Fermionic Reduced Density Low-Rank Matrix Completion, Noise Filtering, and Measurement Reduction in Quantum Simulations.

Fermionic reduced density matrices summarize the key observables in Fermionic systems. In electronic systems, the two-particle reduced density matrix (2-RDM) is sufficient to determine the energy and most physical observables of interest. Here, we consider the possibility of using matrix completion to reconstruct the two-particle reduced density matrix to chemical accuracy from partial information. We consider the case of noiseless matrix completion, where the partial information corresponds to a subset of the 2-RDM elements, as well as noisy completion, where the partial information corresponds to both a subset of elements and statistical noise in their values. Through experiments on a set of 24 molecular systems, we find that 2-RDM can be efficiently reconstructed from a reduced amount of information. In the case of noisy completion, this results in a multiple orders of magnitude reduction in the number of measurements needed to determine the 2-RDM with chemical accuracy. These techniques can be readily applied to both classical and quantum algorithms for quantum simulations.

Block2: A comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond.

block2 is an open source framework to implement and perform density matrix renormalization group and matrix product state algorithms. Out-of-the-box it supports the eigenstate, time-dependent, response, and finite-temperature algorithms. In addition, it carries special optimizations for ab initio electronic structure Hamiltonians and implements many quantum chemistry extensions to the density matrix renormalization group, such as dynamical correlation theories. The code is designed with an emphasis on flexibility, extensibility, and efficiency and to support integration with external numerical packages. Here, we explain the design principles and currently supported features and present numerical examples in a range of applications.

Isolating Clusters of Light Elements in Molecular Sieves with Atom Probe Tomography.

Understanding the 3-D distribution and nature of active sites in heterogeneous catalysts is critical to developing structure-function relationships. However, this is difficult to achieve in microporous materials as there is little relative z-contrast between active and inactive framework elements (e.g., Al, O, P, and Si), making them difficult to differentiate with electron microscopies. We have applied atom probe tomography (APT), currently the only nanometer-scale 3-D microscopy to offer routine light element contrast, to the methanol-to-hydrocarbons (MTH) catalyst SAPO-34, with Si as the active site, which may be present in the framework as either isolated Si species or clusters (islands) of Si atoms. 29Si solid-state NMR data on isotopically enriched and natural abundance materials are consistent with the presence of Si islands, and the APT results have been complemented with simulations to show the smallest detectable cluster size as a function of instrument spatial resolution and detector efficiency. We have identified significant Si-Si affinity in the materials, as well as clustering of coke deposited by the MTH reaction (13CH3OH used) and an affinity between Brønsted acid sites and coke. A comparison with simulations shows that the ultimate spatial resolution that can be attained by APT applied to molecular sieves is 0.5-1 nm. Finally, the observed 13C clusters are consistent with hydrocarbon pool mechanism intermediates that are preferentially located in regions of increased Brønsted acidity.

Nanoscale Chemical Imaging of Zeolites Using Atom Probe Tomography.

Understanding structure-composition-property relationships in zeolite-based materials is critical to engineering improved solid catalysts. However, this can be difficult to realize as even single zeolite crystals can exhibit heterogeneities spanning several orders of magnitude, with consequences for, for example, reactivity, diffusion as well as stability. Great progress has been made in characterizing these porous solids using tomographic techniques, though each method has an ultimate spatial resolution limitation. Atom probe tomography (APT) is the only technique so far capable of producing 3D compositional reconstructions with sub-nanometer-scale resolution, and has only recently been applied to zeolite-based catalysts. Herein, we discuss the use of APT to study zeolites, including the critical aspects of sample preparation, data collection, assignment of mass spectral peaks including the predominant CO peak, the limitations of spatial resolution for the recovery of crystallographic information, and proper data analysis. All sections are illustrated with examples from recent literature, as well as previously unpublished data and analyses to demonstrate practical strategies to overcome potential pitfalls in applying APT to zeolites, thereby highlighting new insights gained from the APT method.