arXiv subjects

Karol Kowalski

Publications and source records attributed to Karol Kowalski.

65 records · Page 4Linked to original sources

arXiv2020

Massively parallel quantum chemical density matrix renormalization group method

We present, to the best of our knowlegde, the first attempt to exploit the supercomputer platform for quantum chemical density matrix renormalization group (QC-DMRG) calculations. We have developed the parallel scheme based on the in-house MPI global memory library, which combines operator and symmetry sector parallelisms, and tested its performance on three different molecules, all typical candidates for QC-DMRG calculations. In case of the largest calculation, which is the nitrogenase FeMo cofactor cluster with the active space comprising 113 electrons in 76 orbitals and bond dimension equal to 6000, our parallel approach scales up to approximately 2000 CPU cores.

physics.chem-ph↗

arXiv2020

Resource Efficient Chemistry on Quantum Computers with the Variational Quantum Eigensolver and The Double Unitary Coupled-Cluster approach

Applications of quantum simulation algorithms to obtain electronic energies of molecules on noisy intermediate-scale quantum (NISQ) devices require careful consideration of resources describing the complex electron correlation effects. In modeling second-quantized problems, the biggest challenge confronted is that the number of qubits scales linearly with the size of molecular basis. This poses a significant limitation on the size of the basis sets and the number of correlated electrons included in quantum simulations of chemical processes. To address this issue and to enable more realistic simulations on NISQ computers, we employ the double unitary coupled-cluster (DUCC) method to effectively downfold correlation effects into the reduced-size orbital space, commonly referred to as the active space. Using downfolding techniques, we demonstrate that properly constructed effective Hamiltonians can capture the effect of the whole orbital space in small-size active spaces. Combining the downfolding pre-processing technique with the Variational Quantum Eigensolver, we solve for the ground-state energy of $\text{H}_2$ and $\text{Li}_2$ in the cc-pVTZ basis using the DUCC-reduced active spaces. We compare these results to full configuration-interaction and high-level coupled-cluster reference calculations.

quant-ph↗

arXiv2020

Equation of motion coupled-cluster approach for intrinsic losses in x-ray spectra

We present an equation of motion coupled cluster approach for calculating and understanding intrinsic inelastic losses in core level x-ray absorption spectra (XAS). The method is based on a factorization of the transition amplitude in the time-domain, which leads to a convolution of an effective one-body spectrum and the core-hole spectral function. The spectral function characterizes these losses in terms of shake-up excitations and satellites, and is calculated using a cumulant representation of the core-hole Green's function that includes non-linear corrections. The one-body spectrum also includes orthogonality corrections that enhance the XAS at the edge.

physics.chem-ph↗

arXiv2019

Green's Function Coupled Cluster Simulation of the Near-valence Ionizations of DNA-fragments

Accurate description of the ionization process in DNA is crucial to the understanding of the DNA damage under exposure to ionizing radiation, and the exploration of the potential application of DNA strands in nano-electronics. In this work, by employing our recently developed Green's function coupled-cluster (GFCC) library on supercomputing facilities, we have studied the spectral functions of several guanine$-$cytosine (G$-$C) base pair structures ([G$-$C]$_n$, $n=1-3$) for the first time in a relatively broad near-valence regime ([-25.0,-5.0] eV) in the coupled-cluster with singles and doubles (CCSD) level. Our focus is to give a preliminary many-body coupled-cluster understanding and guideline of the vertical ionization energy (VIE), spectral profile, and ionization feature changes of these systems as the system size expands in this near-valence regime. The results show that, as the system size expands, even though the lowest VIEs keep decreasing, the changes of spectral function profile and the relative peak positions get unexpectedly smaller. Further analysis of the ionized states associated with the most intensive peak in the spectral functions reveals non-negligible $|2h,1p\rangle$'s in the ionized wave functions of the considered G$-$C base pair systems. The leading $|2h,1p\rangle$'s associated with the main ionizations from the cytosine part of the G$-$C base pairs feature a transition from the intra-base-pair cytosine $π\rightarrowπ^\ast$ excitation to the inter-base-pair electron excitation as the size of G$-$C base pairs expands, which also indicates the minimum quantum region in the many-body calculations of DNA systems.

physics.chem-ph↗

arXiv2019

Coupled Cluster Greens function formulations based on the effective Hamiltonians

We demonstrate that the effective Hamiltonians obtained with the downfolding procedure based on double unitary coupled cluster (DUCC) ansatz can be used in the context of Greens function coupled cluster (GFCC) formalism to calculate spectral functions of molecular systems. This combined approach (DUCC-GFCC) provides a significant reduction of numerical effort and good agreement with the corresponding all-orbital GFCC methods in energy windows that are consistent with the choice of active space. These features are demonstrated on the example of two benchmark systems: H2O and N2, where DUCC-GFCC calculations were performed for active spaces of various sizes.

physics.comp-ph↗

arXiv2019

Quantum simulations of excited states with active-space downfolded Hamiltonians

Many-body techniques based on the double unitary coupled cluster ansatz (DUCC) can be used to downfold electronic Hamiltonians into low-dimensional active spaces. It can be shown that the resulting dimensionality reduced Hamiltonians are amenable for quantum computing. Recent studies performed for several benchmark systems using quantum phase estimation (QPE) algorithms demonstrated that these formulations can recover a significant portion of ground-state dynamical correlation effects that stem from the electron excitations outside of the active space. These results have also been confirmed in studies of ground-state potential energy surfaces using quantum simulators. In this letter, we study the effectiveness of the DUCC formalism in describing excited states. We also emphasize the role of the QPE formalism and its stochastic nature in discovering/identifying excited states or excited-state processes in situations when the knowledge about the true configurational structure of a sought after excited state is limited or postulated (due to the specific physics driving excited-state processes of interest). In this context, we can view the QPE algorithm as an engine for verifying various hypotheses for excited-state processes and providing statistically meaningful results that correspond to the electronic state(s) with the largest overlap with a postulated configurational structure. We illustrate these ideas on examples of strongly correlated molecular systems, characterized by small energy gaps and high density of quasi-degenerate states around the Fermi level.

quant-ph↗

arXiv2019

Q# and NWChem: Tools for Scalable Quantum Chemistry on Quantum Computers

Fault-tolerant quantum computation promises to solve outstanding problems in quantum chemistry within the next decade. Realizing this promise requires scalable tools that allow users to translate descriptions of electronic structure problems to optimized quantum gate sequences executed on physical hardware, without requiring specialized quantum computing knowledge. To this end, we present a quantum chemistry library, under the open-source MIT license, that implements and enables straightforward use of state-of-art quantum simulation algorithms. The library is implemented in Q#, a language designed to express quantum algorithms at scale, and interfaces with NWChem, a leading electronic structure package. We define a standardized schema for this interface, Broombridge, that describes second-quantized Hamiltonians, along with metadata required for effective quantum simulation, such as trial wavefunction ansatzes. This schema is generated for arbitrary molecules by NWChem, conveniently accessible, for instance, through Docker containers and a recently developed web interface EMSL Arrows. We illustrate use of the library with various examples, including ground- and excited-state calculations for LiH, H$_{10}$, and C$_{20}$ with an active-space simplification, and automatically obtain resource estimates for classically intractable examples.

quant-ph↗

arXiv2019

Approximate Green's Function Coupled Cluster Method Employing Effective Dimension Reduction

The Green's function coupled cluster (GFCC) method is a powerful many-body tool for computing the electronic structure of molecular and periodic systems, especially when electrons of the system are strongly correlated. However, for the GFCC to be routinely used in the electronic structure calculations, robust numerical techniques and approximations must be employed to reduce its high computational overhead. In our recent studies, we demonstrated that the GFCC equations can be solved directly in the frequency domain using iterative linear solvers, which can be easily distributed in a massively parallel environment. In the present work, we demonstrate a successful application of model-order-reduction (MOR) techniques in the GFCC framework. Briefly, for a frequency regime which requires high resolution spectral function, instead of solving GFCC linear equation of full dimension for every single frequency point, an efficiently-solvable linear system model of a reduced dimension may be built upon projecting the original GFCC linear system onto a subspace. From this reduced order model is obtained a reasonable approximation to the full dimensional GFCC linear equations in both interpolative and extrapolative spectral regions. Here, we show that the subspace can be properly constructed in an iterative manner from the auxiliary vectors of the GFCC linear equations at some selected frequencies within the spectral region of interest. During the iterations, the quality of the subspace and the linear system model can be systematically improved. The method is tested in terms of the efficiency and accuracy of computing spectral functions for some typical molecular systems such as carbon monoxide, 1,3-butadiene, benzene, and adenine. As a byproduct, the obtained reduced order model may provide a high quality initial guess which improves the convergence rate for the existing iterative linear solver.

physics.comp-ph↗

arXiv2019

Downfolding of many-body Hamiltonians using active-space models: extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms

In this paper we outline the extension of recently introduced the sub-system embedding sub-algebras coupled cluster (SES-CC) formalism to the unitary CC formalism. In analogy to the standard single-reference SES-CC formalism, its unitary CC extension allows one to include the dynamical (outside the active space) correlation effects in an SES induced complete active space (CAS) effective Hamiltonian. In contrast to the standard single-reference SES-CC theory, the unitary CC approach results in a Hermitian form of the effective Hamiltonian. Additionally, for the double unitary CC formalis (DUCC) the corresponding CAS eigenvalue problem provides a rigorous separation of external cluster amplitudes that describe dynamical correlation effects - used to define the effective Hamiltonian - from those corresponding to the internal (inside the active space) excitations that define the components of eigenvectors associated with the energy of the entire system. The proposed formalism can be viewed as an efficient way of downfolding many-electron Hamiltonian to the low-energy model represented by a particular choice of CAS. In principle, this technique can be extended to any type of complete active space representing an arbitrary energy window of a quantum system. The Hermitian character of low-dimensional effective Hamiltonians makes them an ideal target for several types of full configuration interaction (FCI) type eigensolvers. As an example, we also discuss the algebraic form of the perturbative expansions of the effective DUCC Hamiltonians corresponding to composite unitary CC theories and discuss possible algorithms for hybrid classical and quantum computing.

quant-ph↗

arXiv2018

Green's function coupled cluster formulations utilizing extended inner excitations

In this paper we analyze new approximations of the Green's function coupled cluster (GFCC) method where locations of poles are improved by extending the excitation level of inner auxiliary operators. These new GFCC approximations can be categorized as GFCC-i($n,m$) method, where the excitation level of the inner auxiliary operators ($m$) used to describe the ionization potentials and electron affinities effects in the $N$$-$1 and $N$+1 particle spaces is higher than the excitation level ($n$) used to correlate the ground-state coupled cluster wave function for the $N$-electron system. Furthermore, we reveal the so-called "$n$+1" rule in this category (or the GFCC-i($n$,$n$+1) method), which states that in order to maintain size-extensivity of the Green's function matrix elements, the excitation level of inner auxiliary operators $X_p(ω)$ and $Y_q(ω)$ cannot exceed $n$+1. We also discuss the role of the moments of coupled cluster equations that in a natural way assures these properties. Our implementation in the present study is focused on the first approximation in this GFCC category, i.e. the GFCC-i(2,3) method. As our first practice, we use the GFCC-i(2,3) method to compute the spectral functions for the N$_2$ and CO molecules in the inner and outer valence regimes. In comparison with the GFCCSD results, the computed spectral functions from the GFCC-i(2,3) method exhibit better agreement with the experimental results and other theoretical results, particularly in terms of providing higher resolution of satellite peaks and more accurate relative positions of these satellite peaks with respect to the main peak positions.

cond-mat.str-el↗

arXiv2015

Sign learning kink-based (SiLK) quantum Monte Carlo for molecular systems

The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H$_{2}$O, N$_2$, and F$_2$ molecules. The method is based on Feynman's path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of other quantum chemical methods and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem.

physics.comp-ph↗