Many-Body-Expansion Based on Variational Quantum Eigensolver and Deflation for Dynamical Correlation

• URL: http://arxiv.org/abs/2310.03954v1
• Date: Fri, 6 Oct 2023 00:33:30 GMT
• Title: Many-Body-Expansion Based on Variational Quantum Eigensolver and Deflation for Dynamical Correlation
• Authors: Enhua Xu, Yuma Shimomoto, Seiichiro L. Ten-no, Takashi Tsuchimochi
• Abstract summary: We utilize the many-body expansion (MBE) framework to decompose electronic structures into fragments by incrementing the virtual orbitals. Our work aims to accurately solve the ground and excited state energies of each fragment using the variational quantum eigensolver and deflation algorithms.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this study, we utilize the many-body expansion (MBE) framework to decompose electronic structures into fragments by incrementing the virtual orbitals. Our work aims to accurately solve the ground and excited state energies of each fragment using the variational quantum eigensolver and deflation algorithms. Although our approach is primarily based on unitary coupled cluster singles and doubles (UCCSD) and a generalization thereof, we also introduce modifications and approximations to conserve quantum resources in MBE by partially generalizing the UCCSD operator and neglecting the relaxation of the reference states. As a proof of concept, we investigate the potential energy surfaces for the bond-breaking processes of the ground state of two molecules ($\rm H_2O$ and $\rm N_2$) and calculate the ground and excited state energies of three molecules (LiH, CH$^+$, and $\rm H_2O$). The results demonstrate that our approach can, in principle, provide reliable descriptions in all tests, including strongly correlated systems, when appropriate approximations are chosen. Additionally, we perform model simulations to investigate the impact of shot noise on the total MBE energy and show that precise energy estimation is crucial for lower-order MBE fragments.

Related papers

• Thermalization and Criticality on an Analog-Digital Quantum Simulator [133.58336306417294]
  We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions. We digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization.
  arXiv  Detail & Related papers  (2024-05-27T17:40:39Z)
• Neutron-nucleus dynamics simulations for quantum computers [49.369935809497214]
  We develop a novel quantum algorithm for neutron-nucleus simulations with general potentials. It provides acceptable bound-state energies even in the presence of noise, through the noise-resilient training method. We introduce a new commutativity scheme called distance-grouped commutativity (DGC) and compare its performance with the well-known qubit-commutativity scheme.
  arXiv  Detail & Related papers  (2024-02-22T16:33:48Z)
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive [52.77024349608834]
  We present a self consistent field approach (SCF) within the Adaptive Derivative-Assembled Problem-Assembled Ansatz Variational Eigensolver (ADAPTVQE) This framework is used for efficient quantum simulations of chemical systems on nearterm quantum computers.
  arXiv  Detail & Related papers  (2022-12-21T23:15:17Z)
• A pathway to accurate potential energy curves on NISQ devices [0.483420384410068]
  We present a practical workflow to compute the potential energy curve of a hydrogen molecule on quantum devices. The proposed approach uses an extrapolation scheme to deliver, with only few qubits, full configuration interaction results close to the basis-set limit. We show that despite the limitations imposed by the noisy nature of simulated quantum hardware, it is possible to recover realistic electronic correlation values.
  arXiv  Detail & Related papers  (2022-09-19T11:32:43Z)
• Efficient Quantum Analytic Nuclear Gradients with Double Factorization [0.0]
  We report a Lagrangian-based approach for evaluating relaxed one- and two-particle reduced density matrices from double factorized Hamiltonians. We demonstrate the accuracy and feasibility of our Lagrangian-based approach to recover all off-diagonal density matrix elements in classically-simulated examples.
  arXiv  Detail & Related papers  (2022-07-26T18:47:48Z)
• Assessment of the variational quantum eigensolver: application to the Heisenberg model [0.0]
  We present and analyze large-scale simulation results of a hybrid quantum-classical variational method to calculate the ground state energy of the anti-ferromagnetic Heisenberg model. We predict that a fully functional quantum computer with 100 qubits can calculate the ground state energy with a relatively small error.
  arXiv  Detail & Related papers  (2022-01-13T16:49:04Z)
• Numerical Simulations of Noisy Quantum Circuits for Computational Chemistry [51.827942608832025]
  Near-term quantum computers can calculate the ground-state properties of small molecules. We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
  arXiv  Detail & Related papers  (2021-12-31T16:33:10Z)
• Analytical nonadiabatic couplings and gradients within the state-averaged orbital-optimized variational quantum eigensolver [0.0]
  We introduce several technical and analytical extensions to our recent state-averaged orbital-optimized variational quantum eigensolver (SA-OO-VQE) algorithm. Motivated by the limitations of current quantum computers, the first extension consists in an efficient state-resolution procedure to find the SA-OO-VQE eigenstates. The second extension allows for the estimation of analytical gradients and non-adiabatic couplings.
  arXiv  Detail & Related papers  (2021-09-09T22:38:56Z)
• Quantum-Classical Hybrid Algorithm for the Simulation of All-Electron Correlation [58.720142291102135]
  We present a novel hybrid-classical algorithm that computes a molecule's all-electron energy and properties on the classical computer. We demonstrate the ability of the quantum-classical hybrid algorithms to achieve chemically relevant results and accuracy on currently available quantum computers.
  arXiv  Detail & Related papers  (2021-06-22T18:00:00Z)
• 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)
• Resource Efficient Chemistry on Quantum Computers with the Variational Quantum Eigensolver and The Double Unitary Coupled-Cluster approach [0.0]
  We show that the number of qubits scales linearly with the size of molecular basis. We employ the double unitary coupled-cluster (DUCC) method to effectively downfold correlation effects into the reduced-size orbital space. Using downfolding techniques, we demonstrate that properly constructed effective Hamiltonians can capture the effect of the whole orbital space in small-size active spaces.
  arXiv  Detail & Related papers  (2020-04-16T15:59:15Z)

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.