dissipative dynamics in the Dicke model expressed via Lindblad equation of motion
本文通过量子力学推导Dicke模型在超辐射相中与Caldeira-Leggett热浴耦合的Lindblad方程，解析证明了半经典极化激元凝聚运动方程中的有效粘滞在零温极限下仍然存在，并指出该粘滞源于热浴中谐振子的虚激发。
Dissipative frequency converter: from Lindblad dynamics to non-Hermitian topology
本研究通过Lindblad动力学和有效非厄米哈密顿量两种模型，探究三类耗散通道对二能级拓扑频率转换器量子化功率传输的影响，发现耗散会引发量子看门狗效应破坏功率传输，退相导致传输指数衰减，并揭示非厄米描述中存在非绝热过程。
The Lindblad equation describes the dissipative time evolution of a density matrix that characterizes an open quantum system in contact with its environment. The widespread ensemble interpretation of a density matrix requires its time evolution to be linear. However, when the density matrix is obtained from a mean field theory of interacting quantum systems or from a top-down control by a changing classical environment, the ensemble interpretation is inappropriate and nonlinear dynamics arise naturally. We therefore study the dynamical behavior of nonlinear Lindblad equations using the example…
In this work, we investigate the quantum phase transition of light in the dissipative Rabi-Hubbard lattice under the framework of the mean-field theory and quantum dressed master equation. The order parameter of photons in strong qubit-photon coupling regime is derived analytically both at zero and low temperatures. Interestingly, we can locate the localization and delocalization phase transition very well in a wide parameter region. {In particular for the zero-temperature limit, the critical tunneling strength approaches zero generally in the deep-strong qubit-photon coupling regime, regardle…
Simulation of Lindbladian dynamics via adaptive variational quantum trajectory compression
针对NISQ时代开放量子系统模拟难题，提出资源高效算法，推导混合酉伴随通道，引入自适应变分量子轨迹压缩框架，训练参数化量子电路，经数值模拟验证算法准确性与资源效率，为开放量子系统模拟提供实用途径。
A semiclassical approximation for an evolving density operator, driven by a "closed" hamiltonian operator and "open" markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the hamiltonian operator is a quadratic function and the Lindblad operators are linear functions of positions and momenta. Initially, the semiclassical formulae for the case of hermitian Lindblad operators are reinterpreted in terms of a (real) double phase space, generated by a…
Lattice Lindbladian simulation by patching and merging
本文提出利用局域性的拼接与合并技术，为晶格林德布拉德动力学开发近乎最优的量子算法，显著降低门计数，实现耗散多体系统的快速模拟。
In the framework of the Lindblad theory for open quantum systems, a master equation for the quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived for the case when the interaction is based on deformed algebra. The equations of motion for observables strongly depend on the deformation function. The expectation values of the number operator and squared number operator are calculated in the limit of a small deformation parameter for the case of zero temperature of the thermal bath. The steady state solution of the equation for the de…
A direct algebraic proof for the non-positivity of Liouvillian spectral values and controlling the dissipative gap of systems with normal Lindblad operators
本文通过直接代数方法证明了马尔可夫量子动力学中李维illian谱值的非正性，基于李布兰形式的李维illian结构。
Beyond the lemon: Spectra of random Lindblad operators with a Hamiltonian component
本研究针对含哈密顿分量的随机林德布拉德算子，结合算子值自由概率与序贯噪声平均的新框架，分析其谱特性，揭示哈密顿分量对谱支撑的影响。
A Nonrecursive Lindblad Quantization of Dissipative Polynomial Dynamics
本文提出一种非递归的 Lindblad 量子化方法，将任意平面多项式耗散流直接映射为开放量子系统，无需递归消除低阶项，并在半经典极限下恢复经典动力学特征，可用于设计具有指定经典结构的量子系统。
Using Liouville space and superoperator formalism we consider pure stationary states of open and dissipative quantum systems. We discuss stationary states of open quantum systems, which coincide with stationary states of closed quantum systems. Open quantum systems with pure stationary states of linear oscillator are suggested. We consider stationary states for the Lindblad equation. We discuss bifurcations of pure stationary states for open quantum systems which are quantum analogs of classical dynamical bifurcations.
Control of quantum dissipative systems can be challenging because control variables are typically part of the system Hamiltonian, which can only generate motion along unitary orbits of the system. To transit between orbits, one must harness the dissipation super-operator. To separate the inter-orbit dynamics from the Hamiltonian dynamics for a generic two-dimensional system, we project the Lindblad master equation onto the set of spectra of the density matrix, and we interpret the location along the orbit to be a new control variable. The resulting differential equation allows us to analyze th…
Dissipative ground state preparation in ab initio electronic structure theory
本研究提出了一种基于利恩布兰德动力学的耗散方法，用于在量子计算机上高效准备从头电子结构问题的基态，通过两种通用类型的跳跃算符实现，且不依赖变分参数。
A comparison of different master equations for driven-dissipative dynamics in composite quantum systems: Dispersive readout in structured electromagnetic environments
本文通过微观Bloch-Redfield方法比较了Lindblad和Redfield主方程在驱动-耗散量子比特-谐振子系统中的差异，揭示了无驱动时衰减率的定量不同以及驱动强度下时间相关Redfield耗散器的定性新行为，并研究了结构化谱密度中驱动对测量诱导弛豫的抑制。
In this note we explicitly solve the Lindblad equation for a system of three spins with a three-body interaction, coupled to the environment by bath operators that inject or absorb spin carriers. We exemplify the properties of this solution in the context of a simple instance of Feynman's quantum computer in which a two-qubit program line is executed, applying the $\sqrt{NOT}$ primitive to a one-qubit register.
We apply the restricted-path-integral (RPI) theory of non-minimally disturbing continuous measurements for correct description of frictional Brownian motion. The resulting master equation is automatically of the Lindblad form, so that the difficulties typical of other approaches do not exist. In the special case of harmonic oscillator the known familiar master equation describing its frictionally driven Brownian motion is obtained. A thermal reservoir as a measuring environment is considered.
Open quantum systems weakly coupled to the environment are modeled by completely positive, trace preserving semigroups of linear maps. The generators of such evolutions are called Lindbladians. In the setting of quantum many-body systems on a lattice it is natural to consider Lindbladians that decompose into a sum of local interactions with decreasing strength with respect to the size of their support. For both practical and theoretical reasons, it is crucial to estimate the impact that perturbations in the generating Lindbladian, arising as noise or errors, can have on the evolution. These lo…
We consider an open quantum system described by a Lindblad-type master equation with two times-scales. The fast time-scale is strongly dissipative and drives the system towards a low-dimensional decoherence-free space. To perform the adiabatic elimination of this fast relaxation, we propose a geometric asymptotic expansion based on the small positive parameter describing the time-scale separation. This expansion exploits geometric singular perturbation theory and center-manifold techniques. We conjecture that, at any order, it provides an effective slow Lindblad master equation and a completel…
We show that it is possible to modify the stationary state by a feedback control in a two-level dissipative quantum system. Based on the geometric control theory, we also analyze the effect of the feedback on the time-optimal control in the dissipative system governed by the Lindblad master equation. These effects are reflected in the function $Δ_A(\vec{x})$ and $Δ_B(\vec{x})$ that characterize the optimal trajectories, as well as the switching function $Φ(t)$ and $θ(t),$ which characterize the switching point in time for the time-optimal trajectory.
Recent works on quantum resource theories of non-Gaussianity, which are based upon the type of tools available in contemporary experimental settings, put Gaussian states and their convex combinations on equal footing. Motivated by this, in this article, we derive a new model of dissipative time evolution based on unitary Lindblad operators which, while does not preserve the set of Gaussian states, preserves the set of their convex combinations, i.e. so-called quantum Gaussian states. As we demonstrate, the considered evolution proves useful both as a description for random scattering and as a …
The dynamics of entanglement and quantum discord between two identical qubits strongly interacting with a common single mode leaky cavity field have been investigated beyond the rotating wave approximation (RWA) by using recently derived Lindblad type quantum optical master equation [F. Beaudoin, J.M. Gambetta, A. Blais, Phys. Rev. A {\bf 84}, 043832 (2011)] that can describe the losses of the cavity field in a strong atom-field coupling regime. Contrary to previous investigations of the same model in the dissipative regime by using the standard Lindblad quantum optical master equation in a st…
We present a quantum algorithm to simulate general finite dimensional Lindblad master equations without the requirement of engineering the system-environment interactions. The proposed method is able to simulate both Markovian and non-Markovian quantum dynamics. It consists in the quantum computation of the dissipative corrections to the unitary evolution of the system of interest, via the reconstruction of the response functions associated with the Lindblad operators. Our approach is equally applicable to dynamics generated by effectively non-Hermitian Hamiltonians. We confirm the quality of …
Strong Markov dissipation in driven-dissipative quantum systems
本文提出奇异驱动极限，结合奇异耦合与快速周期驱动，为任意强度系统-浴耦合推导马尔可夫Lindblad方程，并产生非平凡稳态。
The aims of this paper are two. The first is to give a brief review of the most relevant theoretical results concerning the uniqueness of the steady-state solution of the Lindblad-Gorini-Kossakowski-Sudarshan master equation and the criteria which guarantee relaxingness and irreducibility of dynamical semigroups. In particular, we test and discuss their physical meaning by considering their applicability to the characterisation of the simplest open quantum system \emph{i.e.} a two-level system coupled to a bath of harmonic oscillators at zero temperature. The second aim is to provide a set of …
Time-evolution of open, dissipative quantum system is a stochastic process that consists of a series of quantum jumps that take place at random times. Between quantum jumps quantum system idles for some time in a particular quantum state. Based on superfermion/superboson formalism and general Kossakowski- Lindblad master equation for an open quantum system we develop a method to compute distribution of waiting times between quantum jumps. We illustrate the use of the theory by computing waiting time distribution for model Fermi-system in thermodynamic equilibrium.
The dwell time for dissipative quantum system is shown to increase with barrier width. It clearly precludes Hartman effect for dissipative systems. Here calculation has been done for inverted parabolic potential barrier.
We propose an analysis of the time-optimal control of a dissipative two-level quantum system whose dynamics is governed by the Lindblad equation. This simple system allows one to use tools of geometric control theory and to construct its optimal synthesis, i.e. to determine the set of all the optimal trajectories starting from a given initial point. We study different processes such as conversion of a pure state into a mixed state and purification of a mixed state. In particular cases, we show that dissipation is not undesirable and can help accelerating the control.
Motivated by correlated decay processes producing gain, loss and lasing in driven semiconductor quantum-dots, we develop a theoretical technique using Keldysh diagrammatic perturbation theory to derive a Lindblad master equation that goes beyond the usual second order perturbation theory. We demonstrate the method on the driven dissipative Rabi model, including terms up to fourth order in the interaction between the qubit and both the resonator and environment. This results in a large class of Lindblad dissipators and associated rates which go beyond the terms that have previously been propose…
Experimentally observed quantum few-body dynamics of neutral atoms excited to a Rydberg state are numerically analyzed with Lindblad master equation formalism. For this, up to five rubidium atoms are trapped with optical tweezers, arranged in various two-dimensional configurations, and excited to Rydberg 67S state in the nearest-neighbor blockade regime. Their coherent evolutions are measured with time-varying ground-state projections. The experimental results are analyzed with a model Lindblad equation with the homogeneous and inhomogeneous dampings determined by systematic and statistical er…
Routes of Transport in the Path Integral Lindblad Dynamics through State-to-State Analysis
本文提出了一种基于状态到状态分析的林blad方法，用于研究开放量子系统中传输路线，特别是在非平衡初始条件下的传输机制和稳态激子电流的计算。
A Lindbladian for exact renormalization of density operators in QFT
本研究将量子场论精确重整化群推广至密度矩阵，证明其流由含哈密顿量项与耗散项的Lindblad主方程描述，验证了耗散项对耦合流的作用，指出有限ERG流对应量子信道且态可区分性度量为ERG单调量。
We propose the Sachdev-Ye-Kitaev Lindbladian as a paradigmatic solvable model of dissipative many-body quantum chaos. It describes $N$ strongly coupled Majorana fermions with random all-to-all interactions, with unitary evolution given by a quartic Hamiltonian and the coupling to the environment described by $M$ quadratic jump operators, rendering the full Lindbladian quartic in the Majorana operators. Analytical progress is possible by developing a dynamical mean-field theory for the Liouvillian time evolution on the Keldysh contour. By disorder-averaging the interactions, we derive an (exact…
Exponential convergence of a dissipative quantum system towards finite-energy grid states of an oscillator
基于量子纠错的稳定子形式体系，提出一种针对量子谐振子的 Lindblad 主方程，通过指数 Lyapunov 函数实现向有限能量网格态的精确稳定化，并在光子损耗下展现自主纠错潜力。
These lecture notes address an audience of physicists or mathematicians who have been exposed to a first course in quantum mechanics. We start with a brief discussion of the general "system-bath" paradigm of quantum dissipative systems, analyze in some detail the simplest example of "pure dephasing" of a two-level system, and review the basic concept of the density matrix. We then treat the general dissipative time-evolution, introducing completely positive maps, their relation to entanglement theory, and their Kraus decomposition. Restricting ourselves to Markovian evolution, we discuss the L…
Reliability Dynamics in a Two-Site Dissipative Quantum Spin Chain
本文提出了一种量子能量存储设备模型，通过两站点自旋-1/2链研究可靠性动态，推导了闭合表达式并建立了基于首次通过时间统计的实验评估协议。
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