Hermitian-preserving ansatz and variational open quantum eigensolver
- URL: http://arxiv.org/abs/2403.03478v2
- Date: Sat, 25 May 2024 07:16:03 GMT
- Title: Hermitian-preserving ansatz and variational open quantum eigensolver
- Authors: Zhong-Xia Shang,
- Abstract summary: We propose a new variational quantum algorithm named Variational Open Quantum Eigensolver (VOQE)
In VOQE, density matrices of mixed states are represented by pure states in doubled Hilbert space.
We show the workflow of VOQE on solving steady states of the LMEs of the driven XXZ model and implement VOQE to solve the spectrum of the non-Hermitian Hamiltonians of the Ising spin chain in an imaginary field.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We propose a new variational quantum algorithm named Variational Open Quantum Eigensolver (VOQE) for solving steady states of open quantum systems described by either Lindblad master equations or non-Hermitian Hamiltonians. In VOQE, density matrices of mixed states are represented by pure states in doubled Hilbert space. We give a framework for building circuit ansatz which we call the Hermitian-preserving ansatz (HPA) to restrict the searching space. We also give a method to efficiently measure the operators' expectation values by post-selection measurements. We show the workflow of VOQE on solving steady states of the LMEs of the driven XXZ model and implement VOQE to solve the spectrum of the non-Hermitian Hamiltonians of the Ising spin chain in an imaginary field.
Related papers
- Path-Integral Formulation of Truncated Wigner Approximation for Bosonic Markovian Open Quantum Systems [0.0]
The Wigner approximation (TWA) enables us to calculate bosonic quantum many-body dynamics while accounting for the effects of quantum fluctuations.
We numerically confirm that the time evolution of physical quantities and the non-equal time correlation functions obtained in our formulation agree well with the exact ones in the numerically solvable models.
arXiv Detail & Related papers (2024-05-18T04:27:32Z) - Ground or Excited State: a State-Specific Variational Quantum
Eigensolver for Them All [0.0]
Variational Quantum Eigensolver (VQE) provides a lucrative platform to determine molecular energetics in quantum devices.
We propose a unified VQE framework that treats the ground and excited states in the same footings.
We introduce the notion of totally symmetric, spin-scalar unitary which maintains the purity of the reference at each step of the optimization.
arXiv Detail & Related papers (2023-08-21T13:39:58Z) - Wasserstein Quantum Monte Carlo: A Novel Approach for Solving the
Quantum Many-Body Schr\"odinger Equation [56.9919517199927]
"Wasserstein Quantum Monte Carlo" (WQMC) uses the gradient flow induced by the Wasserstein metric, rather than Fisher-Rao metric, and corresponds to transporting the probability mass, rather than teleporting it.
We demonstrate empirically that the dynamics of WQMC results in faster convergence to the ground state of molecular systems.
arXiv Detail & Related papers (2023-07-06T17:54:08Z) - Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent
and Incoherent Photons Found with Gradient Search [77.34726150561087]
We consider an environment formed by incoherent photons as a resource for controlling open quantum systems via an incoherent control.
We exploit a coherent control in the Hamiltonian and an incoherent control in the dissipator which induces the time-dependent decoherence rates.
arXiv Detail & Related papers (2023-02-28T07:36:02Z) - Bootstrapping the gap in quantum spin systems [0.7106986689736826]
We use the equations of motion to develop an analogue of the conformal block expansion for matrix elements.
The method can be applied to any quantum mechanical system with a local Hamiltonian.
arXiv Detail & Related papers (2022-11-07T19:07:29Z) - Canonically consistent quantum master equation [68.8204255655161]
We put forth a new class of quantum master equations that correctly reproduce the state of an open quantum system beyond the infinitesimally weak system-bath coupling limit.
Our method is based on incorporating the knowledge of the reduced steady state into its dynamics.
arXiv Detail & Related papers (2022-05-25T15:22:52Z) - Fermionic approach to variational quantum simulation of Kitaev spin
models [50.92854230325576]
Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions.
We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation.
We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
arXiv Detail & Related papers (2022-04-11T18:00:01Z) - Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables.
In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
arXiv Detail & Related papers (2021-02-18T20:55:04Z) - 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) - Variational Quantum Algorithms for Steady States of Open Quantum Systems [2.740982822457262]
We propose a variational quantum algorithm to find the steady state of open quantum systems.
The fidelity between the optimal mixed state and the true steady state is over 99%.
This algorithm is derived from the natural idea of expressing mixed states with purification.
arXiv Detail & Related papers (2020-01-08T14:47:36Z)
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.