Calculating potential energy surfaces with quantum computers by measuring only the density along adiabatic transitions

• URL: http://arxiv.org/abs/2305.08837v1
• Date: Mon, 15 May 2023 17:51:22 GMT
• Title: Calculating potential energy surfaces with quantum computers by measuring only the density along adiabatic transitions
• Authors: James Brown
• Abstract summary: In lieu of using phase estimation, the energy is evaluated by performing line-integration using the inverted TDDFT Kohn-Sham potential. The accuracy of this method depends on the validity of the adiabatic evolution itself and the potential inversion process. It is shown that few accurate measurements can be utilized to obtain chemical accuracy across the full potential energy curve.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that chemically-accurate potential energy surfaces (PESs) can be generated from quantum computers by measuring the density along an adiabatic transition between different molecular geometries. In lieu of using phase estimation, the energy is evaluated by performing line-integration using the inverted TDDFT Kohn-Sham potential obtained from the time-varying densities. The accuracy of this method depends on the validity of the adiabatic evolution itself and the potential inversion process (which is theoretically exact but can be numerically unstable), whereas total evolution time is the defining factor for the precision of phase estimation. We examine the method with a one-dimensional system of two electrons for both the ground and first triplet state in first quantization, as well as the ground state of three- and four- electron systems in second quantization. It is shown that few accurate measurements can be utilized to obtain chemical accuracy across the full potential energy curve, with shorter propagation time than may be required using phase estimation for a similar accuracy. We also show that an accurate potential energy curve can be calculated by making many imprecise density measurements (using few shots) along the time evolution and smoothing the resulting density evolution. We discuss how one can generate full PESs using either sparse grid representations or machine learning density functionals where it is known that training the functional using the density (along with the energy) generates a more transferable functional than only using the energy. Finally, it is important to note that the method is able to classically provide a check of its own accuracy by comparing the density resulting from a time-independent Kohn-Sham calculation using the inverted potential, with the measured density.

Related papers

• A Recipe for Charge Density Prediction [4.017525264569417]
  Machine learning methods are promising in significantly accelerating charge density prediction. We propose a recipe that can achieve both accuracy and scalability. Our method achieves state-of-the-art accuracy while being more than an order of magnitude faster than existing methods.
  arXiv  Detail & Related papers  (2024-05-29T17:07:24Z)
• 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)
• Orbital-Free Density Functional Theory with Continuous Normalizing Flows [54.710176363763296]
  Orbital-free density functional theory (OF-DFT) provides an alternative approach for calculating the molecular electronic energy. Our model successfully replicates the electronic density for a diverse range of chemical systems.
  arXiv  Detail & Related papers  (2023-11-22T16:42:59Z)
• Real-time dynamics of false vacuum decay [49.1574468325115]
  We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
  arXiv  Detail & Related papers  (2023-10-06T12:44:48Z)
• KineticNet: Deep learning a transferable kinetic energy functional for orbital-free density functional theory [13.437597619451568]
  KineticNet is an equivariant deep neural network architecture based on point convolutions adapted to the prediction of quantities on molecular quadrature grids. For the first time, chemical accuracy of the learned functionals is achieved across input densities and geometries of tiny molecules.
  arXiv  Detail & Related papers  (2023-05-08T17:43:31Z)
• Electronic excitations of the charged nitrogen-vacancy center in diamond obtained using time-independent variational density functional calculations [0.0]
  A direct orbital optimization method is used to perform variational density functional calculations of a prototypical defect in diamond. Results are remarkably good agreement with high-level, many-body calculations as well as available experimental estimates. The approach is found to be a promising tool for studying electronic excitations of point defects in solids.
  arXiv  Detail & Related papers  (2023-03-07T12:09:16Z)
• Homogeneous electron gas in arbitrary dimensions beyond the random phase approximation [0.0]
  We use the celebrated approach developed by Singwi, Tosi, Land, and Sj"olander (STLS) to compute correlation energy beyond the random phase approximation (RPA) For two and three dimensions, both in the paramagnetic and ferromagnetic ground states, STLS is capable of producing correlation energies in close agreement with Monte-Carlo values.
  arXiv  Detail & Related papers  (2022-10-06T16:15:14Z)
• Electronic-structure properties from atom-centered predictions of the electron density [0.0]
  electron density of a molecule or material has recently received major attention as a target quantity of machine-learning models. We propose a gradient-based approach to minimize the loss function of the regression problem in an optimized and highly sparse feature space. We show that starting from the predicted density a single Kohn-Sham diagonalization step can be performed to access total energy components that carry an error of just 0.1 meV/atom.
  arXiv  Detail & Related papers  (2022-06-28T15:35:55Z)
• Determining ground-state phase diagrams on quantum computers via a generalized application of adiabatic state preparation [61.49303789929307]
  We use a local adiabatic ramp for state preparation to allow us to directly compute ground-state phase diagrams on a quantum computer via time evolution. We are able to calculate an accurate phase diagram on both two and three site systems using IBM quantum machines.
  arXiv  Detail & Related papers  (2021-12-08T23:59:33Z)
• 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)
• Visualizing spinon Fermi surfaces with time-dependent spectroscopy [62.997667081978825]
  We propose applying time-dependent photo-emission spectroscopy, an established tool in solid state systems, in cold atom quantum simulators. We show in exact diagonalization simulations of the one-dimensional $t-J$ model that the spinons start to populate previously unoccupied states in an effective band structure. The dependence of the spectral function on the time after the pump pulse reveals collective interactions among spinons.
  arXiv  Detail & Related papers  (2021-05-27T18:00:02Z)

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.