The Bold-Thin-Bold Diagrammatic Monte Carlo Method for Open Quantum Systems

• URL: http://arxiv.org/abs/2205.10896v1
• Date: Sun, 22 May 2022 18:17:23 GMT
• Title: The Bold-Thin-Bold Diagrammatic Monte Carlo Method for Open Quantum Systems
• Authors: Zhenning Cai, Geshuo Wang, Siyao Yang
• Abstract summary: We present two diagrammatic Monte Carlo methods for quantum systems coupled with harmonic baths. The underlying mechanism of the governing equations associated with the two methods lies in the recurrence relation of the path integrals. Compared with the algorithms therein, our methods show better performance in terms of computational efficiency and memory cost.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present two diagrammatic Monte Carlo methods for quantum systems coupled with harmonic baths, whose dynamics are described by integro-differential equations. The first approach can be considered as a reformulation of Dyson series, and the second one, called "bold-thin-bold diagrammatic Monte Carlo", is based on resummation of the diagrams in the Dyson series to accelerate its convergence. The underlying mechanism of the governing equations associated with the two methods lies in the recurrence relation of the path integrals, which is the most costly part in the numerical methods. The proposed algorithms give an extension to the work ["Fast algorithms of bath calculations in simulations of quantum system-bath dynamics", Computer Physics Communications, to appear], where the algorithms are designed based on reusing the previous calculations of bath influence functionals. Compared with the algorithms therein, our methods further include the reuse of system associated functionals and show better performance in terms of computational efficiency and memory cost. We demonstrate the two methods in the framework of spin-boson model, and numerical experiments are carried out to verify the validity of the methods.

Related papers

• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
  We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment. We find sufficient conditions under which dynamical decoupling works for such systems. Our bounds reproduce the correct scaling in various relevant system parameters.
  arXiv  Detail & Related papers  (2024-09-24T04:58:28Z)
• Reweight-annealing method for evaluating the partition function via quantum Monte Carlo calculations [4.595034707642593]
  We present an unbiased but low-technical-barrier algorithm within the quantum Monte Carlo framework, which has exceptionally high accuracy and no systemic error. This method can be widely used in both classical and quantum Monte Carlo simulations and is easy to be parallelized on computer.
  arXiv  Detail & Related papers  (2024-03-13T15:54:57Z)
• Solving Systems of Linear Equations: HHL from a Tensor Networks Perspective [39.58317527488534]
  We present an algorithm for solving systems of linear equations based on the HHL algorithm with a novel qudits methodology. We perform a quantum-inspired version on tensor networks, taking advantage of their ability to perform non-unitary operations such as projection.
  arXiv  Detail & Related papers  (2023-09-11T08:18:41Z)
• Real-Time Simulation of Open Quantum Spin Chains with Inchworm Method [0.0]
  We study the real-time simulation of open quantum systems, where the system is modeled by a spin chain, with each spin associated with its own harmonic bath. Our method couples the inchworm method for the spin-boson model and the modular path integral methodology for spin systems.
  arXiv  Detail & Related papers  (2023-07-08T07:46:39Z)
• An Optimization-based Deep Equilibrium Model for Hyperspectral Image Deconvolution with Convergence Guarantees [71.57324258813675]
  We propose a novel methodology for addressing the hyperspectral image deconvolution problem. A new optimization problem is formulated, leveraging a learnable regularizer in the form of a neural network. The derived iterative solver is then expressed as a fixed-point calculation problem within the Deep Equilibrium framework.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• Counting Phases and Faces Using Bayesian Thermodynamic Integration [77.34726150561087]
  We introduce a new approach to reconstruction of the thermodynamic functions and phase boundaries in two-parametric statistical mechanics systems. We use the proposed approach to accurately reconstruct the partition functions and phase diagrams of the Ising model and the exactly solvable non-equilibrium TASEP.
  arXiv  Detail & Related papers  (2022-05-18T17:11:23Z)
• Exact solutions for the time-evolution of quantum spin systems under arbitrary waveforms using algebraic graph theory [0.0966840768820136]
  A general approach is presented that offers exact analytical solutions for the time-evolution of quantum spin systems during parametric waveforms of arbitrary functions of time. The proposed method consistently outperforms conventional numerical methods, including ODE and piecewise-constant propagator approximations.
  arXiv  Detail & Related papers  (2022-05-10T22:34:13Z)
• Fast Algorithms of Bath Calculations in Simulations of Quantum System-Bath Dynamics [5.989041429080286]
  We present fast algorithms for the summation of Dyson series and the inchworm Monte Carlo method for quantum systems. The algorithms are based on evolving the integro-differential equations where the most expensive part comes from the computation of bath influence functionals. It is proven that the proposed fast algorithms reduce the number of such calculations by a factor of $O(N)$, where $N$ is the total number of time steps.
  arXiv  Detail & Related papers  (2022-02-13T03:00:46Z)
• 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)
• Quantum-Classical Hybrid Algorithm for the Simulation of All-Electron Correlation [58.720142291102135]
  We present a novel hybrid-classical algorithm that computes a molecule's all-electron energy and properties on the classical computer. We demonstrate the ability of the quantum-classical hybrid algorithms to achieve chemically relevant results and accuracy on currently available quantum computers.
  arXiv  Detail & Related papers  (2021-06-22T18:00:00Z)
• Inclusion-Exclusion Principle for Open Quantum Systems with Bosonic Bath [5.989041429080286]
  We present two fast algorithms which apply inclusion-exclusion principle to sum over bosonic diagrams in bare diagrammatic quantum Monte Carlo (dQMC) and inchworm Monte Carlo method, respectively. In the case of inchworm Monte Carlo, the proposed fast algorithm gives an extension to the work ["Inclusion-exclusion principle for many-body diagrammatics", Phys. Rev. B, 98:115152, 2018] from fermionic to bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T02:34:29Z)

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.