Compressed intramolecular dispersion interactions.

The feasibility of the compression of localized virtual orbitals is explored in the context of intramolecular long-range dispersion interactions. Singular value decomposition (SVD) of coupled cluster doubles amplitudes associated with the dispersion interactions is analyzed for a number of long-chain systems, including saturated and unsaturated hydrocarbons and a silane chain. Further decomposition of the most important amplitudes obtained from these SVDs allows for the analysis of the dispersion-specific virtual orbitals that are naturally localized. Consistent with previous work on intermolecular dispersion interactions in dimers, it is found that three important geminals arise and account for the majority of dispersion interactions at the long range, even in the many body intramolecular case. Furthermore, it is shown that as few as three localized virtual orbitals per occupied orbital can be enough to capture all pairwise long-range dispersion interactions within a molecule

Identifying challenges towards practical quantum advantage through resource estimation: the measurement roadblock in the variational quantum eigensolver

Recent advances in Noisy Intermediate-Scale Quantum (NISQ) devices have brought much attention to the potential of the Variational Quantum Eigensolver (VQE) and related techniques to provide practical quantum advantage in computational chemistry. However, it is not yet clear whether such algorithms, even in the absence of device error, could achieve quantum advantage for systems of practical interest and how large such an advantage might be. To address these questions, we have performed an exhaustive set of benchmarks to estimate number of qubits and number of measurements required to compute the combustion energies of small organic molecules to within chemical accuracy using VQE as well as state-of-the-art classical algorithms. We consider several key modifications to VQE, including the use of Frozen Natural Orbitals, various Hamiltonian decomposition techniques, and the application of fermionic marginal constraints. Our results indicate that although Frozen Natural Orbitals and low-rank factorizations of the Hamiltonian significantly reduce the qubit and measurement requirements, these techniques are not sufficient to achieve practical quantum computational advantage in the calculation of organic molecule combustion energies. This suggests that new approaches to estimation leveraging quantum coherence, such as Bayesian amplitude estimation [arxiv:2006.09350, arxiv:2006.09349], may be required in order to achieve practical quantum advantage with near-term devices. Our work also highlights the crucial role that resource and performance assessments of quantum algorithms play in identifying quantum advantage and guiding quantum algorithm design.Comment: 27 pages, 18 figure

Assessing Electronic Structure Methods for Long-Range Three-Body Dispersion Interactions: Analysis and Calculations on Well-Separated Metal Atom Trimers.

Three-body dispersion interactions are much weaker than their two-body counterpart. However, their importance grows quickly as the number of interacting monomers rises. To explore the numerical performance of correlation methods for long-range three-body dispersion, we performed calculations on eight very simple dispersion-dominated model metal trimers: Na3, Mg3, Zn3, Cd3, Hg3, Cu3, Ag3, and Au3. One encouraging aspect is that relatively small basis sets of augmented triple-ζ size appear to be adequate for three-body dispersion in the long-range. Coupled cluster calculations were performed at high levels to assess MP3, CCSD, CCSD(T), empirical density functional theory dispersion (D3), and the many-body dispersion (MBD) approach. We found that the accuracy of CCSD(T) was generally significantly lower than for two-body interactions, with errors sometimes reaching 20% in the investigated systems, while CCSD and particularly MP3 were generally more erratic. MBD is found to perform better than D3 at large distances, whereas the opposite is true at shorter distances. When computing reference numbers for three-body dispersion, care should be taken to appropriately represent the effect of the connected triple excitations, which are significant in most cases and incompletely approximated by CCSD(T)

Compressed representation of dispersion interactions and long-range electronic correlations.

The description of electron correlation in quantum chemistry often relies on multi-index quantities. Here, we examine a compressed representation of the long-range part of electron correlation that is associated with dispersion interactions. For this purpose, we perform coupled-cluster singles and doubles (CCSD) computations on localized orbitals, and then extract the portion of CCSD amplitudes corresponding to dispersion energies. Using singular value decomposition, we uncover that a very compressed representation of the amplitudes is possible in terms of occupied-virtual geminal pairs located on each monomer. These geminals provide an accurate description of dispersion energies at medium and long distances. The corresponding virtual orbitals are examined by further singular value decompositions of the geminals. We connect each component of the virtual space to the multipole expansion of dispersion energies. Our results are robust with respect to basis set change and hold for systems as large as the benzene-methane dimer. This compressed representation of dispersion energies paves the way to practical and accurate approximations for dispersion, for example, in local correlation methods

Compressed representation of dispersion interactions and long-range electronic correlations.

The description of electron correlation in quantum chemistry often relies on multi-index quantities. Here, we examine a compressed representation of the long-range part of electron correlation that is associated with dispersion interactions. For this purpose, we perform coupled-cluster singles and doubles (CCSD) computations on localized orbitals, and then extract the portion of CCSD amplitudes corresponding to dispersion energies. Using singular value decomposition, we uncover that a very compressed representation of the amplitudes is possible in terms of occupied-virtual geminal pairs located on each monomer. These geminals provide an accurate description of dispersion energies at medium and long distances. The corresponding virtual orbitals are examined by further singular value decompositions of the geminals. We connect each component of the virtual space to the multipole expansion of dispersion energies. Our results are robust with respect to basis set change and hold for systems as large as the benzene-methane dimer. This compressed representation of dispersion energies paves the way to practical and accurate approximations for dispersion, for example, in local correlation methods

Neural network enhanced measurement efficiency for molecular groundstates

It is believed that one of the first useful applications for a quantum computer will be the preparation of groundstates of molecular Hamiltonians. A crucial task involving state preparation and readout is obtaining physical observables of such states, which are typically estimated using projective measurements on the qubits. At present, measurement data is costly and time-consuming to obtain on any quantum computing architecture, which has significant consequences for the statistical errors of estimators. In this paper, we adapt common neural network models (restricted Boltzmann machines and recurrent neural networks) to learn complex groundstate wavefunctions for several prototypical molecular qubit Hamiltonians from typical measurement data. By relating the accuracy ɛ of the reconstructed groundstate energy to the number of measurements, we find that using a neural network model provides a robust improvement over using single-copy measurement outcomes alone to reconstruct observables. This enhancement yields an asymptotic scaling near ɛ ^−1 for the model-based approaches, as opposed to ɛ ^−2 in the case of classical shadow tomography