Constructing k-local parent Lindbladians for matrix product density operators

• URL: http://arxiv.org/abs/2110.13134v1
• Date: Mon, 25 Oct 2021 17:59:08 GMT
• Title: Constructing k-local parent Lindbladians for matrix product density operators
• Authors: Dmytro Bondarenko
• Abstract summary: Matrix product density operators (MPDOs) are an important class of states with interesting properties. We develop an algorithm that determines if a given (small) linear subspace of MPDOs can be the stable space for some frustration free Lindbladian.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Matrix product density operators (MPDOs) are an important class of states with interesting properties. Consequently, it is important to understand how to prepare these states experimentally. One possible way to do this is to design an open system that evolves only towards desired states. A Markovian evolution of a quantum mechanical system can be generally described by a Lindbladian. In this work we develop an algorithm that for a given (small) linear subspace of MPDOs determines if this subspace can be the stable space for some frustration free Lindbladian consisting of only local terms and, if so, outputs a suitable Lindbladian.

Related papers

• Lindbladian reverse engineering for general non-equilibrium steady states: A scalable null-space approach [49.1574468325115]
  We introduce a method for reconstructing the corresponding Lindbaldian master equation given any target NESS. The kernel (null-space) of the correlation matrix corresponds to Lindbladian solutions. We illustrate the method in different systems, ranging from bosonic Gaussian to dissipative-driven collective spins.
  arXiv  Detail & Related papers  (2024-08-09T19:00:18Z)
• Efficient conversion from fermionic Gaussian states to matrix product states [48.225436651971805]
  We propose a highly efficient algorithm that converts fermionic Gaussian states to matrix product states. It can be formulated for finite-size systems without translation invariance, but becomes particularly appealing when applied to infinite systems. The potential of our method is demonstrated by numerical calculations in two chiral spin liquids.
  arXiv  Detail & Related papers  (2024-08-02T10:15:26Z)
• Wave Matrix Lindbladization II: General Lindbladians, Linear Combinations, and Polynomials [4.62316736194615]
  We investigate the problem of simulating open system dynamics governed by the well-known Lindblad master equation. We introduce an input model in which Lindblad operators are encoded into pure quantum states, called program states. We also introduce a method, called wave matrix Lindbladization, for simulating Lindbladian evolution by means of interacting the system of interest with these program states.
  arXiv  Detail & Related papers  (2023-09-25T18:20:00Z)
• Vectorization of the density matrix and quantum simulation of the von Neumann equation of time-dependent Hamiltonians [65.268245109828]
  We develop a general framework to linearize the von-Neumann equation rendering it in a suitable form for quantum simulations. We show that one of these linearizations of the von-Neumann equation corresponds to the standard case in which the state vector becomes the column stacked elements of the density matrix. A quantum algorithm to simulate the dynamics of the density matrix is proposed.
  arXiv  Detail & Related papers  (2023-06-14T23:08:51Z)
• Lindbladian-Induced Alignment in Quantum Measurements [0.0]
  An expression of the Lindbladian form is proposed that ensures an unambiguous time-continuous reduction of the initial system-pointer wave-packet to one in which the readings and the observable's values are aligned. The jump operators are in the basis of the observables, with uniquely determined parameters derived from the measurement set-up.
  arXiv  Detail & Related papers  (2023-01-06T09:46:57Z)
• Area law for steady states of detailed-balance local Lindbladians [0.0]
  We study steady-states of quantum Markovian processes whose evolution is described by local Lindbladians. We show that under mild assumptions on the Lindbladian terms, the Lindbladian can be mapped to a local Hamiltonian on a doubled Hilbert space that has the same spectrum, and a ground state that is the vectorization of $sigma1/2$.
  arXiv  Detail & Related papers  (2022-12-20T08:09:41Z)
• The vacuum provides quantum advantage to otherwise simulatable architectures [49.1574468325115]
  We consider a computational model composed of ideal Gottesman-Kitaev-Preskill stabilizer states. We provide an algorithm to calculate the probability density function of the measurement outcomes.
  arXiv  Detail & Related papers  (2022-05-19T18:03:17Z)
• Direct solution of multiple excitations in a matrix product state with block Lanczos [62.997667081978825]
  We introduce the multi-targeted density matrix renormalization group method that acts on a bundled matrix product state, holding many excitations. A large number of excitations can be obtained at a small bond dimension with highly reliable local observables throughout the chain.
  arXiv  Detail & Related papers  (2021-09-16T18:36:36Z)
• Non-Markovian Stochastic Schr\"odinger Equation: Matrix Product State Approach to the Hierarchy of Pure States [65.25197248984445]
  We derive a hierarchy of matrix product states (HOMPS) for non-Markovian dynamics in open finite temperature. The validity and efficiency of HOMPS is demonstrated for the spin-boson model and long chains where each site is coupled to a structured, strongly non-Markovian environment.
  arXiv  Detail & Related papers  (2021-09-14T01:47:30Z)
• Efficient simulation of sparse Markovian quantum dynamics [13.996412562440891]
  We give the first efficient quantum algorithms for simulating Markovian quantum dynamics generated by Lindbladians that are not necessarily local. First, we show how to simulate Lindbladians that act within small invariant subspaces using a quantum algorithm to implement sparse Stinespring isometries. Second, we develop a method for simulating sparse Lindblad operators by concatenating a sequence of short-time evolutions.
  arXiv  Detail & Related papers  (2016-11-17T02:55:26Z)

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.