Tensor network methods for non-perturbative dynamics of open quantum systems

• URL: http://arxiv.org/abs/2608.09850v1
• Date: Mon, 10 Aug 2026 17:08:24 GMT
• Title: Tensor network methods for non-perturbative dynamics of open quantum systems
• Abstract summary: tensor networks provide both a new formalism and a toolbox for overcoming previous computational bottlenecks.<n>We present these methods and discuss their commonalities and differences to paint a comprehensive view of the field.
• Score: 0.23670015772069983
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The description of open quantum system dynamics beyond the perturbative treatment (usually associated with Markovian master equations) is a computationally challenging task due to the unfavorable exponential scaling of memory kernels. Developed over recent decades in the context of quantum information and condensed matter, tensor networks provide both a new formalism and a toolbox for overcoming previous computational bottlenecks. This framework enables the formulation of non-perturbative, numerically exact methods for describing the dynamics of open quantum systems to controllable numerical accuracy. In this review, we present these methods and discuss their commonalities and differences to paint a comprehensive view of the field.

Related papers

• Learning Hidden Structures in Open Quantum Dynamics [78.4675086615913]
  We introduce a machine-learning approach for identifying hidden structural features of open quantum dynamics under restricted experimental access.<n>Our framework targets the inference of invariant algebraic structures underlying the effective Markovian evolution.<n>The feasibility of the approach is illustrated on multiple synthetic models and a waveguide quantum electrodynamics system.
  arXiv  Detail & Related papers  (2026-04-01T10:20:38Z)
• Non-perturbative switching rates in bistable open quantum systems: from driven Kerr oscillators to dissipative cat qubits [72.41778531863143]
  We use path integral techniques to predict the switching rate in a single-mode bistable open quantum system.<n>Our results open new avenues for exploring switching phenomena in multistable single- and many-body open quantum systems.
  arXiv  Detail & Related papers  (2025-07-24T18:01:36Z)
• Tensor Network Techniques for Quantum Computation [41.94295877935867]
  This book serves as an introductory yet thorough guide to tensor networks and their applications in quantum computation and quantum information.<n>In Part I, foundational topics are covered, including tensor structures and network representations like Matrix Product States (MPS) and Tree Networks (TTN)<n>Part II explores practical applications of tensor networks in simulating quantum dynamics.<n>A final chapter addresses the emerging role of "quantum magic" in tensor networks.
  arXiv  Detail & Related papers  (2025-03-06T13:31:17Z)
• The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learning [52.77024349608834]
  Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. Key issue is how to address the inherent non-linearity of classical deep learning. We introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning.
  arXiv  Detail & Related papers  (2022-12-22T16:06:24Z)
• Noisy Quantum Kernel Machines [58.09028887465797]
  An emerging class of quantum learning machines is that based on the paradigm of quantum kernels. We study how dissipation and decoherence affect their performance. We show that decoherence and dissipation can be seen as an implicit regularization for the quantum kernel machines.
  arXiv  Detail & Related papers  (2022-04-26T09:52:02Z)
• Description and complexity of Non-markovian open quantum dynamics [0.0]
  We identify a general class of non-Markovian memory kernels, described by complex-environment radon measures. We define their dynamics through a regularization procedure constructing the corresponding system-valued unitary groups. We establish that their dynamics can be efficiently approximated on quantum computers.
  arXiv  Detail & Related papers  (2022-04-14T13:01:58Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Dissipative quasi-particle picture for quadratic Markovian open quantum systems [0.0]
  Correlations between different regions of a quantum many-body system can be quantified. For closed systems, analytical and numerical tools can accurately capture the time-evolution of subsystem entropies. Here, we make progress by formulating a dissipative quasi-particle picture for a general class of noninteracting open quantum systems.
  arXiv  Detail & Related papers  (2021-06-22T18:10:47Z)
• Solving Quantum Master Equations with Deep Quantum Neural Networks [0.0]
  We use deep quantum feedforward neural networks capable of universal quantum computation to represent the mixed states for open quantum many-body systems. Owning to the special structure of the quantum networks, this approach enjoys a number of notable features, including the absence of barren plateaus.
  arXiv  Detail & Related papers  (2020-08-12T18:00:08Z)
• Rate operator unravelling for open quantum system dynamics [0.0]
  There is no unified framework to use quantum jumps to describe open system dynamics in any regime. We develop the Rate Operator Quantum Jump (ROQJ) approach, which applies to both Markovian and non-Markovian evolutions. ROQJ yields a rigorous measurement-scheme interpretation for a wide class of dynamics, including a set of master equations with negative decay rates.
  arXiv  Detail & Related papers  (2020-04-20T18:00:18Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.