Scalable computational chemistry: new developments and applications

The computational part of the thesis is the investigation of titanium chloride (II) as a potential catalyst for the bis-silylation reaction of ethylene with hexaclorodisilane at different levels of theory. Bis-silylation is an important reaction for producing bis(silyl) compounds and new C-Si bonds, which can serve as monomers for silicon containing polymers and silicon carbides. Ab initio calculations on the steps involved in a proposed mechanism are presented. This choice of reactants allows us to study this reaction at reliable levels of theory without compromising accuracy. Our calculations indicate that this is a highly exothermic barrierless reaction. The TiCl 2 catalyst removes a 50 kcal/mol activation energy barrier required for the reaction without the catalyst. The first step is interaction of TiCl 2 with ethylene to form an intermediate that is 60 kcal/mol below the energy of the reactants. This is the driving force for the entire reaction. Dynamic correlation plays a significant role because RHF calculations indicate that the net barrier for the catalyzed reaction is 50 kcal/mol. We conclude that divalent Ti has the potential to become an important industrial catalyst for silylation reactions.;In the programming part of the thesis, parallelization of different quantum chemistry methods is presented. The parallelization of code is becoming important aspect of quantum chemistry code development. Two trends contribute to it: the overall desire to study large chemical systems and the desire to employ highly correlated methods which are usually computationally and memory expensive. In the presented distributed data algorithms computation is parallelized and the largest arrays are evenly distributed among CPUs. First, the parallelization of the Hartree-Fock self-consistent field (SCF) method is considered. SCF method is the most common starting point for more accurate calculations. The Fock build (sub step of SCF) from AO integrals is also often used to avoid MO integral computation. The presented distributed data SCF increases the size of chemical systems that can be calculated by using RHF and DFT. The important ab initio method to study bond formation and breaking as well as excited molecules is CASSCF. The presented distributed data CASSCF algorithm can significantly decrease computational time and memory requirements per node. Therefore, large CASSCF computations can be performed. The most time consuming operation to study potential energy surfaces of reactions and chemical systems is Hessian calculations. The distributed data parallelization of CPHF will allow scientists carry out large analytic Hessian calculations

Evaluating Quantum Approximate Optimization Algorithm: A Case Study

Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising quantum algorithms for the Noisy Intermediate-Scale Quantum (NISQ) era. Quantifying the performance of QAOA in the near-term regime is of utmost importance. We perform a large-scale numerical study of the approximation ratios attainable by QAOA is the low- to medium-depth regime. To find good QAOA parameters we perform 990 million 10-qubit QAOA circuit evaluations. We find that the approximation ratio increases only marginally as the depth is increased, and the gains are offset by the increasing complexity of optimizing variational parameters. We observe a high variation in approximation ratios attained by QAOA, including high variations within the same class of problem instances. We observe that the difference in approximation ratios between problem instances increases as the similarity between instances decreases. We find that optimal QAOA parameters concentrate for instances in out benchmark, confirming the previous findings for a different class of problems

Network Community Detection On Small Quantum Computers

In recent years a number of quantum computing devices with small numbers of qubits became available. We present a hybrid quantum local search (QLS) approach that combines a classical machine and a small quantum device to solve problems of practical size. The proposed approach is applied to the network community detection problem. QLS is hardware-agnostic and easily extendable to new quantum computing devices as they become available. We demonstrate it to solve the 2-community detection problem on graphs of size up to 410 vertices using the 16-qubit IBM quantum computer and D-Wave 2000Q, and compare their performance with the optimal solutions. Our results demonstrate that QLS perform similarly in terms of quality of the solution and the number of iterations to convergence on both types of quantum computers and it is capable of achieving results comparable to state-of-the-art solvers in terms of quality of the solution including reaching the optimal solutions

Quantum Divide and Compute: Hardware Demonstrations and Noisy Simulations

Noisy, intermediate-scale quantum computers come with intrinsic limitations in terms of the number of qubits (circuit "width") and decoherence time (circuit "depth") they can have. Here, for the first time, we demonstrate a recently introduced method that breaks a circuit into smaller subcircuits or fragments, and thus makes it possible to run circuits that are either too wide or too deep for a given quantum processor. We investigate the behavior of the method on one of IBM's 20-qubit superconducting quantum processors with various numbers of qubits and fragments. We build noise models that capture decoherence, readout error, and gate imperfections for this particular processor. We then carry out noisy simulations of the method in order to account for the observed experimental results. We find an agreement within 20% between the experimental and the simulated success probabilities, and we observe that recombining noisy fragments yields overall results that can outperform the results without fragmentation.Comment: Accepted in ISVLSI 202

Of Representation Theory and Quantum Approximate Optimization Algorithm

In this paper, the Quantum Approximate Optimization Algorithm (QAOA) is analyzed by leveraging symmetries inherent in problem Hamiltonians. We focus on the generalized formulation of optimization problems defined on the sets of $n$-element $d$-ary strings. Our main contribution encompasses dimension reductions for the originally proposed QAOA. These reductions retain the same problem Hamiltonian as the original QAOA but differ in terms of their mixer Hamiltonian, and initial state. The vast QAOA space has a daunting dimension of exponential scaling in $n$, where certain reduced QAOA spaces exhibit dimensions governed by polynomial functions. This phenomenon is illustrated in this paper, by providing partitions corresponding to polynomial dimensions in the corresponding subspaces. As a result, each reduced QAOA partition encapsulates unique classical solutions absent in others, allowing us to establish a lower bound on the number of solutions to the initial optimization problem. Our novel approach opens promising practical advantages in accelerating the class of QAOA approaches, both quantum-based and classical simulation of circuits, as well as a potential tool to cope with barren plateaus problem

An efficient MPI/OpenMP parallelization of the Hartree-Fock method for the second generation of Intel Xeon Phi processor

Modern OpenMP threading techniques are used to convert the MPI-only Hartree-Fock code in the GAMESS program to a hybrid MPI/OpenMP algorithm. Two separate implementations that differ by the sharing or replication of key data structures among threads are considered, density and Fock matrices. All implementations are benchmarked on a super-computer of 3,000 Intel Xeon Phi processors. With 64 cores per processor, scaling numbers are reported on up to 192,000 cores. The hybrid MPI/OpenMP implementation reduces the memory footprint by approximately 200 times compared to the legacy code. The MPI/OpenMP code was shown to run up to six times faster than the original for a range of molecular system sizes.Comment: SC17 conference paper, 12 pages, 7 figure