Genetic-Multi-initial Generalized VQE: Advanced VQE method using Genetic Algorithms then Local Search

• URL: http://arxiv.org/abs/2109.02009v1
• Date: Sun, 5 Sep 2021 06:52:57 GMT
• Title: Genetic-Multi-initial Generalized VQE: Advanced VQE method using Genetic Algorithms then Local Search
• Authors: Hikaru Wakaura and Takao Tomono
• Abstract summary: Variational-Quantum-Eigensolver (VQE) method has been known as the method of chemical calculation using quantum computers and classical computers. We performed the calculation of ground and excited states and their energies on hydrogen molecule by modified GA then LS. We obtained a result that Newton method can derive ground and excited states and their energies in higher accuracy than others.
• Score: 1.2691047660244335
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Variational-Quantum-Eigensolver (VQE) method has been known as the method of chemical calculation using quantum computers and classical computers. This method also can derive the energy levels of excited states by Variational-Quantum-Deflation (VQD) method. Although, parameter landscape of excited state have many local minimums that the results are tend to be trapped by them. Therefore, we apply Genetic Algorithms then Local Search (GA then LS) as the classical optimizer of VQE method. We performed the calculation of ground and excited states and their energies on hydrogen molecule by modified GA then LS. Here we uses Powell, Broyden-Fletcher-Goldfarb-Shanno, Nelder-Mead and Newton method as an optimizer of LS. We obtained the result that Newton method can derive ground and excited states and their energies in higher accuracy than others. We are predicting that newton method is more effective for seed up and be more accurate.

Related papers

• Application of Langevin Dynamics to Advance the Quantum Natural Gradient Optimization Algorithm [47.47843839099175]
  A Quantum Natural Gradient (QNG) algorithm for optimization of variational quantum circuits has been proposed recently. In this study, we employ the Langevin equation with a QNG force to demonstrate that its discrete-time solution gives a generalized form, which we call Momentum-QNG.
  arXiv  Detail & Related papers  (2024-09-03T15:21:16Z)
• 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)
• Folded Spectrum VQE : A quantum computing method for the calculation of molecular excited states [0.0]
  Folded Spectrum (FS) method as extension to Variational Quantum Eigensolver (VQE) algorithm for computation of molecular excited states. Inspired by the variance-based methods from the Quantum Monte Carlo literature, the FS method minimizes the energy variance, thus requiring a computationally expensive squared Hamiltonian. We apply the FS-VQE method to small molecules for a significant reduction of the computational cost.
  arXiv  Detail & Related papers  (2023-05-08T15:34:56Z)
• Twisted hybrid algorithms for combinatorial optimization [68.8204255655161]
  Proposed hybrid algorithms encode a cost function into a problem Hamiltonian and optimize its energy by varying over a set of states with low circuit complexity. We show that for levels $p=2,ldots, 6$, the level $p$ can be reduced by one while roughly maintaining the expected approximation ratio.
  arXiv  Detail & Related papers  (2022-03-01T19:47:16Z)
• Noisy Bayesian optimization for variational quantum eigensolvers [0.0]
  The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm used to find the ground state of a Hamiltonian. This work proposes an implementation of GPR and BO specifically tailored to perform VQE on quantum computers already available today.
  arXiv  Detail & Related papers  (2021-12-01T11:28:55Z)
• Evaluation on Genetic Algorithms as an optimizer of Variational Quantum Eigensolver(VQE) method [1.0742675209112622]
  Variational-Quantum-Eigensolver(VQE) method on a quantum computer is a well-known hybrid algorithm to solve the eigenstates and eigenvalues that uses both quantum and classical computers. This method has the potential to solve quantum chemical simulation including polymer and complex optimization problems that are never able to be solved in a realistic time.
  arXiv  Detail & Related papers  (2021-10-14T15:10:16Z)
• Using gradient-based algorithms to determine ground state energies on a quantum computer [0.0]
  Variational algorithms are promising candidates to be implemented on near-term quantum computers. We study how different methods for obtaining the gradient, specifically the finite-difference and the parameter-shift rule, are affected by shot noise and noise of the quantum computer.
  arXiv  Detail & Related papers  (2021-09-17T09:12:43Z)
• Frame Superposition Cluster: The method to derive the transition matrices in high accuracy [1.2691047660244335]
  Variational Quantum Eigensolver (VQE) method is the way to derive the wave functions from their eigen energies using quantum computers. The method to calculate the off diagonal element of observables between two states derived by VQE method requires large numbers of gate operations. We proposed the novel method to drive the superposition state between the states the derived by VQE method.
  arXiv  Detail & Related papers  (2021-07-07T02:16:00Z)
• A Discrete Variational Derivation of Accelerated Methods in Optimization [68.8204255655161]
  We introduce variational which allow us to derive different methods for optimization. We derive two families of optimization methods in one-to-one correspondence. The preservation of symplecticity of autonomous systems occurs here solely on the fibers.
  arXiv  Detail & Related papers  (2021-06-04T20:21:53Z)
• Benchmarking adaptive variational quantum eigensolvers [63.277656713454284]
  We benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves. We find both methods provide good estimates of the energy and ground state. gradient-based optimization is more economical and delivers superior performance than analogous simulations carried out with gradient-frees.
  arXiv  Detail & Related papers  (2020-11-02T19:52:04Z)
• Local optimization on pure Gaussian state manifolds [63.76263875368856]
  We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm. The method is based on notions of descent gradient attuned to the local geometry. We use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states.
  arXiv  Detail & Related papers  (2020-09-24T18:00:36Z)

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.