Article
Chemistry, Physical
Elisabeth Keller, Theodoros Tsatsoulis, Karsten Reuter, Johannes T. Margraf
Summary: This paper explores how regularization can ameliorate the issues of second-order Moller-Plesset perturbation theory (MP2) for metallic, polarizable, and strongly correlated periodic systems. Two regularized second-order methods are applied to various systems, leading to consistent improvements over the MP2 baseline with different regularizers found to be suitable for different systems.
JOURNAL OF CHEMICAL PHYSICS
(2022)
Article
Chemistry, Physical
Alexander E. Doran, So Hirata
Summary: A scalable stochastic algorithm for evaluating fourth-order many-body perturbation (MP4) correction to energy has been proposed. The algorithm involves computer-generated diagrams and algebraic formulas expressed in terms of Green's functions, and is evaluated using Monte Carlo integration accelerated by redundant walker and control variate algorithms. The resulting MC-MP4 method is efficiently parallelized with significantly lower cost dependence compared to deterministic MP4 algorithm. It has been shown to accurately evaluate the energy of various molecules with a statistical uncertainty within a certain range after a large number of Monte Carlo steps.
JOURNAL OF CHEMICAL PHYSICS
(2021)
Article
Physics, Multidisciplinary
Yucheng Wang, Chen Cheng, Xiong-Jun Liu, Dapeng Yu
Summary: This study predicts a novel many-body critical phase in the one-dimensional model, which exhibits distinct characteristics from both the ergodic phase and the many-body localization phase. The level statistics in this new phase follow critical statistics, the wave functions show multifractal behavior, and the entanglement entropy scales with a volume law. These results challenge the eigenstate thermalization hypothesis and provide new insights into the behavior of many-body systems.
PHYSICAL REVIEW LETTERS
(2021)
Article
Chemistry, Physical
Christopher J. N. Coveney, David P. P. Tew
Summary: We propose a scalable single-particle framework for treating electronic correlation in molecules and materials based on Green's function theory. By introducing the Goldstone self-energy, we derive a size-extensive Brillouin-Wigner perturbation theory from the single-particle Green's function. This new ground state correlation energy, named Quasi-Particle MP2 theory (QPMP2), avoids the characteristic divergences in strongly correlated systems present in second-order Moller-Plesset perturbation theory and Coupled Cluster Singles and Doubles methods, and demonstrates excellent performance in reproducing exact ground state energy and properties of the Hubbard dimer as well as larger Hubbard models.
JOURNAL OF CHEMICAL THEORY AND COMPUTATION
(2023)
Article
Chemistry, Physical
Ilia M. Mazin, Alexander Yu Sokolov
Summary: This study presents a new implementation and benchmark of approximations in multireference algebraic diagrammatic construction theory for simulations of neutral electronic excitations and UV/vis spectra of strongly correlated molecular systems. The results demonstrate that the proposed MR-ADC methods outperform third-order single-reference ADC approximation for weakly correlated electronic states and are competitive with equation-of-motion coupled cluster theory results. For states with multireference character, the performance of the MR-ADC methods is similar to that of N-electron valence perturbation theory.
JOURNAL OF CHEMICAL THEORY AND COMPUTATION
(2021)
Article
Mathematics, Interdisciplinary Applications
Surendra Kumar, Paras Sharma
Summary: This paper studies impulsive second-order stochastic differential systems in a separable Hilbert space X. By using projection operators, the given problem is restricted to a finite-dimensional subspace. The existence and convergence of estimated solutions are investigated using the theories of cosine family and fractional powers of a closed linear operator. The existence and convergence of Faedo-Galerkin approximate solutions are also examined. Finally, examples are constructed to demonstrate the effectiveness of the obtained results.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Musa Cakir, Gabil M. Amiraliyev
Summary: This paper presents a monotone numerical method for solving singularly perturbed three-point reaction-diffusion boundary value problems on a uniform mesh. The method is proven to be second-order uniformly convergent with respect to the singular perturbation parameter in discrete maximum norm. The efficiency of the proposed method is demonstrated through a numerical example.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2021)
Article
Economics
Yukitoshi Matsushita, Taisuke Otsu
Summary: This paper investigates the second-order properties of robust t-ratios for instrumental variable regression models, and proposes second-order refinements to improve their size and power properties. The study shows that the second-order terms of the t-ratio expansions have non-trivial impacts on their size and power. Adjusted t-ratios are proposed to improve null rejection probabilities and exhibit desirable power properties. The paper also considers heteroskedasticity robust t-ratios and proposes adjustments for slight deviations from homoskedasticity.
JOURNAL OF ECONOMETRICS
(2023)
Article
Materials Science, Multidisciplinary
Alan Morningstar, Luis Colmenarez, Vedika Khemani, David J. Luitz, David A. Huse
Summary: In this study, we numerically investigate the avalanche instability and many-body resonances in strongly disordered spin chains exhibiting many-body localization (MBL). We find that finite-size systems behave like MBL within the MBL regimes, and we identify landmarks that divide the MBL regimes into different subregimes based on the onset of avalanches and many-body resonances.
Article
Mathematics, Applied
Mustafa Kudu, Ilhame Amirali, Gabil M. Amiraliyev
Summary: This paper investigates a class of parameterized singularly perturbed problems with integral boundary condition and proposes a finite difference scheme of hybrid type with an appropriate Shishkin mesh. It is proven that the method converges almost second order in the discrete maximum norm, which is illustrated by numerical results supporting the theoretical findings.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Robotics
John N. Nganga, Patrick M. Wensing
Summary: This study introduces a method to reduce the computational demands when incorporating second-order dynamics sensitivity information into the DDP algorithm. By leveraging reverse-mode accumulation of derivative information to compute a key vector-tensor product directly, the need for computing the derivative tensor can be avoided, leading to faster computation. The benchmarks show that benefits of DDP can be achieved without sacrificing evaluation time, and in fewer iterations compared to iLQR.
IEEE ROBOTICS AND AUTOMATION LETTERS
(2021)
Article
Physics, Multidisciplinary
David Layden
Summary: Simulating quantum dynamics beyond classical computers' capabilities is a major application of quantum computers. The Trotter formula and its higher-order variants are the most promising quantum algorithms for this purpose in the near future. However, the approximation error of these algorithms is often poorly understood, especially in cases where the target Hamiltonian can be decomposed into two realizable terms. This study provides a simpler understanding of these effects by relating the Trotter formula to its second-order variant for such cases. The findings reduce the required circuit depth for quantum simulation algorithms and illustrate a useful method for bounding simulation error more broadly.
PHYSICAL REVIEW LETTERS
(2022)
Article
Engineering, Aerospace
Xia Jiang, Zhenzhou Lu
Summary: Failure credibility is a measure of the safety degree of a structure under fuzzy uncertainty. The fuzzy first-order and second-moment (FFOSM) method is an efficient and accurate analytical method for solving failure credibility. This study proposes an equivalent regularization (EqRe) method to extend FFOSM to problems with irregularly and diversely distributed fuzzy inputs (Ir-FuI). The proposed E-FFOSM efficiently estimates the failure credibility of problems with Ir-FuI, inheriting the high efficiency and accuracy of classical FFOSM.
AEROSPACE SCIENCE AND TECHNOLOGY
(2022)
Article
Mathematics
Manikandan Mariappan, Chandru Muthusamy, Higinio Ramos
Summary: This article develops and analyzes a numerical scheme to solve a singularly perturbed parabolic system of n reaction-diffusion equations. The scheme considers m equations with a perturbation parameter and the rest without it. It uses finite difference approximations on a uniform mesh in the temporal variable and a piecewise uniform Shishkin mesh in the spatial variable. Convergence properties and error analyses are derived, and numerical experiments are presented to support the theoretical results.
Article
Chemistry, Physical
Alexander P. Fellows, Vasileios Balos, Ben John, Alvaro Diaz Duque, Martin Wolf, Martin Thaemer
Summary: Second-order nonlinear spectroscopy is an important technique for studying interfacial systems due to its ability to analyze molecular structures and interactions. This study demonstrates that information about depth distributions, molecular orientation, and local dielectric properties can be extracted from the phase of the measured signal using multiple nonlinear pathways. This novel information can be correlated to characteristic vibrational spectra, enabling advanced sample characterization and analysis of interfacial molecular structures.
JOURNAL OF CHEMICAL PHYSICS
(2023)
Article
Chemistry, Multidisciplinary
Yu-ya Ohnishi, Seiichiro Ten-no
JOURNAL OF COMPUTATIONAL CHEMISTRY
(2016)
Article
Chemistry, Physical
Andreas Grueneis, So Hirata, Yu-Ya Ohnishi, Seiichiro Ten-no
JOURNAL OF CHEMICAL PHYSICS
(2017)
Article
Chemistry, Physical
Yu-ya Ohnishi, So Hirata
Article
Chemistry, Physical
Yu-ya Ohnishi, Kazuya Ishimura, Seiichiro Ten-no
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY
(2015)
Article
Chemistry, Physical
Yu-ya Ohnishi, Kazuya Ishimura, Seiichiro Ten-no
JOURNAL OF CHEMICAL THEORY AND COMPUTATION
(2014)
Article
Chemistry, Multidisciplinary
Dinesh G. (Dan) Patel, Fude Feng, Yu-ya Ohnishi, Khalil A. Abboud, So Hirata, Kirk S. Schanze, John R. Reynolds
JOURNAL OF THE AMERICAN CHEMICAL SOCIETY
(2012)
Article
Chemistry, Physical
Yu-ya Ohnishi, Seiichiro Ten-no
Article
Chemistry, Physical
So Hirata, Yu-ya Ohnishi
PHYSICAL CHEMISTRY CHEMICAL PHYSICS
(2012)
Review
Physics, Multidisciplinary
Yutaka Shikano, Hiroshi C. Watanabe, Ken M. Nakanishi, Yu-ya Ohnishi
Summary: Quantum computational chemistry is a potential application of quantum computers that aims to effectively solve quantum-chemistry problems, particularly the electronic structure problem. Quantum algorithms, phase estimation, and variational quantum eigensolver have been applied in post-Hartree-Fock methods.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2021)
Article
Chemistry, Physical
Qi Gao, Gavin O. Jones, Mario Motta, Michihiko Sugawara, Hiroshi C. Watanabe, Takao Kobayashi, Eriko Watanabe, Yu-ya Ohnishi, Hajime Nakamura, Naoki Yamamoto
Summary: A quantum chemistry study was conducted on the first singlet and triplet excited states of phenylsulfonyl-carbazole compounds, with quantum simulations on devices showing excellent agreement with experimental data. By utilizing state tomography to purify quantum states and correct energy values, large errors in unmitigated results could be improved to minimal differences with exact values, leading to excellent agreement between predicted values by quantum simulations and those found in experiments.
NPJ COMPUTATIONAL MATERIALS
(2021)
Article
Chemistry, Physical
Yuya O. Nakagawa, Jiabao Chen, Shotaro Sudo, Yu-ya Ohnishi, Wataru Mizukami
Summary: We propose a quantum-classical hybrid algorithm to calculate the analytical second-order derivative of the energy for the orbital-optimized variational quantum eigensolver (OO-VQE). The algorithm allows for the evaluation of all quantities required without the need for any ancillary qubits. Numerical simulations of quantum circuits are used to validate the formula for computing the polarizability of the water molecule, and the polarizabilities and refractive indices of thiophene and furan molecules are calculated as well. Comparison with numerical derivatives obtained by finite difference shows that the proposed analytical derivative requires fewer measurements on quantum computers to achieve the same accuracy.
JOURNAL OF CHEMICAL THEORY AND COMPUTATION
(2023)
Article
Chemistry, Multidisciplinary
Mario Motta, Gavin O. Jones, Julia E. Rice, Tanvi P. Gujarati, Rei Sakuma, Ieva Liepuoniute, Jeannette M. Garcia, Yu-ya Ohnishi
Summary: This study uses the IBM Falcon architecture superconducting quantum processor to simulate the static and dynamic electronic structure of a triply-bonded sulfur cation. By combining quantum computing techniques with error-mitigation techniques, the dominant molecular fragmentation pathways in photo-dissociation experiments were calculated. The results are important for the computational description of photo-dissociation on near-term quantum devices.
Article
Optics
Kaito Wada, Rudy Raymond, Yu-ya Ohnishi, Eriko Kaminishi, Michihiko Sugawara, Naoki Yamamoto, Hiroshi C. Watanabe
Summary: This paper proposes a method to optimize arbitrary single-qubit gates in parametrized quantum circuits for simulating real- and imaginary-time evolution. The method fully utilizes the degrees of freedom of single-qubit gates and optimizes both the axis and angle simultaneously. Numerical experiments show its effectiveness in finding ground states and real-time evolution.
Article
Physics, Multidisciplinary
Nobuyuki Yoshioka, Takeshi Sato, Yuya O. Nakagawa, Yu-ya Ohnishi, Wataru Mizukami
Summary: In this paper, we present a quantum-classical hybrid algorithm for simulating electronic structures of periodic systems. By extending the unitary coupled cluster (UCC) theory and using the quantum subspace expansion method, we successfully optimized the UCC ansatz and computed the quasiparticle band structure.
PHYSICAL REVIEW RESEARCH
(2022)
Article
Physics, Multidisciplinary
Wataru Mizukami, Kosuke Mitarai, Yuya O. Nakagawa, Takahiro Yamamoto, Tennin Yan, Yu-ya Ohnishi
PHYSICAL REVIEW RESEARCH
(2020)