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1. Light-Front Field Theory on Current Quantum Computers

   https://doi.org/10.3390/e23050597  

   Kreshchuk, Michael; Jia, Shaoyang; Kirby, William M.; Goldstein, Gary; Vary, James P.; Love, Peter J. (May 2021, Entropy)

   null (Ed.)

   We present a quantum algorithm for simulation of quantum field theory in the light-front formulation and demonstrate how existing quantum devices can be used to study the structure of bound states in relativistic nuclear physics. Specifically, we apply the Variational Quantum Eigensolver algorithm to find the ground state of the light-front Hamiltonian obtained within the Basis Light-Front Quantization (BLFQ) framework. The BLFQ formulation of quantum field theory allows one to readily import techniques developed for digital quantum simulation of quantum chemistry. This provides a method that can be scaled up to simulation of full, relativistic quantum field theories in the quantum advantage regime. As an illustration, we calculate the mass, mass radius, decay constant, electromagnetic form factor, and charge radius of the pion on the IBM Vigo chip. This is the first time that the light-front approach to quantum field theory has been used to enable simulation of a real physical system on a quantum computer. 

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2. Generalization of Intrinsic Orbitals to Kramers-Paired Quaternion Spinors, Molecular Fragments, and Valence Virtual Spinors

   https://doi.org/10.1021/acs.jctc.0c00964  

   Senjean, Bruno; Sen, Souloke; Repisky, Michal; Knizia, Gerald; Visscher, Lucas (January 2011, Journal of Chemical Theory and Computation)

   null (Ed.)

   Localization of molecular orbitals finds its importance in the representation of chemical bonding (and anti-bonding) and in the local correlation treatments beyond mean-field approximation. In this paper, we generalize the intrinsic atomic and bonding orbitals [G. Knizia, J. Chem. Theory Comput. 2013, 9, 11, 4834-4843] to relativistic applications using complex and quaternion spinors, as well as to molecular fragments instead of atomic fragments only. By performing a singular value decomposition, we show how localized valence virtual orbitals can be expressed in this intrinsic minimal basis. We demonstrate our method on systems of increasing complexity, starting from simple cases such as benzene, acrylic-acid and ferrocene molecules, and then demonstrating the use of molecular fragments and inclusion of relativistic effects for complexes containing heavy elements such as tellurium, iridium and astatine. The aforementioned scheme is implemented into a standalone program interfaced with several different quantum chemistry packages. 

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3. Benchmarking DFT approaches for the calculation of polarizability inputs for refractive index predictions in organic polymers

   https://doi.org/10.1039/C8CP05492D  

   Afzal, Mohammad Atif; Hachmann, Johannes (February 2019, Physical Chemistry Chemical Physics)

   In a previous study, we introduced a new computational protocol to accurately predict the index of refraction (RI) of organic polymers using a combination of first-principles and data modeling. This protocol is based on the Lorentz–Lorenz equation and involves the calculation of static polarizabilities and number densities of oligomer sequences, which are extrapolated to the polymer limit. We chose to compute the polarizabilities within the density functional theory (DFT) framework using the PBE0/def2-TZVP-D3 model chemistry. While this ad hoc choice proved remarkably successful, it is also relatively expensive from a computational perspective. It represents the bottleneck step in the overall RI modeling protocol, thus limiting its utility for virtual high-throughput screening studies, in which efficiency is essential. For polymers that exhibit late-onset extensivity, the employed linear extrapolation scheme can require demanding calculations on long-oligomer sequences, thus becoming another bottleneck. In the work presented here, we benchmark DFT model chemistries to identify approaches that optimize the balance between accuracy and efficiency for this application domain. We compare results for conjugated and non-conjugated polymers, augment our original extrapolation approach with a non-linear option, analyze how the polarizability errors propagate into the RI predictions, and offer guidance for method selection. 

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4. Relativistic nucleon–nucleon potentials in a spin-dependent three-dimensional approach

   https://doi.org/10.1038/s41598-021-96924-1  

   Hadizadeh, M. R.; Radin, M.; Nazari, F. (December 2021, Scientific Reports)

   null (Ed.)

   Abstract The matrix elements of relativistic nucleon–nucleon ( NN ) potentials are calculated directly from the nonrelativistic potentials as a function of relative NN momentum vectors, without a partial wave decomposition. To this aim, the quadratic operator relation between the relativistic and nonrelativistic NN potentials is formulated in momentum-helicity basis states. It leads to a single integral equation for the two-nucleon (2 N ) spin-singlet state, and four coupled integral equations for two-nucleon spin-triplet states, which are solved by an iterative method. Our numerical analysis indicates that the relativistic NN potential obtained using CD-Bonn potential reproduces the deuteron binding energy and neutron-proton elastic scattering differential and total cross-sections with high accuracy. 

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5. A High-Order Well-Balanced Discontinuous Galerkin Method for Hyperbolic Balance Laws Based on the Gauss-Lobatto Quadrature Rules

   https://doi.org/10.1007/s10915-024-02661-8  

   Xu, Ziyao; Shu, Chi-Wang (October 2024, Journal of Scientific Computing)

   Abstract In this paper, we develop a high-order well-balanced discontinuous Galerkin method for hyperbolic balance laws based on the Gauss-Lobatto quadrature rules. Important applications of the method include preserving the non-hydrostatic equilibria of shallow water equations with non-flat bottom topography and Euler equations in gravitational fields. The well-balanced property is achieved through two essential components. First, the source term is reformulated in a flux-gradient form in the local reference equilibrium state to mimic the true flux gradient in the balance laws. Consequently, the source term integral is discretized using the same approach as the flux integral at Gauss-Lobatto quadrature points, ensuring that the source term is exactly balanced by the flux in equilibrium states. Our method differs from existing well-balanced DG methods for shallow water equations with non-hydrostatic equilibria, particularly in the aspect that it does not require the decomposition of the source term integral. The effectiveness of our method is demonstrated through ample numerical tests. 

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