Unified Framework for Open Quantum Dynamics with Memory

• URL: http://arxiv.org/abs/2312.13233v4
• Date: Tue, 4 Jun 2024 00:49:53 GMT
• Title: Unified Framework for Open Quantum Dynamics with Memory
• Authors: Felix Ivander, Lachlan P. Lindoy, Joonho Lee,
• Abstract summary: We show the formal connection between the memory kernel and the influence functions. We also show how approximate path integral methods can be understood in terms of approximate memory kernels. The insights we provide will significantly advance the understanding of non-Markovian dynamics.
• Score: 1.639482556214273
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Studies of the dynamics of a quantum system coupled to baths are typically performed by utilizing the Nakajima-Zwanzig memory kernel (${\mathcal{K}}$) or the influence functions ($\mathbf{{I}}$), especially when the dynamics exhibit memory effects (i.e., non-Markovian). Despite their significance, the formal connection between the memory kernel and the influence functions has not been explicitly made. We reveal their relation by inspecting the system propagator for a broad class of problems where an $N$-level system is linearly coupled to Gaussian baths (bosonic, fermionic, and spin.) With this connection, we also show how approximate path integral methods can be understood in terms of approximate memory kernels. For a certain class of open quantum system problems, we devised a non-perturbative, diagrammatic approach to construct ${\mathcal{K}}$ from $\mathbf{{I}}$ for (driven) systems interacting with Gaussian baths without the use of any projection-free dynamics inputs required by standard approaches. Lastly, we demonstrate a Hamiltonian learning procedure to extract the bath spectral density from a set of reduced system trajectories obtained experimentally or by numerically exact methods, opening new avenues in quantum sensing and engineering. The insights we provide in this work will significantly advance the understanding of non-Markovian dynamics, and they will be an important stepping stone for theoretical and experimental developments in this area.

Related papers

• Unified analysis of non-Markovian open quantum systems in Gaussian environment using superoperator formalism [4.504072151606679]
  We present perturbative error bounds for the non-Markovian dynamics of observables in open quantum systems. This extends the work of [Mascherpa et al., Phys. Rev. Lett. 118, 100401, 2017], which demonstrated qualitatively tighter bounds over the standard Gr"onwall-type analysis.
  arXiv  Detail & Related papers  (2024-11-13T16:19:32Z)
• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• Bexcitonics: Quasi-particle approach to open quantum dynamics [0.0]
  We develop a quasiparticle approach to capture the dynamics of open quantum systems coupled to bosonic thermal baths. Bexcitonic properties offer a coarse-grained view of the correlated system-bath dynamics and its numerical convergence.
  arXiv  Detail & Related papers  (2024-01-19T22:29:13Z)
• Detecting Quantum Anomalies in Open Systems [0.0]
  We introduce a novel and experimentally feasible approach to detect quantum anomalies in open systems. We numerically demonstrate the unavoidable singular behavior of $exp(rmitheta Sz_rm tot)$ for half-integer spin chains.
  arXiv  Detail & Related papers  (2023-12-18T13:29:07Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• Correspondence between open bosonic systems and stochastic differential equations [77.34726150561087]
  We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment. A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
  arXiv  Detail & Related papers  (2023-02-03T19:17:37Z)
• Scrambling of Algebras in Open Quantum Systems [0.0]
  We introduce an algebraic OTOC ($mathcalA$-OTOC) that allows us to study information scrambling of quantum subsystems under quantum channels. For closed quantum systems, this framework was recently employed to unify quantum information-theoretic notions of operator entanglement, coherence-generating power, and Loschmidt echo. Our numerical results reveal connections with many-body scars and the stability of decoherence-free subspaces.
  arXiv  Detail & Related papers  (2022-06-04T17:54:41Z)
• 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)
• 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)
• Tracing Information Flow from Open Quantum Systems [52.77024349608834]
  We use photons in a waveguide array to implement a quantum simulation of the coupling of a qubit with a low-dimensional discrete environment. Using the trace distance between quantum states as a measure of information, we analyze different types of information transfer.
  arXiv  Detail & Related papers  (2021-03-22T16:38:31Z)
• 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.