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Quantum algorithm for an additive approximation of Ising partition functions

Physical Review A 2014年第2期90卷 022304-022304页

作者： Akira Matsuo Keisuke Fujii Nobuyuki Imoto Graduate School of Engineering Science Osaka University Toyonaka Osaka 560-8531 Japan The Hakubi Center for Advanced Research Kyoto University Yoshida-Ushinomiya-cho Sakyo-ku Kyoto 606-8302 Japan Graduate School of Informatics Kyoto University Yoshida Honmachi Sakyo-ku Kyoto 606-8501 Japan

We investigate quantum-computational complexity of calculating partition functions of Ising models. We construct a quantum algorithm for an additive approximation of Ising partition functions on square lattices. To this end, we utilize the overlap mapping developed by M. Van den Nest, W. Dür, and H. J. Briegel [Phys. Rev. Lett. 98, 117207 (2007)] and its interpretation through measurement-based quantum computation (MBQC). We specify an algorithmic domain, on which the proposed algorithm works, and an approximation scale, which determines the accuracy of the approximation. We show that the proposed algorithm performs a nontrivial task, which would be intractable on any classical computer, by showing that the problem that is solvable by the proposed quantum algorithm is BQP-complete. In the construction of the BQP-complete problem coupling strengths and magnetic fields take complex values. However, the Ising models that are of central interest in statistical physics and computer science consist of real coupling strengths and magnetic fields. Thus we extend the algorithmic domain of the proposed algorithm to such a real physical parameter region and calculate the approximation scale explicitly. We found that the overlap mapping and its MBQC interpretation improve the approximation scale exponentially compared to a straightforward constant-depth quantum algorithm. On the other hand, the proposed quantum algorithm also provides partial evidence that there exist no efficient classical algorithm for a multiplicative approximation of the Ising partition functions even on the square lattice. This result supports the observation that the proposed quantum algorithm also performs a nontrivial task in the physical parameter region.

关键词： QUANTUM theory QUANTUM computing COMPUTATIONAL complexity APPROXIMATION theory ISING model partition functions ALGORITHMS

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Fundamental view on the calculation of internal partition functions using occupational probabilities

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PHYSICS LETTERS A 2013年第15期377卷 1119-1126页

作者： Zaghloul, Mofreh R. United Arab Emirates Univ Coll Sci Dept Phys Al Ain U Arab Emirates

From first principles, the author gathers a few general rules that need to be abided by in the calculation of the internal partition functions (IPFs) of individual molecules. These rules are violated in many schemes in the literature where occupational probabilities are used including those using the Planck-Larkin partition function (PLPF) within the chemical picture. Considering these rules is useful from conceptual and practical points of view. A solution is introduced to assure fulfilling the above mentioned rules when using occupational probabilities. Sample calculations are performed showing quantitative significance of inaccuracies caused by dishonoring such rules. (C) 2013 Elsevier B.V. All rights reserved.

关键词： PROBABILITY theory partition functions MOLECULES functions (Mathematics) QUANTITATIVE chemical analysis

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Ab initio the thermodynamic properties and UV spectrum of AlCl⁺

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CHEMICAL PHYSICS LETTERS 2024年 856卷

作者： Fang, Nan Zhang, Chuan-Yu Wan, Ming-Jie Huang, Xiao-Peng Chengdu Univ Technol Sch Math & Phys Chengdu 610059 Peoples R China Yibin Univ Computat Phys Key Lab Sichuan Prov Yibin 644000 Peoples R China

AlCl+ as a potential interstellar molecule has attracted significant attention, but gaps remain in our understanding of its thermodynamic properties and spectral line intensities. This study employed the icMRCI+Q method to compute potential energy curves for the 13 Lambda-S states of AlCl+. Based on these curves, spectroscopic parameters and vibrational-rotational energy levels were determined. Subsequently, partition functions were calculated over a temperature range from 50 K to 10000 K, and the thermodynamic properties were derived. Using transition dipole moments, the UV spectra for transitions from the ground state (X (2)Sigma(+)) to the third excited state (2(2)Pi) were computed at 298.15 K.

关键词： partition functions Line intensities Ultraviolet spectrum Thermodynamic properties

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The 2024 release of the ExoMol database: Molecular line lists for exoplanet and other hot atmospheres

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JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER 2024年 326卷

作者： Tennyson, Jonathan Yurchenko, Sergei N. Zhang, Jingxin Bowesman, Charles A. Brady, Ryan P. Buldyreva, Jeanna Chubb, Katy L. Gamache, Robert R. Gorman, Maire N. Guest, Elizabeth R. Hill, Christian Kefala, Kyriaki Lynas-Gray, A. E. Mellor, Thomas M. McKemmish, Laura K. Mitev, Georgi B. Mizus, Irina I. Owens, Alec Peng, Zhijian Perri, Armando N. Pezzella, Marco Polyansky, Oleg L. Qu, Qianwei Semenov, Mikhail Smola, Oleksiy Solokov, Andrei Somogyi, Wilfrid Upadhyay, Apoorva Wright, Samuel O. M. Zobov, Nikolai F. UCL Dept Phys & Astron Gower St London WC1E 6BT England HH Wills Phys Lab Sch Phys Tyndall Ave Bristol BS8 1TL England Univ Oxford Dept Phys Keble Rd Oxford OX1 3RH England Univ Western Cape Dept Phys & Astron Private Bag X17 ZA-7535 Bellville South Africa IAEA Nucl Data Sect A-1400 Vienna Austria Univ New South Wales Sch Chem Sydney 2052 Australia Univ Franche Comte Inst UTINAM UMR 6213 CNRS 16 Route Gray F-25030 Besancon France Univ Massachusetts Lowell Dept Environm Earth & Atmospher Sci Lowell MA 01854 USA Univ Perugia Dipartimento Fis & Geol Via Pascoli SNC Perugia 06123 Italy Univ Sussex Sch Math & Phys Sci Brighton BN1 9QH England Russian Acad Sci Inst Appl Phys 46 Ulyanov St Nizhnii Novgorod 603950 Russia

The ExoMol database (***) provides molecular data for spectroscopic studies of hot atmospheres. These data are widely used to model atmospheres of exoplanets, cool stars and other astronomical objects, as well as a variety of terrestrial applications. The 2024 data release reports the current status of the database which contains recommended line lists for 91 molecules and 224 isotopologues giving a total of almost 1012 12 individual transitions. New features of the database include extensive "MARVELization"of line lists to allow them to be used for high resolutions studies, extension of several line lists to ultraviolet wavelengths, provision of photodissociation cross-sections and extended provision of broadening parameters. Some of the in-house data specifications have been rewritten in JSON and moved for conformity with other international standards. Data products, including specific heats, a database of lifetimes for plasma studies, and the ExoMolHR web app which allows exclusively high resolution data to be extracted, are discussed.

关键词： Infrared Visible Einstein A coefficients Transition frequencies partition functions Cooling functions Lifetimes Cross-sections k coefficients Pressure broadening Photodissociation Ultraviolet

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Ultraviolet spectroscopy of AlO from first principle

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JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER 2023年第1期302卷

作者： Bai, Tianrui Qin, Zhi Liu, Linhua Jiangsu Univ Sci & Technol Sch Energy & Power Zhenjiang 212100 Jiangsu Peoples R China Shandong Univ Inst Frontier & Interdisciplinary Sci Opt & Thermal Radiat Res Ctr Qingdao 266237 Shandong Peoples R China Shandong Univ Sch Energy & Power Engn Jinan 250061 Shandong Peoples R China Harbin Inst Technol Sch Energy Sci & Engn Harbin 150001 Heilongjiang Peoples R China

The spectrum of AlO is widely used in various applications including the explorations of interstellar space, studies of laser ablation, combustions of Al-containing fuels and so on. In this work, we reported the spectroscopy of the AlO radical at temperatures of 300 similar to 15,000 K for the wavenumber range of 1 similar to 55,000 cm(-1). Firstly, we extended our previous calculations of the potential energy curves (PECs) and transition dipole moments (TDMs) for AlO (Bai, Qin & Liu, MNRAS, 2022, 510:1649-1656) to higher B-2 Sigma(+), D-2 Sigma(+), 1'(2)Pi and 1(''2)Pi electronic states, with the consideration of Davidson correction, scalar relativistic correction and core-valence correlation. partition functions, Einstein coefficients and radiative lifetimes of AlO were then obtained by solving the nuclear-motion Schrodinger equation. The partition functions reveal that the AlO molecules mainly exist in the X-2 Sigma(+) state at temperatures of 10 similar to 6270 K and in the A(2)Pi state at temperatures of 6270 similar to 15,000 K in the thermodynamic equilibrium. Finally, line intensities and spectra for different electronic transitions of AlO were calculated. The results show that the X-2 Sigma(+) -> C-2 Pi and X-2 Sigma(+) -> D-2 Sigma(+) transitions dominate in the ultraviolet waveband. Comparisons of the TDMs, radiative lifetimes, line intensities and spectra with previous theoretical and experimental values indicate that our calculated data in the ultraviolet waveband are reliable and may be used for the radiation field calculation. (c) 2023 Elsevier Ltd. All rights reserved.

关键词： partition functions Radiative lifetimes Line intensities Ultraviolet spectrum AlO

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Quantitative analysis of carbon content in fly ash using LIBS based on support vector regression

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ADVANCED POWDER TECHNOLOGY 2021年第8期32卷 2978-2987页

作者： Liu, Renwei Chen, Peng Wang, Zhenzhen Rong, Kai Yan, Junjie Liu, Jiping Deguchi, Yoshihiro Xi An Jiao Tong Univ Moe Key Lab Thermofluid Sci & Engn Xian 710049 Peoples R China Tokushima Univ Grad Sch Technol Ind & Social Sci Tokushima 7708501 Japan Xi An Jiao Tong Univ State Key Lab Multiphase Flow Power Engn Xian 710049 Peoples R China 28 Xianning West Rd Xian 710049 Peoples R China

Laser-induced breakdown spectroscopy (LIBS) has been proved as an on-line detection technology to measure the carbon content in fly ash, which is beneficial for immediate assessment of the boiler combustion efficiency. Support vector regression (SVR) was adopted as the quantitative model for the carbon content measurement in fly ash in this study. Ash species was one of the key factors affecting quantitative accuracy. Experiments have proven that, the index of plasma temperature and the electron density among different species could be similar, while the partition function ratios and the temperature correction factor showed obvious differences among different ash species. Based on the partition function ratios, the Matrix Effect Correction Factor (MECF) was defined. SVR model was optimized by MECF and the analysis results showed that the correlation coefficient of calibration (R-2) increased from 0.989 to 0.991, the root-mean-square error of calibration (RMSEC) decreased from 2.02% to 0.850%, the root-mean-square error of prediction (RMSEP) decreased from 2.13% to 1.07%, and averaged relative standard deviation (ARSD) decreased from 8.62% to 1.89%. The results showed that SVR combined with MECF was an effective method to improve the accuracy of LIBS quantitative analysis of the carbon content in fly ash. (C) 2021 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.

关键词： Laser-induced breakdown spectroscopy (LIBS) Fly ash Carbon content Support vector regression partition functions

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The Complexity of Approximating the Matching Polynomial in the Complex Plane

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ACM TRANSACTIONS ON COMPUTATION THEORY 2021年第2期13卷 1-37页

作者： Bezakova, Ivona Galanis, Andreas Goldberg, Leslie Ann Stefankovic, Daniel Rochester Inst Technol Rochester NY 14623 USA Univ Oxford Oxford England Univ Rochester Rochester NY USA

We study the problem of approximating the value of the matching polynomial on graphs with edge parameter gamma, where gamma takes arbitrary values in the complex plane. When gamma is a positive real, Jerrum and Sinclair showed that the problem admits an FPRAS on general graphs. For general complex values of gamma, Patel and Regts, building on methods developed by Barvinok, showed that the problem admits an FPTAS on graphs of maximum degree Delta as long as gamma is not a negative real number less than or equal to -1/(4(Delta - 1)). Our first main result completes the picture for the approximability of the matching polynomial on bounded degree graphs. We show that for all Delta >= 3 and all real gamma less than -1/(4(Delta - 1)), the problem of approximating the value of the matching polynomial on graphs of maximum degree Delta with edge parameter gamma is #P-hard. We then explore whether the maximum degree parameter can be replaced by the connective constant. Sinclair et al. showed that for positive real gamma, it is possible to approximate the value of the matching polynomial using a correlation decay algorithm on graphs with bounded connective constant (and potentially unbounded maximum degree). We first show that this result does not extend in general in the complex plane;in particular, the problem is #P-hard on graphs with bounded connective constant for a dense set of gamma values on the negative real axis. Nevertheless, we show that the result does extend for any complex value gamma that does not lie on the negative real axis. Our analysis accounts for complex values of gamma using geodesic distances in the complex plane in the metric defined by an appropriate density function.

关键词： Approximate counting partition functions matchings monomer-dimer model connective constant

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MSTor 2023: A new version of the computer code for multistructural torsional anharmonicity, now with automatic torsional identification using redundant internal coordinates

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COMPUTER PHYSICS COMMUNICATIONS 2023年第1期288卷

作者： Chen, Wenqi Zheng, Jingjing Bao, Junwei Lucas Truhlar, Donald G. Xu, Xuefei Tsinghua Univ Ctr Combust Energy Dept Energy & Power Engn Beijing 100084 Peoples R China Tsinghua Univ Key Lab Thermal Sci & Power Engn Minist Educ Beijing 100084 Peoples R China Gaussian Inc 340 Quinnipiac StBldg 40 Wallingford CT 06492 USA Boston Coll Dept Chem Chestnut Hill MA 02467 USA Univ Minnesota Chem Theory Ctr Dept Chem Minneapolis MN 55455 USA Univ Minnesota Minnesota Supercomp Inst Minneapolis MN 55455 USA

The MSTor program is a computer program for calculating partition functions and thermodynamic functions of complex gas-phase molecules with multiple torsions;the multi-structural approximation with torsional anharmonicity (MS-T) can be used based on either a coupled torsional potential or an uncoupled torsional potential. The program can also carry out calculations in the multiple-structure local harmonic (MS-LH) approximation or multi-structural local quasiharmonic (MS-LQ) approximation or by the dual-level MS-T method. Furthermore, the program package includes eight utility codes that can be used as stand-alone programs to help the user to generate the input files for the code or to generate comparison results. The 2023 version of MSTor includes a new capability, namely automatic identification of torsional modes with redundant internal coordinates.

关键词： Complex molecules Coupled torsional potential Internal coordinates Multistructural method partition functions Thermochemistry Torsional anharmonicity Torsional identification

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Computability of width of submodular partition functions

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EUROPEAN JOURNAL OF COMBINATORICS 2013年第3期34卷 660-665页

作者： Skoda, Petr Simon Fraser Univ Dept Math Burnaby BC V5A 1S6 Canada

The notion of submodular partition functions generalizes many of well-known tree decompositions of graphs. For fixed k, there are polynomial-time algorithms to determine whether a graph has tree-width, branch-width, etc. at most k. Contrary to these results, we show that there is no sub-exponential algorithm for determining whether the width of a given submodular partition function is at most two. (c) 2012 Elsevier Ltd. All rights reserved.

关键词： SUBMODULAR functions partition functions GENERALIZATION DECOMPOSITION (Mathematics) GRAPH theory ALGORITHMS

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Refined partition functions for open superstrings with 4, 8 and 16 supercharges

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NUCLEAR PHYSICS B 2013年第1期876卷 55-146页

作者： Luest, Dieter Mekareeya, Noppadol Schlotterer, Oliver Thomson, Andrew Univ Munich Dept Phys Arnold Sommerfeld Ctr Theoret Phys D-80333 Munich Germany Werner Heisenberg Inst Max Planck Inst Phys D-80805 Munich Germany CERN Theory Grp CH-1211 Geneva 23 Switzerland Albert Einstein Inst Max Planck Inst Gravitat Phys D-14476 Golm Germany Univ London Imperial Coll Sci Technol & Med Blackett Lab Theoret Phys Grp London SW7 2AZ England

We analyze the perturbative massive open string spectrum of even-dimensional superstring compactifications with four, eight and sixteen supercharges. In each of such cases, we focus on universal states that exist independently on the internal geometry and other compatification details. We analytically compute refined partition functions that count these states at each mass level. Such refined partition functions are written in a super-Poincare covariant form, providing information on how supermultiplets transform under the little group and the R symmetry. Various asymptotic limits of the partition functions and their associated quantities, such as the leading and subleading Regge trajectories, are studied empirically and analytically. In the phenomenologically relevant case of four supercharges, the partition function can be cast into the most compact form and the asymptotic formula in the large spin limit is derived explicitly. Crown Copyright (C) 2013 Published by Elsevier B.V. All rights reserved.

关键词： Refined partition functions open superstrings Regge trajectories partitions Countries (nations) partition function superstrings

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