Periodic Plane-Wave Electronic Structure Calculations on Quantum Computers

• URL: http://arxiv.org/abs/2208.04444v2
• Date: Mon, 17 Oct 2022 13:28:58 GMT
• Title: Periodic Plane-Wave Electronic Structure Calculations on Quantum Computers
• Authors: Duo Song, Nicholas P. Bauman, Guen Prawiroatmodjo, Bo Peng, Cassandra Granade, Kevin M. Rosso, Guang Hao Low, Martin Roetteler, Karol Kowalski, Eric J. Bylaska
• Abstract summary: We develop a procedure for defining virtual spaces, and the periodic one-electron and two-electron integrals, for plane-wave second quantized Hamiltonians. This work is an extension to periodic systems of algorithms in which the virtual spaces were generated by optimizing orbitals from small pairwise CI Hamiltonians.
• Score: 13.19719148303433
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A procedure for defining virtual spaces, and the periodic one-electron and two-electron integrals, for plane-wave second quantized Hamiltonians has been developed and demonstrated using full configuration interaction (FCI) simulations and variational quantum eigensolver (VQE) circuits on Quantinuum's ion trap quantum computers accessed through Microsoft's Azure Quantum service. This work is an extension to periodic systems of a new class of algorithms in which the virtual spaces were generated by optimizing orbitals from small pairwise CI Hamiltonians, which we term as correlation optimized virtual orbitals with the abbreviation COVOs. In this extension, the integration of the first Brillouin zone is automatically incorporated into the two-electron integrals. With these procedures we have been able to derive virtual spaces, containing only a few orbitals, that were able to capture a significant amount of correlation. The focus in this manuscript is on comparing the simulations of small molecules calculated with plane-wave basis sets with large periodic unit cells at the $\Gamma$-point, including images, to results for plane-wave basis sets with aperiodic unit cells. The results for this approach were promising as we were able to obtain good agreement between periodic and aperiodic results for an LiH molecule. Simulations performed on the Quantinuum H1-1 quantum computer were able to produce surprisingly good energies, reproducing the FCI values for the 1 COVO Hamiltonian to within 11 milliHartree (6.9 kcal/mol), when corrected for noise.

Related papers

• H\"uckel Molecular Orbital Theory on a Quantum Computer: A Scalable System-Agnostic Variational Implementation with Compact Encoding [0.0]
  H"uckel molecular orbital (HMO) theory provides a semi-empirical treatment of the electronic structure in pi-electronic systems. A scalable system-agnostic execution of HMO theory on a quantum computer is reported here.
  arXiv  Detail & Related papers  (2023-12-04T16:44:53Z)
• 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)
• Orbital-optimized pair-correlated electron simulations on trapped-ion quantum computers [0.471876092032107]
  Variational quantum eigensolvers (VQE) are among the most promising approaches for solving electronic structure problems on quantum computers. A critical challenge for VQE in practice is that one needs to strike a balance between the expressivity of the VQE ansatz versus the number of quantum gates required to implement the ansatz. We run end-to-end VQE algorithms with up to 12 qubits and 72 variational parameters - the largest full VQE simulation with a correlated wave function on quantum hardware.
  arXiv  Detail & Related papers  (2022-12-05T18:40:54Z)
• Recompilation-enhanced simulation of electron-phonon dynamics on IBM Quantum computers [62.997667081978825]
  We consider the absolute resource cost for gate-based quantum simulation of small electron-phonon systems. We perform experiments on IBM quantum hardware for both weak and strong electron-phonon coupling. Despite significant device noise, through the use of approximate circuit recompilation we obtain electron-phonon dynamics on current quantum computers comparable to exact diagonalisation.
  arXiv  Detail & Related papers  (2022-02-16T19:00:00Z)
• Computing molecular excited states on a D-Wave quantum annealer [52.5289706853773]
  We demonstrate the use of a D-Wave quantum annealer for the calculation of excited electronic states of molecular systems. These simulations play an important role in a number of areas, such as photovoltaics, semiconductor technology and nanoscience.
  arXiv  Detail & Related papers  (2021-07-01T01:02:17Z)
• 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)
• Engineering analog quantum chemistry Hamiltonians using cold atoms in optical lattices [69.50862982117127]
  We benchmark the working conditions of the numerically analog simulator and find less demanding experimental setups. We also provide a deeper understanding of the errors of the simulation appearing due to discretization and finite size effects.
  arXiv  Detail & Related papers  (2020-11-28T11:23:06Z)
• Dynamical Self-energy Mapping (DSEM) for quantum computing [0.0]
  For noisy intermediate-scale quantum (NISQ) devices only a moderate number of qubits with a limited coherence is available. We present how to bypass this challenge in practical molecular chemistry simulations on NISQ devices by employing a classical-quantum hybrid algorithm.
  arXiv  Detail & Related papers  (2020-10-12T04:12:21Z)
• Quantum Solvers for Plane-Wave Hamiltonians: Abridging Virtual Spaces Through the Optimization of Pairwise Correlations [0.2462953128215087]
  We develop new classes of algorithms to define virtual spaces by optimizing orbitals from small pairwise CI Hamiltonians. Using these derived basis sets for quantum computing calculations targeting full CI (FCI) quality-results can also be used in many-body approaches.
  arXiv  Detail & Related papers  (2020-08-31T19:55:48Z)
• Simulating periodic systems on quantum computer [7.332046127518237]
  We present two schemes to improve the accuracy of quantum simulations for extended systems. One is a modified VQE algorithm, which introduces a unitary transformation of Hartree-Fock orbitals to avoid the complex Hamiltonian. The second is a Post-VQE approach combining VQE with the quantum subspace expansion approach (VQE/QSE)
  arXiv  Detail & Related papers  (2020-08-07T01:56:32Z)
• Quantum Simulation of 2D Quantum Chemistry in Optical Lattices [59.89454513692418]
  We propose an analog simulator for discrete 2D quantum chemistry models based on cold atoms in optical lattices. We first analyze how to simulate simple models, like the discrete versions of H and H$+$, using a single fermionic atom. We then show that a single bosonic atom can mediate an effective Coulomb repulsion between two fermions, leading to the analog of molecular Hydrogen in two dimensions.
  arXiv  Detail & Related papers  (2020-02-21T16:00:36Z)

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.