Wave Matrix Lindbladization II: General Lindbladians, Linear Combinations, and Polynomials

• URL: http://arxiv.org/abs/2309.14453v1
• Date: Mon, 25 Sep 2023 18:20:00 GMT
• Title: Wave Matrix Lindbladization II: General Lindbladians, Linear Combinations, and Polynomials
• Authors: Dhrumil Patel and Mark M. Wilde
• Abstract summary: 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.
• Score: 4.62316736194615
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we investigate the problem of simulating open system dynamics governed by the well-known Lindblad master equation. In our prequel paper, we introduced an input model in which Lindblad operators are encoded into pure quantum states, called program states, and we also introduced a method, called wave matrix Lindbladization, for simulating Lindbladian evolution by means of interacting the system of interest with these program states. Therein, we focused on a simple case in which the Lindbladian consists of only one Lindblad operator and a Hamiltonian. Here, we extend the method to simulating general Lindbladians and other cases in which a Lindblad operator is expressed as a linear combination or a polynomial of the operators encoded into the program states. We propose quantum algorithms for all these cases and also investigate their sample complexity, i.e., the number of program states needed to simulate a given Lindbladian evolution approximately. Finally, we demonstrate that our quantum algorithms provide an efficient route for simulating Lindbladian evolution relative to full tomography of encoded operators, by proving that the sample complexity for tomography is dependent on the dimension of the system, whereas the sample complexity of wave matrix Lindbladization is dimension independent.

Related papers

• Effective (Floquet) Lindblad generators from spectral unwinding [44.99833362998488]
  We show that Floquet theory can significantly facilitate the search for an effective generator by making use of Floquet theory. Our results are relevant for engineering Floquet Lindbladians in complex many-body systems.
  arXiv  Detail & Related papers  (2024-09-25T16:32:01Z)
• 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)
• A quantum algorithm to simulate Lindblad master equations [1.104960878651584]
  We present a quantum algorithm for simulating a family of Markovian master equations. Our approach employs a second-order product formula for the Lindblad master equation.
  arXiv  Detail & Related papers  (2024-06-18T16:08:11Z)
• Computational-Statistical Gaps in Gaussian Single-Index Models [77.1473134227844]
  Single-Index Models are high-dimensional regression problems with planted structure. We show that computationally efficient algorithms, both within the Statistical Query (SQ) and the Low-Degree Polynomial (LDP) framework, necessarily require $Omega(dkstar/2)$ samples.
  arXiv  Detail & Related papers  (2024-03-08T18:50:19Z)
• Simulating Open Quantum Systems Using Hamiltonian Simulations [4.328210085579236]
  We present a novel method to simulate the Lindblad equation, drawing on the relationship between Lindblad dynamics, differential equations, and Hamiltonian simulations. We derive a sequence of unitary dynamics in an enlarged Hilbert space that can approximate the Lindblad dynamics up to an arbitrarily high order. This unitary representation can then be simulated using a quantum circuit that involves only Hamiltonian simulation and tracing out the ancilla qubits.
  arXiv  Detail & Related papers  (2023-11-27T04:38:13Z)
• 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)
• 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)
• Constructing k-local parent Lindbladians for matrix product density operators [0.0]
  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.
  arXiv  Detail & Related papers  (2021-10-25T17:59:08Z)
• Einselection from incompatible decoherence channels [62.997667081978825]
  We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators. We show that Fock states remain the most robust states to decoherence up to a critical coupling.
  arXiv  Detail & Related papers  (2020-01-29T14:15:19Z)
• 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.