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Journal articles on the topic 'Quantum Monte Carlo'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Mitas, Lubos. "Quantum Monte Carlo." Current Opinion in Solid State and Materials Science 2, no. 6 (1997): 696–700. http://dx.doi.org/10.1016/s1359-0286(97)80012-5.

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2

CEPERLEY, D., and B. ALDER. "Quantum Monte Carlo." Science 231, no. 4738 (1986): 555–60. http://dx.doi.org/10.1126/science.231.4738.555.

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3

Bozkus, Zeki, Ahmad Anbar, and Tarek El-Ghazawi. "Adaptive Computing Library for Quantum Monte Carlo Simulations." International Journal of Computer Theory and Engineering 6, no. 3 (2014): 200–205. http://dx.doi.org/10.7763/ijcte.2014.v6.862.

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4

Chen, Jiming. "Monte Carlo Simulations in Complex Systems: Challenges and New Approaches." Theoretical and Natural Science 86, no. 1 (2025): 114–19. https://doi.org/10.54254/2753-8818/2025.20172.

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Monte Carlo simulations are crucial for examining the Ising model, especially when it's tough to find analytical solutions. However, traditional Monte Carlo methods, like the Metropolis algorithm, encounter significant hurdles, such as slowing down near phase transitions and issues related to finite sizes. This paper looks into both the advantages and limitations of these traditional Monte Carlo techniques. It also covers recent developments like Tensor Network Monte Carlo and Quantum Monte Carlo methods, which have shown promise in overcoming these challenges. Furthermore, the paper explores

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5

Kawashima, Naoki. "Quantum Monte Carlo Methods." Progress of Theoretical Physics Supplement 145 (2002): 138–49. http://dx.doi.org/10.1143/ptps.145.138.

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6

Reynolds, Peter J., Jan Tobochnik, and Harvey Gould. "Diffusion Quantum Monte Carlo." Computers in Physics 4, no. 6 (1990): 662. http://dx.doi.org/10.1063/1.4822960.

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7

Wang, Yazhen. "Quantum Monte Carlo simulation." Annals of Applied Statistics 5, no. 2A (2011): 669–83. http://dx.doi.org/10.1214/10-aoas406.

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8

Lüchow, Arne. "Quantum Monte Carlo methods." Wiley Interdisciplinary Reviews: Computational Molecular Science 1, no. 3 (2011): 388–402. http://dx.doi.org/10.1002/wcms.40.

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9

The Lam, Nguyen. "QUANTUM DIFFUSION MONTE CARLO METHOD FOR LOW-DIMENTIONAL SYSTEMS." Journal of Science, Natural Science 60, no. 7 (2015): 81–87. http://dx.doi.org/10.18173/2354-1059.2015-0036.

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10

Doll, J. D., Steven W. Rick, and David L. Freeman. "Stationary phase Monte Carlo methods: interference effects in quantum Monte Carlo dynamics." Canadian Journal of Chemistry 70, no. 2 (1992): 497–505. http://dx.doi.org/10.1139/v92-071.

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As summarized by Hamming's motto, "the purpose of computing is insight, not numbers." In the spirit of this dictum, we describe here recent algorithmic developments in the theory of quantum dynamics. Through the use of the somewhat unlikely combination of modern numerical simulations and a visualization device borrowed from 19th century optics, the present efforts suggest the existence of an important, underlying structure in the general problem. This structure, verified for a relatively simple class of model problems, provides broad guidelines for the Keywords: Monte Carlo, stationary phase,

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11

Grossman, Jeffrey C. "Benchmark quantum Monte Carlo calculations." Journal of Chemical Physics 117, no. 4 (2002): 1434–40. http://dx.doi.org/10.1063/1.1487829.

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12

Lingua, F., B. Capogrosso-Sansone, A. Safavi-Naini, A. J. Jahangiri, and V. Penna. "Multiworm algorithm quantum Monte Carlo." Physica Scripta 93, no. 10 (2018): 105402. http://dx.doi.org/10.1088/1402-4896/aadd7a.

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13

DePasquale, Michael F., Stuart M. Rothstein, and Jan Vrbik. "Reliable diffusion quantum Monte Carlo." Journal of Chemical Physics 89, no. 6 (1988): 3629–37. http://dx.doi.org/10.1063/1.454883.

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14

Fantoni, Riccardo, and Saverio Moroni. "Quantum Gibbs ensemble Monte Carlo." Journal of Chemical Physics 141, no. 11 (2014): 114110. http://dx.doi.org/10.1063/1.4895974.

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15

Shifren, L., and D. K. Ferry. "Wigner function quantum Monte Carlo." Physica B: Condensed Matter 314, no. 1-4 (2002): 72–75. http://dx.doi.org/10.1016/s0921-4526(01)01392-8.

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16

Lüchow, Arne, Rene Petz, and Annett Schwarz. "Electron Structure Quantum Monte Carlo." Zeitschrift für Physikalische Chemie 224, no. 3-4 (2010): 343–55. http://dx.doi.org/10.1524/zpch.2010.6109.

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17

Anderson, James B. "Fixed-node quantum Monte Carlo." International Reviews in Physical Chemistry 14, no. 1 (1995): 85–112. http://dx.doi.org/10.1080/01442359509353305.

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18

Yuen, Wai Kong, Daniel G. Oblinsky, Robert D. Giacometti, and Stuart M. Rothstein. "Improving reptation quantum Monte Carlo." International Journal of Quantum Chemistry 109, no. 14 (2009): 3229–34. http://dx.doi.org/10.1002/qua.22134.

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19

Towler, M. D. "The quantum Monte Carlo method." physica status solidi (b) 243, no. 11 (2006): 2573–98. http://dx.doi.org/10.1002/pssb.200642125.

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20

Montanaro, Ashley. "Quantum speedup of Monte Carlo methods." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2181 (2015): 20150301. http://dx.doi.org/10.1098/rspa.2015.0301.

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Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the

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21

Xu, Xiaosi, and Ying Li. "Quantum-assisted Monte Carlo algorithms for fermions." Quantum 7 (August 3, 2023): 1072. http://dx.doi.org/10.22331/q-2023-08-03-1072.

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Quantum computing is a promising way to systematically solve the longstanding computational problem, the ground state of a many-body fermion system. Many efforts have been made to realise certain forms of quantum advantage in this problem, for instance, the development of variational quantum algorithms. A recent work by Huggins et al. [1] reports a novel candidate, i.e. a quantum-classical hybrid Monte Carlo algorithm with a reduced bias in comparison to its fully-classical counterpart. In this paper, we propose a family of scalable quantum-assisted Monte Carlo algorithms where the quantum com

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22

FYE, R. M. "PROJECTOR APPROXIMATION AND QUANTUM MONTE CARLO." International Journal of Modern Physics C 05, no. 03 (1994): 483–88. http://dx.doi.org/10.1142/s0129183194000660.

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We derive a general approximation for performing quantum Monte Carlo simulations within a desired subspace of the full Hilbert space. We analytically determine the form of the resulting systematic error, allowing controlled extrapolation to exact results. We discuss some numerical applications, including fermion impurity and lattice models with infinite on-site Colulomb repulsion U and quantum spin systems. We demonstrate the use of the approximation in simulations with a test model.

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23

Zarezadeh, Zakarya, and Giovanni Costantini. "Particle diffusion Monte Carlo (PDMC)." Monte Carlo Methods and Applications 25, no. 2 (2019): 121–30. http://dx.doi.org/10.1515/mcma-2019-2037.

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Abstract General expressions for anisotropic particle diffusion Monte Carlo (PDMC) in a d-dimensional space are presented. The calculations of ground state energy of a helium atom for solving the many-body Schrödinger equation is carried out by the proposed method. The accuracy and stability of the results are discussed relative to other alternative methods, and our experimental results within the statistical errors agree with the quantum Monte Carlo methods. We also clarify the benefits of the proposed method by modeling the quantum probability density of a free particle in a plane (energy ei

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24

Hong-Xin, Huang, Lian Shi-Xun, and Cao Ze-Xing. "Surplus Function Quantum Monte Carlo Approach." Acta Physico-Chimica Sinica 15, no. 07 (1999): 599–605. http://dx.doi.org/10.3866/pku.whxb19990705.

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25

Mongwe, Wilson Tsakane, Rendani Mbuvha, and Tshilidzi Marwala. "Quantum-Inspired Magnetic Hamiltonian Monte Carlo." PLOS ONE 16, no. 10 (2021): e0258277. http://dx.doi.org/10.1371/journal.pone.0258277.

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Hamiltonian Monte Carlo (HMC) is a Markov Chain Monte Carlo algorithm that is able to generate distant proposals via the use of Hamiltonian dynamics, which are able to incorporate first-order gradient information about the target posterior. This has driven its rise in popularity in the machine learning community in recent times. It has been shown that making use of the energy-time uncertainty relation from quantum mechanics, one can devise an extension to HMC by allowing the mass matrix to be random with a probability distribution instead of a fixed mass. Furthermore, Magnetic Hamiltonian Mont

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26

Mølmer, Klaus, and Yvan Castin. "Monte Carlo wavefunctions in quantum optics." Quantum and Semiclassical Optics: Journal of the European Optical Society Part B 8, no. 1 (1996): 49–72. http://dx.doi.org/10.1088/1355-5111/8/1/007.

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27

Yuen, Wai Kong, Thomas J. Farrar, and Stuart M. Rothstein. "No-compromise reptation quantum Monte Carlo." Journal of Physics A: Mathematical and Theoretical 40, no. 27 (2007): F639—F646. http://dx.doi.org/10.1088/1751-8113/40/27/f09.

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28

Foulkes, W. M. C., L. Mitas, R. J. Needs, and G. Rajagopal. "Quantum Monte Carlo simulations of solids." Reviews of Modern Physics 73, no. 1 (2001): 33–83. http://dx.doi.org/10.1103/revmodphys.73.33.

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29

Tobochnik, Jan, Harvey Gould, and Kenneth Mulder. "An Introduction to Quantum Monte Carlo." Computers in Physics 4, no. 4 (1990): 431. http://dx.doi.org/10.1063/1.4822931.

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30

Tobochnik, Jan, George Batrouni, and Harvey Gould. "Quantum Monte Carlo on a Lattice." Computers in Physics 6, no. 6 (1992): 673. http://dx.doi.org/10.1063/1.4823122.

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31

Bande, Annika, Arne Lüchow, Fabio Della Sala, and Andreas Görling. "Rydberg states with quantum Monte Carlo." Journal of Chemical Physics 124, no. 11 (2006): 114114. http://dx.doi.org/10.1063/1.2180773.

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32

Gupta, Lalit, Tameem Albash, and Itay Hen. "Permutation matrix representation quantum Monte Carlo." Journal of Statistical Mechanics: Theory and Experiment 2020, no. 7 (2020): 073105. http://dx.doi.org/10.1088/1742-5468/ab9e64.

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33

Melton, Cody A., M. Chandler Bennett, and Lubos Mitas. "Quantum Monte Carlo with variable spins." Journal of Chemical Physics 144, no. 24 (2016): 244113. http://dx.doi.org/10.1063/1.4954726.

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34

Kim, Jeongnim, Kenneth P. Esler, Jeremy McMinis, et al. "Hybrid algorithms in quantum Monte Carlo." Journal of Physics: Conference Series 402 (December 20, 2012): 012008. http://dx.doi.org/10.1088/1742-6596/402/1/012008.

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35

Jones, Matthew D., Gerardo Ortiz, and David M. Ceperley. "Released-phase quantum Monte Carlo method." Physical Review E 55, no. 5 (1997): 6202–10. http://dx.doi.org/10.1103/physreve.55.6202.

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36

Dubecký, Matúš, Lubos Mitas, and Petr Jurečka. "Noncovalent Interactions by Quantum Monte Carlo." Chemical Reviews 116, no. 9 (2016): 5188–215. http://dx.doi.org/10.1021/acs.chemrev.5b00577.

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37

Pieper, Steven C. "Quantum Monte Carlo for light nuclei." Nuclear Physics A 701, no. 1-4 (2002): 357–62. http://dx.doi.org/10.1016/s0375-9474(01)01610-4.

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38

Heinrich, Stefan. "From Monte Carlo to quantum computation." Mathematics and Computers in Simulation 62, no. 3-6 (2003): 219–30. http://dx.doi.org/10.1016/s0378-4754(02)00239-2.

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39

Cerf, N. J., and S. E. Koonin. "Monte Carlo simulation of quantum computation." Mathematics and Computers in Simulation 47, no. 2-5 (1998): 143–52. http://dx.doi.org/10.1016/s0378-4754(98)00099-8.

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40

Austin, Brian M., Dmitry Yu Zubarev, and William A. Lester. "Quantum Monte Carlo and Related Approaches." Chemical Reviews 112, no. 1 (2011): 263–88. http://dx.doi.org/10.1021/cr2001564.

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41

Assaraf, Roland, and Michel Caffarel. "Computing forces with quantum Monte Carlo." Journal of Chemical Physics 113, no. 10 (2000): 4028–34. http://dx.doi.org/10.1063/1.1286598.

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42

Jadhao, Vikram, and Nancy Makri. "Iterative Monte Carlo for quantum dynamics." Journal of Chemical Physics 129, no. 16 (2008): 161102. http://dx.doi.org/10.1063/1.3000393.

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43

Pudliner, B. S., V. R. Pandharipande, J. Carlson, and R. B. Wiringa. "Quantum Monte Carlo Calculations ofA≤6Nuclei." Physical Review Letters 74, no. 22 (1995): 4396–99. http://dx.doi.org/10.1103/physrevlett.74.4396.

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44

Michalke, W., and S. Kreitmeier. "Quantum-Monte-Carlo simulations of polyethylene." European Physical Journal B 4, no. 4 (1998): 469–73. http://dx.doi.org/10.1007/s100510050404.

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45

Bitar, Khalil, A. D. Kennedy, Roger Horsley, Steffen Meyer, and Pietro Rossi. "Hybrid Monte Carlo and quantum chromodynamics." Nuclear Physics B 313, no. 2 (1989): 377–92. http://dx.doi.org/10.1016/0550-3213(89)90324-6.

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46

Suzuki, Masuo. "Quantum Monte Carlo methods — recent developments." Physica A: Statistical Mechanics and its Applications 194, no. 1-4 (1993): 432–49. http://dx.doi.org/10.1016/0378-4371(93)90375-e.

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47

Bianchi, R., D. Bressanini, P. Cremaschi, and G. Morosi. "Antisymmetry in quantum Monte Carlo methods." Computer Physics Communications 74, no. 2 (1993): 153–63. http://dx.doi.org/10.1016/0010-4655(93)90086-r.

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48

FAHY, S. "ChemInform Abstract: Quantum Monte Carlo Methods." ChemInform 27, no. 40 (2010): no. http://dx.doi.org/10.1002/chin.199640314.

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49

Layden, David, Guglielmo Mazzola, Ryan V. Mishmash, et al. "Quantum-enhanced Markov chain Monte Carlo." Nature 619, no. 7969 (2023): 282–87. http://dx.doi.org/10.1038/s41586-023-06095-4.

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50

Leung, W. K., R. J. Needs, G. Rajagopal, S. Itoh, and S. Ihara. "Quantum Monte Carlo Study of Silicon Self-interstitial Defects." VLSI Design 13, no. 1-4 (2001): 229–35. http://dx.doi.org/10.1155/2001/83797.

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We give a brief description of the variational and diffusion quantum Monte Carlo methods and their application to the study of self-interstitial defects in silicon. The diffusion quantum Monte Carlo calculations give formation energies for the most stable defects of about 4.9 eV, which is considerably larger than the values obtained in density functional theory methods. The quantum Monte Carlo results indicate a value for the formation+migration energy of the self-interstitial contribution to self-diffusion of about 5 eV, which is consistent with the experimental data.

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