Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation

We introduce a unitary coupled-cluster (UCC) ansatz termed $k$-UpCCGSD that is based on a family of sparse generalized doubles (D) operators which provides an affordable and systematically improvable unitary coupled-cluster wavefunction suitable for implementation on a near-term quantum computer. $k$-UpCCGSD employs $k$ products of the exponential of pair coupled-cluster double excitation operators (pCCD), together with generalized single (S) excitation operators. We compare its performance in both efficiency of implementation and accuracy with that of the generalized UCC ansatz employing the full generalized SD excitation operators (UCCGSD), as well as with the standard ansatz employing only SD excitations (UCCSD). $k$-UpCCGSD is found to show the best scaling for quantum computing applications, requiring a circuit depth of $\mathcal O(kN)$, compared with $\mathcal O(N^3)$ for UCCGSD and $\mathcal O((N-\eta)^2 \eta)$ for UCCSD where $N$ is the number of spin orbitals and $\eta$ is the number of electrons. We analyzed the accuracy of these three ans\"atze by making classical benchmark calculations on the ground state and the first excited state of H$_4$ (STO-3G, 6-31G), H$_2$O (STO-3G), and N$_2$ (STO-3G), making additional comparisons to conventional coupled cluster methods. The results for ground states show that $k$-UpCCGSD offers a good tradeoff between accuracy and cost, achieving chemical accuracy for lower cost of implementation on quantum computers than both UCCGSD and UCCSD. Excited states are calculated with an orthogonally constrained variational quantum eigensolver approach. This is seen to generally yield less accurate energies than for the corresponding ground states. We demonstrate that using a specialized multi-determinantal reference state constructed from classical linear response calculations allows these excited state energetics to be improved

Cluster decomposition of full configuration interaction wave functions: a tool for chemical interpretation of systems with strong correlation

Approximate full configuration interaction (FCI) calculations have recently become tractable for systems of unforeseen size thanks to stochastic and adaptive approximations to the exponentially scaling FCI problem. The result of an FCI calculation is a weighted set of electronic configurations, which can also be expressed in terms of excitations from a reference configuration. The excitation amplitudes contain information on the complexity of the electronic wave function, but this information is contaminated by contributions from disconnected excitations, i.e. those excitations that are just products of independent lower-level excitations. The unwanted contributions can be removed via a cluster decomposition procedure, making it possible to examine the importance of connected excitations in complicated multireference molecules which are outside the reach of conventional algorithms. We present an implementation of the cluster decomposition analysis and apply it to both true FCI wave functions, as well as wave functions generated from the adaptive sampling CI (ASCI) algorithm. The cluster decomposition is useful for interpreting calculations in chemical studies, as a diagnostic for the convergence of various excitation manifolds, as well as as a guidepost for polynomially scaling electronic structure models. Applications are presented for (i) the double dissociation of water, (ii) the carbon dimer, (iii) the {\pi} space of polyacenes, as well as (iv) the chromium dimer. While the cluster amplitudes exhibit rapid decay with increasing rank for the first three systems, even connected octuple excitations still appear important in Cr$_2$, suggesting that spin-restricted single-reference coupled-cluster approaches may not be tractable for some problems in transition metal chemistry.Comment: 15 pages, 5 figure

A deterministic alternative to the full configuration interaction quantum Monte Carlo method

Development of exponentially scaling methods has seen great progress in tackling larger systems than previously thought possible. One such technique, full configuration interaction quantum Monte Carlo, is a useful algorithm that allows exact diagonalization through stochastically sampling determinants. The method derives its utility from the information in the matrix elements of the Hamiltonian, along with a stochastic projected wave function, to find the important parts of Hilbert space. However, the stochastic representation of the wave function is not required to search Hilbert space efficiently, and here we describe a highly efficient deterministic method to achieve chemical accuracy for a wide range of systems, including the difficult Cr$_{2}$ dimer. In addition our method also allows efficient calculation of excited state energies, for which we illustrate with benchmark results for the excited states of C$_{2}$.Comment: 4 pages, 2 figure

Modern Approaches to Exact Diagonalization and Selected Configuration Interaction with the Adaptive Sampling CI Method.

Recent advances in selected configuration interaction methods have made them competitive with the most accurate techniques available and, hence, creating an increasingly powerful tool for solving quantum Hamiltonians. In this work, we build on recent advances from the adaptive sampling configuration interaction (ASCI) algorithm. We show that a useful paradigm for generating efficient selected CI/exact diagonalization algorithms is driven by fast sorting algorithms, much in the same way iterative diagonalization is based on the paradigm of matrix vector multiplication. We present several new algorithms for all parts of performing a selected CI, which includes new ASCI search, dynamic bit masking, fast orbital rotations, fast diagonal matrix elements, and residue arrays. The ASCI search algorithm can be used in several different modes, which includes an integral driven search and a coefficient driven search. The algorithms presented here are fast and scalable, and we find that because they are built on fast sorting algorithms they are more efficient than all other approaches we considered. After introducing these techniques, we present ASCI results applied to a large range of systems and basis sets to demonstrate the types of simulations that can be practically treated at the full-CI level with modern methods and hardware, presenting double- and triple-ζ benchmark data for the G1 data set. The largest of these calculations is Si2H6 which is a simulation of 34 electrons in 152 orbitals. We also present some preliminary results for fast deterministic perturbation theory simulations that use hash functions to maintain high efficiency for treating large basis sets

Star-Forming or Starbursting? The Ultraviolet Conundrum

Compared to starburst galaxies, normal star forming galaxies have been shown to display a much larger dispersion of the dust attenuation at fixed reddening through studies of the IRX-beta diagram (the IR/UV ratio "IRX" versus the UV color "beta"). To investigate the causes of this larger dispersion and attempt to isolate second parameters, we have used GALEX UV, ground-based optical, and Spitzer infrared imaging of 8 nearby galaxies, and examined the properties of individual UV and 24 micron selected star forming regions. We concentrated on star-forming regions, in order to isolate simpler star formation histories than those that characterize whole galaxies. We find that 1) the dispersion is not correlated with the mean age of the stellar populations, 2) a range of dust geometries and dust extinction curves are the most likely causes for the observed dispersion in the IRX-beta diagram 3) together with some potential dilution of the most recent star-forming population by older unrelated bursts, at least in the case of star-forming regions within galaxies, 4) we also recover some general characteristics of the regions, including a tight positive correlation between the amount of dust attenuation and the metal content. Although generalizing our results to whole galaxies may not be immediate, the possibility of a range of dust extinction laws and geometries should be accounted for in the latter systems as well.Comment: 18 pages, 17 figures, accepted for publication in Ap

Characteristics of Diffuse X-Ray Line Emission within 20 pc of the Galactic Center

Over the last 3 yrs, the Galactic center (GC) region has been monitored with the Chandra X-Ray Observatory. With 11 Chandra observations through 2002 June, the total effective exposure reaches ~590 ks, providing significant photon statistics on the faint, filamentary, diffuse X-ray emission. The true-color X-ray image and the equivalent width (EW) images for the detected elemental species demonstrate that the diffuse X-ray features have a broad range of spatio-spectral properties. Enhancements of the low-ionization-state, or ``neutral'' Fe line emission (E~6.4 keV) to the northeast of Sgr A* can be interpreted as fluorescence within the dense ISM resulting from irradiation by hard, external X-ray sources. They may also be explained by emission induced by the bombardments by high energy particles on the ISM, such as unresolved supernova (SN) ejecta intruding into dense ISM. The detection of molecular cloud counterparts to the 6.4 keV Fe line features indicates that these Fe line features are associated with dense GC clouds and/or active star-forming regions, which supports the X-ray reflection and/or SN ejecta origins for the Fe line emission. We detect highly ionized S and Si lines which are generally coincident with the neutral Fe line emission and the dense molecular clouds in the northeast of Sgr A*. These hot plasmas are likely produced by massive star-forming activities and/or SNRs. In contrast, we find that highly ionized He-like Fe line emission (E~6.7 keV) is primarily distributed along the plane instead of being concentrated in the northeast of Sgr A*. The implied high temperature and the alignment along the plane are consistent with the magnetic confinement model.Comment: 13 pages (ApJ emulator style) including 4 figures (2 color figs). Accepted by ApJ. For full-quality figures, contact [email protected]

Simulation study of pressure and temperature dependence of the negative thermal expansion in Zn(CN)(2)

12 pages, 16 figures12 pages, 16 figures12 pages, 16 figures12 pages, 16 figure

Fungal Chitin Dampens Inflammation through IL-10 Induction Mediated by NOD2 and TLR9 Activation

Funding: JW and NARG thank the Wellcome Trust (080088, 086827, 075470), The Wellcome Trust Strategic Award in Medical Mycology and Fungal Immunology (097377) and the European Union ALLFUN (FP7/2007 2013, HEALTH-2010-260338) for funding. MGN was supported by a Vici grant of the Netherlands Organisation for Scientific Research. AJPB and DMM were funded by STRIFE, ERC-2009-AdG-249793 and AJPB additionally by FINSysB, PITN-GA-2008-214004 and the BBSRC [BB/F00513X/1]. MDL was supported by the MRC (MR/J008230/1). GDB and SV were funded by the Wellcome Trust (086558) and TB and MK were funded by the Deutsche Forschungsgemeinschaft (Bi 696/3-1; Bi 696/5-2; Bi 696/10-1). MS was supported by the Deutsche Forschungsgemeinschaft (Sch 897/1-3) and the National Institute of Dental and Craniofacial Research (R01 DE017514-01). TDK and RKSM were funded by the National Institute of Health (AR056296, AI101935) and the American Lebanese Syrian Associated Charities (ALSAC). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Peer reviewedPublisher PD