Tensor network simulation of chains of non-Markovian open quantum systems

Fux, Gerald E.; Kilda, Dainius; Lovett, Brendon W.; Keeling, Jonathan

doi:10.48550/arxiv.2201.05529

Cited by 5 publications

(5 citation statements)

References 66 publications

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“…Popovic等 [55] 在2021年研究了量子开放系统中的热统计问题 . Fux等 [56] 在 2021年提出一种非马尔可夫开放系统的最优控制序列设计方法, 并在2022年研究了自旋链与环境…”

Section: 放系统中关联函数的方法该方法给出的关联函数是非马尔可夫的因此超越了通常使用的量子回归unclassified

Time-evolving matrix product operator method and its applications in open quantum system

Chen¹

2023

Acta Phys. Sin.

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Quantum open systems play an important role in the development of quantum sciences, therefore the study of corresponding numerical method is of great significance. For calculation of quantum open systems, the quasi-adiabatic propagator path integral, which was invented in 1990s, is one of the few numerically exact methods. However, its computational complexity scales exponentially with system size and correlation length, and due to this disadvantage its application is limited in practical calculation. In recent years, the study and application of tensor network has made rapid progress. Representing the path integral by tensor network makes scaling of the computational complexity polynomially, which greatly improve the computational efficiency. Such a new method is called time-evolving matrix product operators. At the very beginning, the reduced density matrix is represented as a matrix product state. Then the time evolution of the system can be achieved by iteratively applying matrix product operators on the matrix product state. The iterative process is amenable to the standard matrix product states compression algorithm, which keeps the computational cost at polynomial scales. The time-evolving matrix product operators is an efficient, numerically exact and fully non-Markovian method, which has a broad application prospect in the study of quantum open systems. For instance, it is already used in the study of the thermalization, heat statistic, heat transfer and optimal control of the quantum open systems, and conversely it can be also used to investigate the effect of the system on the environment. In addition, the TEMPO method is naturally connected to the process tensor which can be used to calculate the correlation function of the system efficiently. This article gives a review of this method and its applications.

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Section: 放系统中关联函数的方法该方法给出的关联函数是非马尔可夫的因此超越了通常使用的量子回归unclassified

Time-evolving matrix product operator method and its applications in open quantum system

Chen¹

2023

Acta Phys. Sin.

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“…This is particularly aided by the fact that local Lindblad equations are favourable for tensor network techniques. Studying such dynamics at finite temperatures is often quite challenging otherwise, requiring simulation of non-Markovian dynamics [56][57][58].…”

Section: Discussionmentioning

confidence: 99%

Searching for Lindbladians obeying local conservation laws and showing thermalization

Tupkary¹,

Dhar²,

Kulkarni³

et al. 2023

Preprint

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We investigate the possibility of a Markovian quantum master equation (QME) that consistently describes a finite-dimensional system, a part of which is weakly coupled to a thermal bath. In order to preserve complete positivity and trace, such a QME must be of Lindblad form. For physical consistency, it should additionally preserve local conservation laws and be able to show thermalization. First, we show that the microscopically derived Redfield equation (RE) violates complete positivity unless in extremely special cases. We then prove that imposing complete positivity and demanding preservation of local conservation laws enforces the Lindblad operators and the lamb-shift Hamiltonian to be 'local', i.e, to be supported only on the part of the system directly coupled to the bath. We then cast the problem of finding 'local' Lindblad QME which can show thermalization into a semidefinite program (SDP). We call this the thermalization optimization problem (TOP). For given system parameters and temperature, the solution of the TOP conclusively shows whether the desired type of QME is possible up to a given precision. Whenever possible, it also outputs a form for such a QME. For a XXZ chain of few qubits, fixing a reasonably high precision, we find that such a QME is impossible over a considerably wide parameter regime when only the first qubit is coupled to the bath. Remarkably, we find that when the first two qubits are attached to the bath, such a QME becomes possible over much of the same paramater regime, including a wide range of temperatures.

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“…Recent advances have extended the applicability of numerically exact process tensor techniques to many-body systems [63] and multiple environments [64]. Those techniques could be combined with the moment generating functional method we have described here to expose the dynamics of environments in such situations.…”

Section: Discussionmentioning

confidence: 99%

Using the Environment to Understand non-Markovian Open Quantum Systems

Gribben

Strathearn

Fux

et al. 2022

Quantum

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Tracing out the environmental degrees of freedom is a necessary procedure when simulating open quantum systems. While being an essential step in deriving a tractable master equation it represents a loss of information. In situations where there is strong interplay between the system and environmental degrees of freedom this loss makes understanding the dynamics challenging. These dynamics, when viewed in isolation, have no time-local description: they are non-Markovian and memory effects induce complex features that are difficult to interpret. To address this problem, we here show how to use system correlations, calculated by any method, to infer any correlation function of a Gaussian environment, so long as the coupling between system and environment is linear. This not only allows reconstruction of the full dynamics of both system and environment, but also opens avenues into studying the effect of a system on its environment. In order to obtain accurate bath dynamics, we exploit a numerically exact approach to simulating the system dynamics, which is based on the construction and contraction of a tensor network that represents the process tensor of this open quantum system. Using this we are able to find any system correlation function exactly. To demonstrate the applicability of our method we show how heat moves between different modes of a bosonic bath when coupled to a two-level system that is subject to an off-resonant drive.

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Tensor network simulation of chains of non-Markovian open quantum systems

Cited by 5 publications

References 66 publications

Time-evolving matrix product operator method and its applications in open quantum system

Time-evolving matrix product operator method and its applications in open quantum system

Searching for Lindbladians obeying local conservation laws and showing thermalization

Using the Environment to Understand non-Markovian Open Quantum Systems

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