Discontinuous Galerkin discretization for quantum simulation of chemistry

Methods for electronic structure based on Gaussian and molecular orbital discretizations offer a well established, compact representation that forms much of the foundation of correlated quantum chemistry calculations on both classical and quantum computers. Despite their ability to describe essential physics with relatively few basis functions, these representations can suffer from a quartic growth of the number of integrals. Recent results have shown that, for some quantum and classical algorithms, moving to representations with diagonal two-body operators can result in dramatically lower asymptotic costs, even if the number of functions required increases significantly. We introduce a way to interpolate between the two regimes in a systematic and controllable manner, such that the number of functions is minimized while maintaining a block diagonal structure of the two-body operator and desirable properties of an original, primitive basis. Techniques are analyzed for leveraging the structure of this new representation on quantum computers. Empirical results for hydrogen chains suggest a scaling improvement from $O(N^{4.5})$ in molecular orbital representations to $O(N^{2.6})$ in our representation for quantum evolution in a fault-tolerant setting, and exhibit a constant factor crossover at 15 to 20 atoms. Moreover, we test these methods using modern density matrix renormalization group methods classically, and achieve excellent accuracy with respect to the complete basis set limit with a speedup of 1-2 orders of magnitude with respect to using the primitive or Gaussian basis sets alone. These results suggest our representation provides significant cost reductions while maintaining accuracy relative to molecular orbital or strictly diagonal approaches for modest-sized systems in both classical and quantum computation for correlated systems

Establishing the carrier scattering phase diagram for ZrNiSn-based half-Heusler thermoelectric materials

Chemical doping is one of the most important strategies for tuning electrical properties of semiconductors, particularly thermoelectric materials. Generally, the main role of chemical doping lies in optimizing the carrier concentration, but there can potentially be other important effects. Here, we show that chemical doping plays multiple roles for both electron and phonon transport properties in half-Heusler thermoelectric materials. With ZrNiSn-based half-Heusler materials as an example, we use high-quality single and polycrystalline crystals, various probes, including electrical transport measurements, inelastic neutron scattering measurement, and first-principles calculations, to investigate the underlying electron-phonon interaction. We find that chemical doping brings strong screening effects to ionized impurities, grain boundary, and polar optical phonon scattering, but has negligible influence on lattice thermal conductivity. Furthermore, it is possible to establish a carrier scattering phase diagram, which can be used to select reasonable strategies for optimization of the thermoelectric performance.Comment: 21 pages, 5 figure

Cholesterol-Modified Amino-Pullulan Nanoparticles as a Drug Carrier: Comparative Study of Cholesterol-Modified Carboxyethyl Pullulan and Pullulan Nanoparticles

To search for nano-drug preparations with high efficiency in tumor treatment, we evaluated the drug-loading capacity and cell-uptake toxicity of three kinds of nanoparticles (NPs). Pullulan was grafted with ethylenediamine and hydrophobic groups to form hydrophobic cholesterol-modified amino-pullulan (CHAP) conjugates. Fourier transform infrared spectroscopy and nuclear magnetic resonance were used to identify the CHAP structure and calculate the degree of substitution of the cholesterol group. We compared three types of NPs with close cholesterol hydrophobic properties: CHAP, cholesterol-modified pullulan (CHP), and cholesterol-modified carboxylethylpullulan (CHCP), with the degree of substitution of cholesterol of 2.92%, 3.11%, and 3.46%, respectively. As compared with the two other NPs, CHAP NPs were larger, 263.9 nm, and had a positive surface charge of 7.22 mV by dynamic light-scattering measurement. CHAP NPs showed low drug-loading capacity, 12.3%, and encapsulation efficiency of 70.8%, which depended on NP hydrophobicity and was affected by surface charge. The drug release amounts of all NPs increased in the acid media, with CHAP NPs showing drug-release sensitivity with acid change. Cytotoxicity of HeLa cells was highest with mitoxantrone-loaded CHAP NPs on MTT assay. CHAP NPs may have potential as a high-efficiency drug carrier for tumor treatment