Computing molecular excited states on a D-Wave quantum annealer

Abstract

The possibility of using quantum computers for electronic structure calculations has opened up a promising avenue for computational chemistry. Towards this direction, numerous algorithmic advances have been made in the last five years. The potential of quantum annealers, which are the prototypes of adiabatic quantum computers, is yet to be fully explored. In this work, 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. The excited states are treated using two methods, time-dependent Hartree–Fock (TDHF) and time-dependent density-functional theory (TDDFT), both within a commonly used Tamm–Dancoff approximation (TDA). The resulting TDA eigenvalue equations are solved on a D-Wave quantum annealer using the Quantum Annealer Eigensolver (QAE), developed previously. The method is shown to reproduce a typical basis set convergence on the example $$\hbox {H}_2$$ H 2 molecule and is also applied to several other molecular species. Characteristic properties such as transition dipole moments and oscillator strengths are computed as well. Three potential energy profiles for excited states are computed for $$\hbox {NH}_3$$ NH 3 as a function of the molecular geometry. Similar to previous studies, the accuracy of the method is dependent on the accuracy of the intermediate meta-heuristic software called qbsolv.

Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits

“…In addition, subspace expansion based on excited determinants has been proposed, , including the equation of motion (EOM) operator-based qEOM method that provides a size-intensive approach for excitation energy calculations. In addition to the gate-based quantum devices, quantum annealers have also been employed to calculate the TD-HF and TD-DFT excitation energies using the quantum annealer eigensolver algorithm …”

Sampling electronic structure quadratic unconstrained binary optimization problems (QUBOs) with Ocean and Mukai solvers

“…For example, previously we have manually limited the largest elements of the complex vibrational Hamiltonian matrix [11] to improve the results. In another QAE-based study [13],…”

“…We focus on the electronic structure problem, where the Quantum Annealer Eigensolver (QAE) is used to map the electronic structure eigenvalue equation to QUBO problems, which are in turn solved using either the qbsolv or Mukai QUBO solver. Previously, the QAE was shown to work for a variety of theoretical chemistry tasks including vibrational [10], scattering [11] and electronic [12,13] problems. Since a substantial body of results was obtained in the latter two studies [12,13], we will use the electronic/QAE setup as a representative case study to compare the two versions of qbsolv.…”

“…Previously, the QAE was shown to work for a variety of theoretical chemistry tasks including vibrational [10], scattering [11] and electronic [12,13] problems. Since a substantial body of results was obtained in the latter two studies [12,13], we will use the electronic/QAE setup as a representative case study to compare the two versions of qbsolv. The comparison is completely classical, because the Mukai QUBO solver is purely classical at the present moment (i.e., all subQUBOs are solved on the CPU) [9].…”

Effects of Graph Network Connections on The Efficiency of Quantum Annealing

“…Applications include data analysis [9], optimization problems mapped into spin-glasses [10,11], and graph network problems [12,13]. D-Wave annealers and their chimera architecture Ising model spin networks offer the state of the art solutions [14,15].…”