A Universal Framework for Quantum Dissipation:Minimally Extended State Space and Exact Time-Local Dynamics

• URL: http://arxiv.org/abs/2307.16790v1
• Date: Mon, 31 Jul 2023 15:57:10 GMT
• Title: A Universal Framework for Quantum Dissipation:Minimally Extended State Space and Exact Time-Local Dynamics
• Authors: Meng Xu and Vasilii Vadimov and Malte Krug and J. T. Stockburger and J. Ankerhold
• Abstract summary: dynamics of open quantum systems is formulated in a minimally extended state space. Time-local evolution equation is created in a mixed Liouville-Fock space.
• Score: 5.221249829454763
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The dynamics of open quantum systems is formulated in a minimally extended state space comprising the degrees of freedom of a system of interest and a finite set of non-unitary, pure-state reservoir modes. This formal structure, derived from the Feynman-Vernon path integral for the reduced density, is shown to lead to an exact time-local evolution equation in a mixed Liouville-Fock space. The crucial ingredient is a mathematically consistent decomposition of the reservoir auto-correlation in terms of harmonic modes with complex-valued frequencies and amplitudes, which are obtained from any given spectral noise power of the physical reservoir. This formulation provides a universal framework to obtain a family of equivalent representations which are directly related to new and established schemes for efficient numerical simulations. By restricting some of the complex-valued mode parameters and performing linear transformations, we make connections to previous approaches, whose auxiliary degrees of freedom are thus revealed as restricted versions of the minimally extended state space presented here. From a practical perspective, the new framework offers a computational tool which combines numerical efficiency and accuracy with long time stability and broad applicability over the whole temperature range and also for strongly structured reservoir mode densities. It can thus deliver high precision data with modest computational resources and simulation times for actual quantum technological devices.

Related papers

• Space-time correlations in monitored kinetically constrained discrete-time quantum dynamics [0.0]
  We show a kinetically constrained many-body quantum system that has a natural implementation on Rydberg quantum simulators. Despite featuring an uncorrelated infinite-temperature average stationary state, the dynamics displays coexistence of fast and slow space-time regions. Our work establishes the large deviation framework for discrete-time open quantum many-body systems as a means to characterize complex dynamics and collective phenomena in quantum processors and simulators.
  arXiv  Detail & Related papers  (2024-08-19T10:24:07Z)
• 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)
• Taming Quantum Noise for Efficient Low Temperature Simulations of Open Quantum Systems [4.866728358750297]
  We introduce an effective treatment of quantum noise in frequency space by systematically clustering higher order Matsubara poles equivalent to an optimized rational decomposition. This leads to an elegant extension of the HEOM to arbitrary temperatures and very general reservoirs in combination with efficiency, high accuracy and long-time stability. As one highly non-trivial application, for the sub-ohmic spin-boson model at vanishing temperature the Shiba relation is quantitatively verified which predicts the long-time decay of correlation functions.
  arXiv  Detail & Related papers  (2022-02-08T18:46:11Z)
• Unraveling correlated material properties with noisy quantum computers: Natural orbitalized variational quantum eigensolving of extended impurity models within a slave-boson approach [0.0]
  We propose a method for computing space-resolved correlation properties of the two-dimensional Hubbard model within a quantum-classical embedding strategy. We solve a two-impurity embedded model requiring eight qubits with an advanced hybrid scheme on top of the Variational Quantum Eigensolver algorithm. This paves the way to a controlled solution of the Hubbard model with larger and larger embedded problems solved by quantum computers.
  arXiv  Detail & Related papers  (2021-08-24T14:58:14Z)
• Fast and differentiable simulation of driven quantum systems [58.720142291102135]
  We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods. We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
  arXiv  Detail & Related papers  (2020-12-16T21:43:38Z)
• Fast Gravitational Approach for Rigid Point Set Registration with Ordinary Differential Equations [79.71184760864507]
  This article introduces a new physics-based method for rigid point set alignment called Fast Gravitational Approach (FGA) In FGA, the source and target point sets are interpreted as rigid particle swarms with masses interacting in a globally multiply-linked manner while moving in a simulated gravitational force field. We show that the new method class has characteristics not found in previous alignment methods.
  arXiv  Detail & Related papers  (2020-09-28T15:05:39Z)
• Analytic expressions for the steady-state current with finite extended reservoirs [0.0]
  We derive analytical solutions, and associated analyses, for the steady-state current driven by finite reservoirs. We present a simplified and unified derivation of the non-interacting and many-body steady-state currents through arbitrary junctions.
  arXiv  Detail & Related papers  (2020-09-09T18:00:01Z)
• The role of boundary conditions in quantum computations of scattering observables [58.720142291102135]
  Quantum computing may offer the opportunity to simulate strongly-interacting field theories, such as quantum chromodynamics, with physical time evolution. As with present-day calculations, quantum computation strategies still require the restriction to a finite system size. We quantify the volume effects for various $1+1$D Minkowski-signature quantities and show that these can be a significant source of systematic uncertainty.
  arXiv  Detail & Related papers  (2020-07-01T17:43:11Z)
• Method of spectral Green functions in driven open quantum dynamics [77.34726150561087]
  A novel method based on spectral Green functions is presented for the simulation of driven open quantum dynamics. The formalism shows remarkable analogies to the use of Green functions in quantum field theory. The method dramatically reduces computational cost compared with simulations based on solving the full master equation.
  arXiv  Detail & Related papers  (2020-06-04T09:41:08Z)
• Towards quantum simulation of Sachdev-Ye-Kitaev model [5.931069258860319]
  We study a simplified version of the Sachdev-Ye-Kitaev (SYK) model with real interactions by exact diagonalization. A quantum phase transition from a chaotic state to an integrable state is observed by increasing the discrete separation.
  arXiv  Detail & Related papers  (2020-03-03T14:18:07Z)
• Gaussian Process States: A data-driven representation of quantum many-body physics [59.7232780552418]
  We present a novel, non-parametric form for compactly representing entangled many-body quantum states. The state is found to be highly compact, systematically improvable and efficient to sample. It is also proven to be a universal approximator' for quantum states, able to capture any entangled many-body state with increasing data set size.
  arXiv  Detail & Related papers  (2020-02-27T15:54:44Z)

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.