Molecular dynamics on quantum annealers.

In this work we demonstrate a practical prospect of using quantum annealers for simulation of molecular dynamics. A methodology developed for this goal, dubbed Quantum Differential Equations (QDE), is applied to propagate classical trajectories for the vibration of the hydrogen molecule in several regimes: nearly harmonic, highly anharmonic, and dissociative motion. The results obtained using the D-Wave 2000Q quantum annealer are all consistent and quickly converge to the analytical reference solution.

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

The most advanced D-Wave Advantage quantum annealer has 5000+ qubits, however, every qubit is connected to a small number of neighbors. As such, implementation of a fully-connected graph results in an order of magnitude reduction in qubit count. To compensate for the reduced number of qubits, one has to rely on special heuristic software such as qbsolv, the purpose of which is to decompose a large quadratic unconstrained binary optimization (QUBO) problem into smaller pieces that fit onto a quantum annealer.

Computing molecular excited states on a D-Wave quantum annealer.

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.

Four Isotope-Labeled Recombination Pathways of Ozone Formation.

A theoretical approach is developed for the description of all possible recombination pathways in the ozone forming reaction, without neglecting any process , and without decoupling the individual pathways one from another. These pathways become physically distinct when a rare isotope of oxygen is introduced, such as O, which represents a sensitive probe of the ozone forming reaction. Each isotopologue of O contains two types of physically distinct entrance channels and two types of physically distinct product wells, creating four recombination pathways.

Electronic structure with direct diagonalization on a D-wave quantum annealer.

Quantum chemistry is regarded to be one of the first disciplines that will be revolutionized by quantum computing. Although universal quantum computers of practical scale may be years away, various approaches are currently being pursued to solve quantum chemistry problems on near-term gate-based quantum computers and quantum annealers by developing the appropriate algorithm and software base. This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer.

Solving complex eigenvalue problems on a quantum annealer with applications to quantum scattering resonances.

Quantum computing is a new and rapidly evolving paradigm for solving chemistry problems. In previous work, we developed the Quantum Annealer Eigensolver (QAE) and applied it to the calculation of the vibrational spectrum of a molecule on the D-Wave quantum annealer. However, the original QAE methodology was applicable to real symmetric matrices only.

The role of rotation-vibration coupling in symmetric and asymmetric isotopomers of ozone.

A theoretical framework and a computer code (SpectrumSDT) are developed for accurate calculations of coupled rotational-vibrational states in triatomic molecules using hyper-spherical coordinates and taking into account the Coriolis coupling effect. Concise final formulas are derived for the construction of the Hamiltonian matrix using an efficient combination of the variational basis representation and discrete variable representation methods with locally optimized basis sets and grids. First, the new code is tested by comparing its results with those of the APH3D program of Kendrick et al.

Theoretical Treatment of the Coriolis Effect Using Hyperspherical Coordinates, with Application to the Ro-Vibrational Spectrum of Ozone.

Several alternative methods for the description of the interaction between rotation and vibration are compared and contrasted using hyperspherical coordinates for a triatomic molecule. These methods differ by the choice of the -axis and by the assumption of a prolate or oblate rotor shape of the molecule. For each case, a block-structure of the rotational-vibrational Hamiltonian matrix is derived and analyzed, and the advantages and disadvantages of each method are made explicit.

Three-dimensional potential energy surfaces of ArNO (X̃ Π).

Until now, the potential energy surfaces (PESs) of the ArNO complex found in the literature were two-dimensional, with the NO interatomic distance being fixed. In this work, we present the first accurate three-dimensional ground state X̃ Π PESs (both A' and A″) of ArNO computed at the CCSD(T)/CBS level of theory. The equilibrium geometries and the well depths (D) are compared to several other electronic structure methods.

Calculation of Molecular Vibrational Spectra on a Quantum Annealer.

Until recently molecular energy calculations using quantum computing hardware have been limited to gate-based quantum computers. In this paper, a new methodology is presented to calculate the vibrational spectrum of a molecule on a quantum annealer. The key idea of the method is a mapping of the ground state variational problem onto an Ising or quadratic unconstrained binary optimization (QUBO) problem by expressing the expansion coefficients using spins or qubits.

The ratio of the number of states in asymmetric and symmetric ozone molecules deviates from the statistical value of 2.

Accurate calculations of vibrational states in singly and doubly substituted ozone molecules are carried out, up to dissociation threshold. Analysis of these spectra reveals noticeable deviations from the statistical factor of 2 for the ratio between the number of states in asymmetric and symmetric ozone molecules. It is found that, for the lower energy parts of spectra, the ratio is less than 2 in the singly substituted ozone molecules, but it is more than 2 in the doubly substituted ozone molecules.

Several levels of theory for description of isotope effects in ozone: Effect of resonance lifetimes and channel couplings.

In this paper, two levels of theory are developed to determine the role of scattering resonances in the process of ozone formation. At the lower theory level, we compute resonance lifetimes in the simplest possible way, by neglecting all couplings between the diabatic vibrational channels in the problem. This permits to determine the effect of "shape" resonances, trapped behind the centrifugal barrier and populated by quantum tunneling.

Several Levels of Theory for Description of Isotope Effects in Ozone: Symmetry Effect and Mass Effect.

The essential components of theory for the description of isotope effects in recombination reaction that forms ozone are presented, including the introduction of three reaction pathways for symmetric and asymmetric isotopomers, a brief review of relevant experimental data for singly- and doubly substituted isotopologues, the definitions of ζ-effect and η-effect, and the introduction of isotopic enrichment δ. Two levels of theory are developed to elucidate the role of molecular symmetry, atomic masses, vibrational zero-point energies, and rotational excitations in the recombination process. The issue of symmetry is not trivial, since the important factors, such as 1/2 and 2, appear in seven different places in the formalism.

Properties of Feshbach and "shape"-resonances in ozone and their role in recombination reactions and anomalous isotope effects.

Computational modelling of recombination reactions that form ozone require the inclusion of several quantum mechanical effects such as symmetry, zero-point energy, scattering resonances and tunneling. Major elements of theory for rigorous description of this process are reviewed, with emphasis on interpreting the famous anomalous isotope effect due to substitutions of 18O. Three reaction pathways, for the formation of symmetric and asymmetric isotopologues of ozone, are introduced and a hierarchy of theory levels is outlined.

A full-dimensional model of ozone forming reaction: the absolute value of the recombination rate coefficient, its pressure and temperature dependencies.

Rigorous calculations of scattering resonances in ozone are carried out for a broad range of rotational excitations. The accurate potential energy surface of Dawes is adopted, and a new efficient method for calculations of ro-vibrational energies, wave functions and resonance lifetimes is employed (which uses hyper-spherical coordinates, the sequential diagonalization/truncation approach, grid optimization and complex absorbing potential). A detailed analysis is carried out to characterize distributions of resonance energies and lifetimes, their rotational/vibrational content and their positions with respect to the centrifugal barrier.

Frozen rotor approximation in the mixed quantum/classical theory for collisional energy transfer: application to ozone stabilization.

A frozen-rotor approximation is formulated for the mixed quantum/classical theory of collisional energy transfer and ro-vibrational energy flow [M. Ivanov and D. Babikov, J.