1
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Zhao Z, Filip MA, Thom AJW. Rapidly convergent quantum Monte Carlo using a Chebyshev projector. Faraday Discuss 2024. [PMID: 39083360 DOI: 10.1039/d4fd00035h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/02/2024]
Abstract
The multireference coupled-cluster Monte Carlo (MR-CCMC) algorithm is a determinant-based quantum Monte Carlo (QMC) algorithm that is conceptually similar to Full Configuration Interaction QMC (FCIQMC). It has been shown to offer a balanced treatment of both static and dynamic correlation while retaining polynomial scaling, although application to large systems with significant strong correlation remained impractical. In this paper, we document recent algorithmic advances that enable rapid convergence and a more black-box approach to the multireference problem. These include a logarithmically scaling metric-tree-based excitation acceptance algorithm to search for determinants connected to the reference space at the desired excitation level and a symmetry-screening procedure for the reference space. We show that, for moderately sized reference spaces, the new search algorithm brings about an approximately 8-fold acceleration of one MR-CCMC iteration, while the symmetry screening procedure reduces the number of active reference space determinants with essentially no loss of accuracy. We also introduce a stochastic implementation of an approximate wall projector, which is the infinite imaginary time limit of the exponential projector, using a truncated expansion of the wall function in Chebyshev polynomials. Notably, this wall-Chebyshev projector can be used to accelerate any projector-based QMC algorithm. We show that it requires significantly fewer applications of the Hamiltonian to achieve the same statistical convergence. We benchmark these acceleration methods on the beryllium and carbon dimers, using initiator FCIQMC and MR-CCMC with basis sets up to cc-pVQZ quality.
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Affiliation(s)
- Zijun Zhao
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, UK.
| | - Maria-Andreea Filip
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, UK.
| | - Alex J W Thom
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, UK.
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2
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Aldossary A, Campos-Gonzalez-Angulo JA, Pablo-García S, Leong SX, Rajaonson EM, Thiede L, Tom G, Wang A, Avagliano D, Aspuru-Guzik A. In Silico Chemical Experiments in the Age of AI: From Quantum Chemistry to Machine Learning and Back. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2024; 36:e2402369. [PMID: 38794859 DOI: 10.1002/adma.202402369] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2024] [Revised: 04/28/2024] [Indexed: 05/26/2024]
Abstract
Computational chemistry is an indispensable tool for understanding molecules and predicting chemical properties. However, traditional computational methods face significant challenges due to the difficulty of solving the Schrödinger equations and the increasing computational cost with the size of the molecular system. In response, there has been a surge of interest in leveraging artificial intelligence (AI) and machine learning (ML) techniques to in silico experiments. Integrating AI and ML into computational chemistry increases the scalability and speed of the exploration of chemical space. However, challenges remain, particularly regarding the reproducibility and transferability of ML models. This review highlights the evolution of ML in learning from, complementing, or replacing traditional computational chemistry for energy and property predictions. Starting from models trained entirely on numerical data, a journey set forth toward the ideal model incorporating or learning the physical laws of quantum mechanics. This paper also reviews existing computational methods and ML models and their intertwining, outlines a roadmap for future research, and identifies areas for improvement and innovation. Ultimately, the goal is to develop AI architectures capable of predicting accurate and transferable solutions to the Schrödinger equation, thereby revolutionizing in silico experiments within chemistry and materials science.
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Affiliation(s)
- Abdulrahman Aldossary
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
| | | | - Sergio Pablo-García
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
- Department of Computer Science, University of Toronto, 40 St. George Street, Toronto, ON, M5S 2E4, Canada
| | - Shi Xuan Leong
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
| | - Ella Miray Rajaonson
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
- Vector Institute for Artificial Intelligence, 661 University Ave. Suite 710, Toronto, ON, M5G 1M1, Canada
| | - Luca Thiede
- Department of Computer Science, University of Toronto, 40 St. George Street, Toronto, ON, M5S 2E4, Canada
- Vector Institute for Artificial Intelligence, 661 University Ave. Suite 710, Toronto, ON, M5G 1M1, Canada
| | - Gary Tom
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
- Vector Institute for Artificial Intelligence, 661 University Ave. Suite 710, Toronto, ON, M5G 1M1, Canada
| | - Andrew Wang
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
| | - Davide Avagliano
- Chimie ParisTech, PSL University, CNRS, Institute of Chemistry for Life and Health Sciences (iCLeHS UMR 8060), Paris, F-75005, France
| | - Alán Aspuru-Guzik
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
- Department of Computer Science, University of Toronto, 40 St. George Street, Toronto, ON, M5S 2E4, Canada
- Vector Institute for Artificial Intelligence, 661 University Ave. Suite 710, Toronto, ON, M5G 1M1, Canada
- Department of Materials Science & Engineering, University of Toronto, 184 College St., Toronto, ON, M5S 3E4, Canada
- Department of Chemical Engineering & Applied Chemistry, University of Toronto, 200 College St., Toronto, ON, M5S 3E5, Canada
- Lebovic Fellow, Canadian Institute for Advanced Research (CIFAR), 66118 University Ave., Toronto, M5G 1M1, Canada
- Acceleration Consortium, 80 St George St, Toronto, M5S 3H6, Canada
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3
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Mazzola G. Quantum computing for chemistry and physics applications from a Monte Carlo perspective. J Chem Phys 2024; 160:010901. [PMID: 38165101 DOI: 10.1063/5.0173591] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2023] [Accepted: 10/18/2023] [Indexed: 01/03/2024] Open
Abstract
This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo solutions into quantum algorithms. These include refined energy estimators, parameter optimization, real and imaginary-time dynamics, and variational circuits. Conversely, we will review new ideas for utilizing quantum hardware to accelerate the sampling in statistical classical models, with applications in physics, chemistry, optimization, and machine learning. This review aims to be accessible to both communities and intends to foster further algorithmic developments at the intersection of quantum computing and Monte Carlo methods. Most of the works discussed in this Perspective have emerged within the last two years, indicating a rapidly growing interest in this promising area of research.
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Affiliation(s)
- Guglielmo Mazzola
- Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
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4
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Nomura Y. Boltzmann machines and quantum many-body problems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 36:073001. [PMID: 37918107 DOI: 10.1088/1361-648x/ad0916] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2023] [Accepted: 11/02/2023] [Indexed: 11/04/2023]
Abstract
Analyzing quantum many-body problems and elucidating the entangled structure of quantum states is a significant challenge common to a wide range of fields. Recently, a novel approach using machine learning was introduced to address this challenge. The idea is to 'embed' nontrivial quantum correlations (quantum entanglement) into artificial neural networks. Through intensive developments, artificial neural network methods are becoming new powerful tools for analyzing quantum many-body problems. Among various artificial neural networks, this topical review focuses on Boltzmann machines and provides an overview of recent developments and applications.
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Affiliation(s)
- Yusuke Nomura
- Department of Applied Physics and Physico-Informatics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
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5
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Motta M, Sung KJ, Whaley KB, Head-Gordon M, Shee J. Bridging physical intuition and hardware efficiency for correlated electronic states: the local unitary cluster Jastrow ansatz for electronic structure. Chem Sci 2023; 14:11213-11227. [PMID: 37860666 PMCID: PMC10583744 DOI: 10.1039/d3sc02516k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2023] [Accepted: 09/20/2023] [Indexed: 10/21/2023] Open
Abstract
A prominent goal in quantum chemistry is to solve the molecular electronic structure problem for ground state energy with high accuracy. While classical quantum chemistry is a relatively mature field, the accurate and scalable prediction of strongly correlated states found, e.g., in bond breaking and polynuclear transition metal compounds remains an open problem. Within the context of a variational quantum eigensolver, we propose a new family of ansatzes which provides a more physically appropriate description of strongly correlated electrons than a unitary coupled cluster with single and double excitations (qUCCSD), with vastly reduced quantum resource requirements. Specifically, we present a set of local approximations to the unitary cluster Jastrow wavefunction motivated by Hubbard physics. As in the case of qUCCSD, exactly computing the energy scales factorially with system size on classical computers but polynomially on quantum devices. The local unitary cluster Jastrow ansatz removes the need for SWAP gates, can be tailored to arbitrary qubit topologies (e.g., square, hex, and heavy-hex), and is well-suited to take advantage of continuous sets of quantum gates recently realized on superconducting devices with tunable couplers. The proposed family of ansatzes demonstrates that hardware efficiency and physical transparency are not mutually exclusive; indeed, chemical and physical intuition regarding electron correlation can illuminate a useful path towards hardware-friendly quantum circuits.
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Affiliation(s)
- Mario Motta
- IBM Quantum, IBM Research - Almaden San Jose CA 95120 USA
| | - Kevin J Sung
- IBM Quantum, IBM T. J. Watson Research Center Yorktown Heights NY 10598 USA
| | - K Birgitta Whaley
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Berkeley Quantum Information and Computation Center, University of California Berkeley CA 94720 USA
- Challenge Institute for Quantum Computation, University of California Berkeley CA 94720 USA
| | - Martin Head-Gordon
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory Berkeley CA 94720 USA
| | - James Shee
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Department of Chemistry, Rice University Houston TX 77005 USA
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6
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Reboredo FA, Kent PRC, Krogel JT. Evaluation of the excitation spectra with diffusion Monte Carlo on an auxiliary bosonic ground state. J Chem Phys 2023; 159:114118. [PMID: 37724730 DOI: 10.1063/5.0155513] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2023] [Accepted: 08/29/2023] [Indexed: 09/21/2023] Open
Abstract
We aim to improve upon the variational Monte Carlo (VMC) approach for excitations replacing the Jastrow factor by an auxiliary bosonic (AB) ground state and multiplying it by a fermionic component factor. The instantaneous change in imaginary time of an arbitrary excitation in the original interacting fermionic system is obtained by measuring observables via the ground-state distribution of walkers of an AB system that is subject to an auxiliary effective potential. The effective potential is used to (i) drive the AB system's ground-state configuration space toward the configuration space of the excitations of the original fermionic system and (ii) subtract from a diffusion Monte Carlo (DMC) calculation contributions that can be included in conventional approximations, such as mean-field and configuration interaction (CI) methods. In this novel approach, the AB ground state is treated statistically in DMC, whereas the fermionic component of the original system is expanded in a basis. The excitation energies of the fermionic eigenstates are obtained by sampling a fermion-boson coupling term on the AB ground state. We show that this approach can take advantage of and correct for approximate eigenstates obtained via mean-field calculations or truncated interactions. We demonstrate that the AB ground-state factor incorporates the correlations missed by standard Jastrow factors, further reducing basis truncation errors. Relevant parts of the theory have been tested in soluble model systems and exhibit excellent agreement with exact analytical data and CI and VMC approaches. In particular, for limited basis set expansions and sufficient statistics, AB approaches outperform CI and VMC in terms of basis size for the same systems. The implementation of this method in current codes, despite being demanding, will be facilitated by reusing procedures already developed for calculating ground-state properties with DMC and excitations with VMC.
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Affiliation(s)
- Fernando A Reboredo
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Paul R C Kent
- Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Jaron T Krogel
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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7
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Thorpe JH, Feller D, Bross DH, Ruscic B, Stanton JF. Sub 20 cm -1 computational prediction of the CH bond energy - a case of systematic error in computational thermochemistry. Phys Chem Chem Phys 2023; 25:21162-21172. [PMID: 36200428 DOI: 10.1039/d2cp03964h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
The bond dissociation energy of methylidyne, D0(CH), is studied using an improved version of the High-Accuracy Extrapolated ab initio Thermochemistry (HEAT) approach as well as the Feller-Peterson-Dixon (FPD) model chemistry. These calculations, which include basis sets up to nonuple (aug-cc-pCV9Z) quality, are expected to be capable of providing results substantially more accurate than the ca. 1 kJ mol-1 level that is characteristic of standard high-accuracy protocols for computational thermochemistry. The calculated 0 K CH bond energy (27 954 ± 15 cm-1 for HEAT and 27 956 ± 15 cm-1 for FPD), along with equivalent treatments of the CH ionization energy and the CH+ dissociation energy (85 829 ± 15 cm-1 and 32 946 ± 15 cm-1, respectively), were compared to the existing benchmarks from Active Thermochemical Tables (ATcT), uncovering an unexpected difference for D0(CH). This has prompted a detailed reexamination of the provenance of the corresponding ATcT benchmark, allowing the discovery and subsequent correction of a systematic error present in several published high-level calculations, ultimately yielding an amended ATcT benchmark for D0(CH). Finally, the current theoretical results were added to the ATcT Thermochemical Network, producing refined ATcT estimates of 27 957.3 ± 6.0 cm-1 for D0(CH), 32 946.7 ± 0.6 cm-1 for D0(CH+), and 85 831.0 ± 6.0 cm-1 for IE(CH).
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Affiliation(s)
- James H Thorpe
- The Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida, 32611, USA.
| | - David Feller
- Washington State University, Pullman, Washington 99164-4630, USA
- University of Alabama, Tuscaloosa, Alabama 35487-0336, USA
| | - David H Bross
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, USA.
| | - Branko Ruscic
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, USA.
| | - John F Stanton
- The Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida, 32611, USA.
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8
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Sukurma Z, Schlipf M, Humer M, Taheridehkordi A, Kresse G. Benchmark Phaseless Auxiliary-Field Quantum Monte Carlo Method for Small Molecules. J Chem Theory Comput 2023; 19:4921-4934. [PMID: 37470356 PMCID: PMC10413869 DOI: 10.1021/acs.jctc.3c00322] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2023] [Indexed: 07/21/2023]
Abstract
We report a scalable Fortran implementation of the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) and demonstrate its excellent performance and beneficial scaling with respect to system size. Furthermore, we investigate modifications of the phaseless approximation that can help to reduce the overcorrelation problems common to the ph-AFQMC. We apply the method to the 26 molecules in the HEAT set, the benzene molecule, and water clusters. We observe a mean absolute deviation of the total energy of 1.15 kcal/mol for the molecules in the HEAT set, close to chemical accuracy. For the benzene molecule, the modified algorithm despite using a single-Slater-determinant trial wavefunction yields the same accuracy as the original phaseless scheme with 400 Slater determinants. Despite these improvements, we find systematic errors for the CN, CO2, and O2 molecules that need to be addressed with more accurate trial wavefunctions. For water clusters, we find that the ph-AFQMC yields excellent binding energies that differ from CCSD(T) by typically less than 0.5 kcal/mol.
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Affiliation(s)
- Zoran Sukurma
- Faculty
of Physics and Center for Computational Materials Science, University of Vienna, Kolingasse 14-16, A-1090 Vienna, Austria
- Faculty
of Physics & Vienna Doctoral School in Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
| | | | - Moritz Humer
- Faculty
of Physics and Center for Computational Materials Science, University of Vienna, Kolingasse 14-16, A-1090 Vienna, Austria
- Faculty
of Physics & Vienna Doctoral School in Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Amir Taheridehkordi
- Faculty
of Physics and Center for Computational Materials Science, University of Vienna, Kolingasse 14-16, A-1090 Vienna, Austria
| | - Georg Kresse
- Faculty
of Physics and Center for Computational Materials Science, University of Vienna, Kolingasse 14-16, A-1090 Vienna, Austria
- VASP
Software GmbH, Sensengasse 8, 1090 Vienna, Austria
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9
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Atanasova H, Bernheimer L, Cohen G. Stochastic representation of many-body quantum states. Nat Commun 2023; 14:3601. [PMID: 37328458 DOI: 10.1038/s41467-023-39244-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2022] [Accepted: 06/02/2023] [Indexed: 06/18/2023] Open
Abstract
The quantum many-body problem is ultimately a curse of dimensionality: the state of a system with many particles is determined by a function with many dimensions, which rapidly becomes difficult to efficiently store, evaluate and manipulate numerically. On the other hand, modern machine learning models like deep neural networks can express highly correlated functions in extremely large-dimensional spaces, including those describing quantum mechanical problems. We show that if one represents wavefunctions as a stochastically generated set of sample points, the problem of finding ground states can be reduced to one where the most technically challenging step is that of performing regression-a standard supervised learning task. In the stochastic representation the (anti)symmetric property of fermionic/bosonic wavefunction can be used for data augmentation and learned rather than explicitly enforced. We further demonstrate that propagation of an ansatz towards the ground state can then be performed in a more robust and computationally scalable fashion than traditional variational approaches allow.
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Affiliation(s)
| | - Liam Bernheimer
- School of Chemistry, Tel Aviv University, Tel Aviv, 6997801, Israel
| | - Guy Cohen
- School of Chemistry, Tel Aviv University, Tel Aviv, 6997801, Israel.
- The Raymond and Beverley Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, 6997801, Israel.
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10
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Wheeler WA, Pathak S, Kleiner KG, Yuan S, Rodrigues JNB, Lorsung C, Krongchon K, Chang Y, Zhou Y, Busemeyer B, Williams KT, Muñoz A, Chow CY, Wagner LK. PyQMC: An all-Python real-space quantum Monte Carlo module in PySCF. J Chem Phys 2023; 158:114801. [PMID: 36948839 DOI: 10.1063/5.0139024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/19/2023] Open
Abstract
We describe a new open-source Python-based package for high accuracy correlated electron calculations using quantum Monte Carlo (QMC) in real space: PyQMC. PyQMC implements modern versions of QMC algorithms in an accessible format, enabling algorithmic development and easy implementation of complex workflows. Tight integration with the PySCF environment allows for a simple comparison between QMC calculations and other many-body wave function techniques, as well as access to high accuracy trial wave functions.
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Affiliation(s)
- William A Wheeler
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Shivesh Pathak
- Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
| | - Kevin G Kleiner
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Shunyue Yuan
- Department of Applied Physics and Materials Science, California Institute of Technology, Pasadena, California 91125, USA
| | - João N B Rodrigues
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC-UFABC, Santo André, São Paulo 09210-580, Brazil
| | - Cooper Lorsung
- Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
| | - Kittithat Krongchon
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Yueqing Chang
- Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
| | - Yiqing Zhou
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA
| | | | | | - Alexander Muñoz
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Chun Yu Chow
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Lucas K Wagner
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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11
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Watanabe H, Shirakawa T, Seki K, Sakakibara H, Kotani T, Ikeda H, Yunoki S. Monte Carlo study of cuprate superconductors in a four-bandd-pmodel: role of orbital degrees of freedom. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:195601. [PMID: 36866651 DOI: 10.1088/1361-648x/acc0bf] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2022] [Accepted: 03/02/2023] [Indexed: 06/18/2023]
Abstract
Understanding the various competing phases in cuprate superconductors is a long-standing challenging problem. Recent studies have shown that orbital degrees of freedom, both Cuegorbitals and Oporbitals, are a key ingredient for a unified understanding of cuprate superconductors, including the material dependence. Here we investigate a four-bandd-pmodel derived from the first-principles calculations with the variational Monte Carlo method, which allows us to elucidate competing phases on an equal footing. The obtained results can consistently explain the doping dependence of superconductivity, antiferromagnetic and stripe phases, phase separation in the underdoped region, and also novel magnetism in the heavily-overdoped region. The presence ofporbitals is critical to the charge-stripe features, which induce two types of stripe phases withs)-wave andd-wave bond stripe. On the other hand, the presence ofdz2orbital is indispensable to material dependence of the superconducting transition temperature (Tc), and enhances local magnetic moment as a source of novel magnetism in the heavily-overdoped region as well. These findings beyond one-band description could provide a major step toward a full explanation of unconventional normal state and highTcin cuprate supercondutors.
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Affiliation(s)
- Hiroshi Watanabe
- Research Organization of Science and Technology, Ritsumeikan University, Shiga 525-8577, Japan
| | - Tomonori Shirakawa
- Computational Materials Science Research Team, RIKEN Center for Computational Science (R-CCS), Hyogo 650-0047, Japan
- Quantum Computational Science Research Team, RIKEN Center for Quantum Computing (RQC), Saitama 351-0198, Japan
| | - Kazuhiro Seki
- Quantum Computational Science Research Team, RIKEN Center for Quantum Computing (RQC), Saitama 351-0198, Japan
| | - Hirofumi Sakakibara
- Advanced Mechanical and Electronic System Research Center (AMES), Faculty of Engineering, Tottori University, Tottori 680-8552, Japan
- Center of Spintronics Research Network (CSRN), Graduate School of Engineering Science, Osaka University, Osaka 560-8531, Japan
- Computational Condensed Matter Physics Laboratory, RIKEN Cluster for Pioneering Research (CPR), Saitama 351-0198, Japan
| | - Takao Kotani
- Advanced Mechanical and Electronic System Research Center (AMES), Faculty of Engineering, Tottori University, Tottori 680-8552, Japan
- Center of Spintronics Research Network (CSRN), Graduate School of Engineering Science, Osaka University, Osaka 560-8531, Japan
| | - Hiroaki Ikeda
- Department of Physics, Ritsumeikan University, Shiga 525-8577, Japan
| | - Seiji Yunoki
- Computational Materials Science Research Team, RIKEN Center for Computational Science (R-CCS), Hyogo 650-0047, Japan
- Quantum Computational Science Research Team, RIKEN Center for Quantum Computing (RQC), Saitama 351-0198, Japan
- Computational Condensed Matter Physics Laboratory, RIKEN Cluster for Pioneering Research (CPR), Saitama 351-0198, Japan
- Computational Quantum Matter Research Team, RIKEN Center for Emergent Matter Science (CEMS), Saitama 351-0198, Japan
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12
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Zhang SX, Wan ZQ, Lee CK, Hsieh CY, Zhang S, Yao H. Variational Quantum-Neural Hybrid Eigensolver. PHYSICAL REVIEW LETTERS 2022; 128:120502. [PMID: 35394326 DOI: 10.1103/physrevlett.128.120502] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2021] [Revised: 08/22/2021] [Accepted: 02/22/2022] [Indexed: 06/14/2023]
Abstract
The variational quantum eigensolver (VQE) is one of the most representative quantum algorithms in the noisy intermediate-scale quantum (NISQ) era, and is generally speculated to deliver one of the first quantum advantages for the ground-state simulations of some nontrivial Hamiltonians. However, short quantum coherence time and limited availability of quantum hardware resources in the NISQ hardware strongly restrain the capacity and expressiveness of VQEs. In this Letter, we introduce the variational quantum-neural hybrid eigensolver (VQNHE) in which the shallow-circuit quantum Ansatz can be further enhanced by classical post-processing with neural networks. We show that the VQNHE consistently and significantly outperforms the VQE in simulating ground-state energies of quantum spins and molecules given the same amount of quantum resources. More importantly, we demonstrate that, for arbitrary postprocessing neural functions, the VQNHE only incurs a polynomial overhead of processing time and represents the first scalable method to exponentially accelerate the VQE with nonunitary postprocessing that can be efficiently implemented in the NISQ era.
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Affiliation(s)
- Shi-Xin Zhang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- Tencent Quantum Laboratory, Tencent, Shenzhen, Guangdong 518057, China
| | - Zhou-Quan Wan
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- Tencent Quantum Laboratory, Tencent, Shenzhen, Guangdong 518057, China
| | | | - Chang-Yu Hsieh
- Tencent Quantum Laboratory, Tencent, Shenzhen, Guangdong 518057, China
| | - Shengyu Zhang
- Tencent Quantum Laboratory, Tencent, Shenzhen, Guangdong 518057, China
| | - Hong Yao
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
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13
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Blunt NS. Fixed- and Partial-Node Approximations in Slater Determinant Space for Molecules. J Chem Theory Comput 2021; 17:6092-6104. [PMID: 34549947 DOI: 10.1021/acs.jctc.1c00500] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present a study of fixed- and partial-node approximations in Slater determinant basis sets, using full configuration interaction quantum Monte Carlo (FCIQMC) to perform sampling. Walker annihilation in the FCIQMC method allows partial-node simulations to be performed, relaxing the nodal constraint to converge to the FCI solution. This is applied to ab initio molecular systems, using symmetry-projected Jastrow mean-field wave functions for complete active space (CAS) problems. Convergence and the sign problem within the partial-node approximation are studied, which is shown to eventually be limited in its use due to the large walker populations required. However, the fixed-node approximation results in an accurate and practical method. We apply these approaches to various molecular systems and active spaces, including ferrocene and acenes. This also provides a test of symmetry-projected Jastrow mean-field wave functions in variational Monte Carlo for a new set of problems. For trans-polyacetylene molecules and acenes, we find that the time to perform a constant number of fixed-node FCIQMC iterations scales as O(N1.44) and O(N1.75), respectively, resulting in an efficient method for CAS-based problems that can be applied accurately to large active spaces.
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Affiliation(s)
- Nick S Blunt
- Yusuf Hamied Department of Chemistry, Lensfield Road, Cambridge CB2 1EW, U.K.,St John's College, St John's Street, Cambridge CB2 1TP, U.K
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15
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Nomura Y. Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:174003. [PMID: 33530063 DOI: 10.1088/1361-648x/abe268] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2020] [Accepted: 02/02/2021] [Indexed: 06/12/2023]
Abstract
The variational wave functions based on neural networks have recently started to be recognized as a powerful ansatz to represent quantum many-body states accurately. In order to show the usefulness of the method among all available numerical methods, it is imperative to investigate the performance in challenging many-body problems for which the exact solutions are not available. Here, we construct a variational wave function with one of the simplest neural networks, the restricted Boltzmann machine (RBM), and apply it to a fundamental but unsolved quantum spin Hamiltonian, the two-dimensionalJ1-J2Heisenberg model on the square lattice. We supplement the RBM wave function with quantum-number projections, which restores the symmetry of the wave function and makes it possible to calculate excited states. Then, we perform a systematic investigation of the performance of the RBM. We show that, with the help of the symmetry, the RBM wave function achieves state-of-the-art accuracy both in ground-state and excited-state calculations. The study shows a practical guideline on how we achieve accuracy in a controlled manner.
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Affiliation(s)
- Yusuke Nomura
- RIKEN Center for Emergent Matter Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
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16
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Kessler J, Calcavecchia F, Kühne TD. Artificial Neural Networks as Trial Wave Functions for Quantum Monte Carlo. ADVANCED THEORY AND SIMULATIONS 2021. [DOI: 10.1002/adts.202000269] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Jan Kessler
- Dynamics of Condensed Matter and Center for Sustainable Systems Design Chair of Theoretical Chemistry University of Paderborn Warburger Str. 100 D‐33098 Paderborn Germany
| | - Francesco Calcavecchia
- Dynamics of Condensed Matter and Center for Sustainable Systems Design Chair of Theoretical Chemistry University of Paderborn Warburger Str. 100 D‐33098 Paderborn Germany
| | - Thomas D. Kühne
- Dynamics of Condensed Matter and Center for Sustainable Systems Design Chair of Theoretical Chemistry University of Paderborn Warburger Str. 100 D‐33098 Paderborn Germany
- Paderborn Center for Parallel Computing and Institute for Lightweight Design University of Paderborn Warburger Str. 100 D‐33098 Paderborn Germany
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17
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The First Two Decades of Neutron Scattering at the Chalk River Laboratories. QUANTUM BEAM SCIENCE 2021. [DOI: 10.3390/qubs5010003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The early advances in neutron scattering at the Chalk River Laboratories of Atomic Energy of Canada are recorded. From initial nuclear physics measurements at the National Research Experimental (NRX) reactor came the realization that, with the flux available and improvements in monochromator technology, direct measurements of the normal modes of vibrations of solids and the structure and dynamics of liquids would be feasible. With further flux increases at the National Research Universal (NRU) reactor, the development of the triple-axis crystal spectrometer, and the invention of the constant-Q technique, the fields of lattice dynamics and magnetism and their interpretation in terms of the long-range forces between atoms and exchange interactions between spins took a major step forward. Experiments were performed over a seven-year period on simple metals such as potassium, complex metals such as lead, transition metals, semiconductors, and alkali halides. These were analyzed in terms of the atomic forces and demonstrated the long-range nature of the forces. The first measurements of spin wave excitations, in magnetite and in the 3D metal alloy CoFe, also came in this period. The first numerical estimates of the superfluid fraction of liquid helium II came from extensive measurements of the phonon–roton and multiphonon parts of the inelastic scattering. After the first two decades, neutron experiments continued at Chalk River until the shut-down of the NRU reactor in 2018 and the disbanding of the neutron effort in 2019, seventy years after the first experiments.
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18
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Zhao T, Carleo G, Stokes J, Veerapaneni S. Natural evolution strategies and variational Monte Carlo. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2020. [DOI: 10.1088/2632-2153/abcb50] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Abstract
Abstract
A notion of quantum natural evolution strategies is introduced, which provides a geometric synthesis of a number of known quantum/classical algorithms for performing classical black-box optimization. The recent work of Gomes et al (2019 arXiv:1910.10675) on heuristic combinatorial optimization using neural quantum states is pedagogically reviewed in this context, emphasizing the connection with natural evolution strategies (NES). The algorithmic framework is illustrated for approximate combinatorial optimization problems, and a systematic strategy is found for improving the approximation ratios. In particular, it is found that NES can achieve approximation ratios competitive with widely used heuristic algorithms for Max-Cut, at the expense of increased computation time.
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19
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Powell AD, Kroes GJ, Doblhoff-Dier K. Quantum Monte Carlo calculations on dissociative chemisorption of H2 + Al(110): Minimum barrier heights and their comparison to DFT values. J Chem Phys 2020; 153:224701. [DOI: 10.1063/5.0022919] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Andrew D. Powell
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, Netherlands
| | - Geert-Jan Kroes
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, Netherlands
| | - Katharina Doblhoff-Dier
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, Netherlands
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20
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Azadi S, Booth GH, Kühne TD. Equation of state of atomic solid hydrogen by stochastic many-body wave function methods. J Chem Phys 2020; 153:204107. [DOI: 10.1063/5.0026499] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sam Azadi
- Department of Physics, King’s College London, Strand, WC2R 2LS London, United Kingdom
| | - George H. Booth
- Department of Physics, King’s College London, Strand, WC2R 2LS London, United Kingdom
| | - Thomas D. Kühne
- Department of Chemistry, Paderborn Center for Parallel Computing, Paderborn University, 33098 Paderborn, Germany
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21
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Krogel JT, Reboredo FA. Hybridizing pseudo-Hamiltonians and non-local pseudopotentials in diffusion Monte Carlo. J Chem Phys 2020; 153:104111. [DOI: 10.1063/5.0016778] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jaron T. Krogel
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Fernando A. Reboredo
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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22
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Needs RJ, Towler MD, Drummond ND, López Ríos P, Trail JR. Variational and diffusion quantum Monte Carlo calculations with the CASINO code. J Chem Phys 2020; 152:154106. [DOI: 10.1063/1.5144288] [Citation(s) in RCA: 35] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- R. J. Needs
- TCM Group, Cavendish Laboratory, University of Cambridge, 19 J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - M. D. Towler
- University College London, London WC1E 6BT, United Kingdom
| | - N. D. Drummond
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - P. López Ríos
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - J. R. Trail
- TCM Group, Cavendish Laboratory, University of Cambridge, 19 J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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23
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Westerhout T, Astrakhantsev N, Tikhonov KS, Katsnelson MI, Bagrov AA. Generalization properties of neural network approximations to frustrated magnet ground states. Nat Commun 2020; 11:1593. [PMID: 32221284 PMCID: PMC7101385 DOI: 10.1038/s41467-020-15402-w] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2019] [Accepted: 02/28/2020] [Indexed: 01/18/2023] Open
Abstract
Neural quantum states (NQS) attract a lot of attention due to their potential to serve as a very expressive variational ansatz for quantum many-body systems. Here we study the main factors governing the applicability of NQS to frustrated magnets by training neural networks to approximate ground states of several moderately-sized Hamiltonians using the corresponding wave function structure on a small subset of the Hilbert space basis as training dataset. We notice that generalization quality, i.e. the ability to learn from a limited number of samples and correctly approximate the target state on the rest of the space, drops abruptly when frustration is increased. We also show that learning the sign structure is considerably more difficult than learning amplitudes. Finally, we conclude that the main issue to be addressed at this stage, in order to use the method of NQS for simulating realistic models, is that of generalization rather than expressibility.
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Affiliation(s)
- Tom Westerhout
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ, Nijmegen, The Netherlands.
| | - Nikita Astrakhantsev
- Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057, Zürich, Switzerland.
- Moscow Institute of Physics and Technology, Institutsky lane 9, 141700, Dolgoprudny, Russia.
- Institute for Theoretical and Experimental Physics NRC Kurchatov Institute, 117218, Moscow, Russia.
| | - Konstantin S Tikhonov
- Skolkovo Institute of Science and Technology, 143026, Skolkovo, Russia.
- Institut für Nanotechnologie, Karlsruhe Institute of Technology, 76021, Karlsruhe, Germany.
- Landau Institute for Theoretical Physics RAS, 119334, Moscow, Russia.
| | - Mikhail I Katsnelson
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ, Nijmegen, The Netherlands
- Theoretical Physics and Applied Mathematics Department, Ural Federal University, 620002, Yekaterinburg, Russia
| | - Andrey A Bagrov
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ, Nijmegen, The Netherlands.
- Theoretical Physics and Applied Mathematics Department, Ural Federal University, 620002, Yekaterinburg, Russia.
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120, Uppsala, Sweden.
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24
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Sharir O, Levine Y, Wies N, Carleo G, Shashua A. Deep Autoregressive Models for the Efficient Variational Simulation of Many-Body Quantum Systems. PHYSICAL REVIEW LETTERS 2020; 124:020503. [PMID: 32004039 DOI: 10.1103/physrevlett.124.020503] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2019] [Indexed: 06/10/2023]
Abstract
Artificial neural networks were recently shown to be an efficient representation of highly entangled many-body quantum states. In practical applications, neural-network states inherit numerical schemes used in variational Monte Carlo method, most notably the use of Markov-chain Monte Carlo (MCMC) sampling to estimate quantum expectations. The local stochastic sampling in MCMC caps the potential advantages of neural networks in two ways: (i) Its intrinsic computational cost sets stringent practical limits on the width and depth of the networks, and therefore limits their expressive capacity; (ii) its difficulty in generating precise and uncorrelated samples can result in estimations of observables that are very far from their true value. Inspired by the state-of-the-art generative models used in machine learning, we propose a specialized neural-network architecture that supports efficient and exact sampling, completely circumventing the need for Markov-chain sampling. We demonstrate our approach for two-dimensional interacting spin models, showcasing the ability to obtain accurate results on larger system sizes than those currently accessible to neural-network quantum states.
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Affiliation(s)
- Or Sharir
- The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
| | - Yoav Levine
- The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
| | - Noam Wies
- The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
| | - Giuseppe Carleo
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
| | - Amnon Shashua
- The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
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25
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Mechanism of superconductivity and electron-hole doping asymmetry in κ-type molecular conductors. Nat Commun 2019; 10:3167. [PMID: 31320623 PMCID: PMC6639402 DOI: 10.1038/s41467-019-11022-1] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2018] [Accepted: 06/13/2019] [Indexed: 11/19/2022] Open
Abstract
Unconventional superconductivity in molecular conductors is observed at the border of metal-insulator transitions in correlated electrons under the influence of geometrical frustration. The symmetry as well as the mechanism of the superconductivity (SC) is highly controversial. To address this issue, we theoretically explore the electronic properties of carrier-doped molecular Mott system κ-(BEDT-TTF)2X. We find significant electron-hole doping asymmetry in the phase diagram where antiferromagnetic (AF) spin order, different patterns of charge order, and SC compete with each other. Hole-doping stabilizes AF phase and promotes SC with dxy-wave symmetry, which has similarities with high-Tc cuprates. In contrast, in the electron-doped side, geometrical frustration destabilizes the AF phase and the enhanced charge correlation induces another SC with extended-s + \documentclass[12pt]{minimal}
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\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$d_{x^2 - y^2}$$\end{document}dx2-y2wave symmetry. Our results disclose the mechanism of each phase appearing in filling-control molecular Mott systems, and elucidate how physics of different strongly-correlated electrons are connected, namely, molecular conductors and high-Tc cuprates. The mechanism of unconventional superconductivity in molecular conductors remains controversial. Here, Watanabe et al. theoretically study and report electron-hole doping asymmetry and competing orders with superconductivity in a doped molecular Mott system.
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26
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Mahajan A, Sharma S. Symmetry-Projected Jastrow Mean-Field Wave Function in Variational Monte Carlo. J Phys Chem A 2019; 123:3911-3921. [DOI: 10.1021/acs.jpca.9b01583] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Ankit Mahajan
- Department of Chemistry and Biochemistry, University of Colorado Boulder, Boulder, Colorado 80302, United States
| | - Sandeep Sharma
- Department of Chemistry and Biochemistry, University of Colorado Boulder, Boulder, Colorado 80302, United States
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27
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Spencer JS, Blunt NS, Choi S, Etrych J, Filip MA, Foulkes WMC, Franklin RST, Handley WJ, Malone FD, Neufeld VA, Di Remigio R, Rogers TW, Scott CJC, Shepherd JJ, Vigor WA, Weston J, Xu R, Thom AJW. The HANDE-QMC Project: Open-Source Stochastic Quantum Chemistry from the Ground State Up. J Chem Theory Comput 2019; 15:1728-1742. [DOI: 10.1021/acs.jctc.8b01217] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- James S. Spencer
- Department of Physics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
- Department of Materials, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Nick S. Blunt
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- St. John’s College, St. John’s Street, Cambridge, CB2 1TP, United Kingdom
| | - Seonghoon Choi
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Jiří Etrych
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Maria-Andreea Filip
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - W. M. C. Foulkes
- Department of Physics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
- Department of Physics, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
| | - Ruth S. T. Franklin
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Will J. Handley
- Astrophysics Group, Cavendish Laboratory, Cambridge, CB3 OHE, United Kingdom
- Kavli Institute for Cosmology, Madingley Road, Cambridge, CB3 0HA, United Kingdom
- Gonville & Caius College, Trinity Street, Cambridge, CB2 1TA, United Kingdom
| | - Fionn D. Malone
- Department of Physics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
- Quantum Simulations Group, Lawrence Livermore National Laboratory, Livermore, California 94550, United States
| | - Verena A. Neufeld
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Roberto Di Remigio
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Tromsø—The Arctic University of Norway, N-9037 Tromsø, Norway
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Thomas W. Rogers
- Department of Physics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Charles J. C. Scott
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | | | - William A. Vigor
- Department of Chemistry, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Joseph Weston
- Department of Physics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - RuQing Xu
- Department of Modern Physics, University of Science and Technology, Hefei, Anhui 230026, China
| | - Alex J. W. Thom
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Department of Chemistry, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
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28
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Liu YYF, Andrews B, Conduit GJ. Direct evaluation of the force constant matrix in quantum Monte Carlo. J Chem Phys 2019; 150:034104. [DOI: 10.1063/1.5070138] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Y. Y. F. Liu
- Theory of Condensed Matter Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - B. Andrews
- Theory of Condensed Matter Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - G. J. Conduit
- Theory of Condensed Matter Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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29
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Pierleoni C, Rillo G, Ceperley DM, Holzmann M. Electron localization properties in high pressure hydrogen at the liquid-liquid phase transition by Coupled Electron-Ion Monte Carlo. ACTA ACUST UNITED AC 2018. [DOI: 10.1088/1742-6596/1136/1/012005] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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30
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Sabzevari I, Sharma S. Improved Speed and Scaling in Orbital Space Variational Monte Carlo. J Chem Theory Comput 2018; 14:6276-6286. [PMID: 30418769 DOI: 10.1021/acs.jctc.8b00780] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In this work, we introduce three algorithmic improvements to reduce the cost and improve the scaling of orbital space variational Monte Carlo (VMC). First, we show that, by appropriately screening the one- and two-electron integrals of the Hamiltonian, one can improve the efficiency of the algorithm by several orders of magnitude. This improved efficiency comes with the added benefit that the cost of obtaining a constant error per electron scales as the second power of the system size O( N2), down from the fourth power O( N4). Using numerical results, we demonstrate that the practical scaling obtained is, in fact, O( N1.5) for a chain of hydrogen atoms. Second, we show that, by using the adaptive stochastic gradient descent algorithm called AMSGrad, one can optimize the wave function energies robustly and efficiently. Remarkably, AMSGrad is almost as inexpensive as the simple stochastic gradient descent but delivers a convergence rate that is comparable to that of the Stochastic Reconfiguration algorithm, which is significantly more expensive and has a worse scaling with the system size. Third, we introduce the use of the rejection-free continuous time Monte Carlo (CTMC) to sample the determinants. Unlike the first two improvements, CTMC does come at an overhead that the local energy must be calculated at every Monte Carlo step. However, this overhead is mitigated to a large extent because of the reduced scaling algorithm, which ensures that the asymptotic cost of calculating the local energy is equal to that of updating the walker. The resulting algorithm allows us to calculate the ground state energy of a chain of 160 hydrogen atoms using a wave function containing ∼2 × 105 variational parameters with an accuracy of 1 mEh/particle at a cost of just 25 CPU h, which when split over 2 nodes of 24 processors each amounts to only about half hour of wall time. This low cost coupled with embarrassing parallelizability of the VMC algorithm and great freedom in the forms of usable wave functions, represents a highly effective method for calculating the electronic structure of model and ab initio systems.
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Affiliation(s)
- Iliya Sabzevari
- Department of Chemistry and Biochemistry , University of Colorado, Boulder , Boulder , Colorado 80302 , United States
| | - Sandeep Sharma
- Department of Chemistry and Biochemistry , University of Colorado, Boulder , Boulder , Colorado 80302 , United States
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31
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Archibald R, Krogel JT, Kent PRC. Gaussian process based optimization of molecular geometries using statistically sampled energy surfaces from quantum Monte Carlo. J Chem Phys 2018; 149:164116. [DOI: 10.1063/1.5040584] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Affiliation(s)
- R. Archibald
- Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - J. T. Krogel
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - P. R. C. Kent
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
- Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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32
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Nakatsuji H, Nakashima H, Kurokawa YI. Solving the Schrödinger equation of atoms and molecules with the free-complement chemical-formula theory: First-row atoms and small molecules. J Chem Phys 2018; 149:114106. [PMID: 30243284 DOI: 10.1063/1.5040377] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The free-complement chemical-formula theory (FC-CFT) for solving the Schrödinger equation (SE) was applied to the first-row atoms and several small molecules, limiting only to the ground state of a spin symmetry. Highly accurate results, satisfying chemical accuracy (kcal/mol accuracy for the absolute total energy), were obtained for all the cases. The local Schrödinger equation (LSE) method was applied for obtaining the solutions accurately and stably. For adapting the sampling method to quantum mechanical calculations, we developed a combined method of local sampling and Metropolis sampling. We also reported the method that leads the calculations to the accurate energies and wave functions as definite converged results with minimum ambiguities. We have also examined the possibility of the stationarity principle in the sampling method: it certainly works, though more extensive applications are necessary. From the high accuracy and the constant stability of the results, the present methodology seems to provide a useful tool for solving the SE of atoms and molecules.
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Affiliation(s)
- Hiroshi Nakatsuji
- Quantum Chemistry Research Institute, Kyoto Technoscience Center 16, 14 Yoshida Kawaramachi, Sakyo-ku, Kyoto 606-8305, Japan
| | - Hiroyuki Nakashima
- Quantum Chemistry Research Institute, Kyoto Technoscience Center 16, 14 Yoshida Kawaramachi, Sakyo-ku, Kyoto 606-8305, Japan
| | - Yusaku I Kurokawa
- Quantum Chemistry Research Institute, Kyoto Technoscience Center 16, 14 Yoshida Kawaramachi, Sakyo-ku, Kyoto 606-8305, Japan
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33
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Luo Y, Esler KP, Kent PRC, Shulenburger L. An efficient hybrid orbital representation for quantum Monte Carlo calculations. J Chem Phys 2018; 149:084107. [DOI: 10.1063/1.5037094] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ye Luo
- Argonne Leadership Computing Facility, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Kenneth P. Esler
- Stone Ridge Technology, 2015 Emmorton Rd. Suite 204, Bel Air, Maryland 21015, USA
| | - Paul R. C. Kent
- Center for Nanophase Materials Sciences and Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Luke Shulenburger
- HEDP Theory Department, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
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Rubio-García A, Alcoba DR, Capuzzi P, Dukelsky J. Benchmarking the Variational Reduced Density Matrix Theory in the Doubly Occupied Configuration Interaction Space with Integrable Pairing Models. J Chem Theory Comput 2018; 14:4183-4192. [PMID: 29906104 DOI: 10.1021/acs.jctc.8b00387] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The variational reduced density matrix theory has been recently applied with great success to models within the truncated doubly occupied configuration interaction space, which corresponds to the seniority zero subspace. Conservation of the seniority quantum number restricts the Hamiltonians to be based on the SU(2) algebra. Among them there is a whole family of exactly solvable Richardson-Gaudin pairing Hamiltonians. We benchmark the variational theory against two different exactly solvable models, the Richardson-Gaudin-Kitaev and the reduced BCS Hamiltonians. We obtain exact numerical results for the so-called [Formula: see text] N-representability conditions in both cases for systems that go from 10 to 100 particles. However, when random single-particle energies as appropriate for small superconducting grains are considered, the exactness is lost but still a high accuracy is obtained.
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Affiliation(s)
- A Rubio-García
- Instituto de Estructura de la Materia, CSIC, Serrano 123 , 28006 Madrid , Spain
| | - D R Alcoba
- Departamento de Física, Facultad de Ciencias Exactas y Naturales , Universidad de Buenos Aires, Ciudad Universitaria , 1428 Buenos Aires , Argentina.,Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas , Ciudad Universitaria , 1428 Buenos Aires , Argentina
| | - P Capuzzi
- Departamento de Física, Facultad de Ciencias Exactas y Naturales , Universidad de Buenos Aires, Ciudad Universitaria , 1428 Buenos Aires , Argentina.,Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas , Ciudad Universitaria , 1428 Buenos Aires , Argentina
| | - J Dukelsky
- Instituto de Estructura de la Materia, CSIC, Serrano 123 , 28006 Madrid , Spain
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Calcavecchia F, Kühne TD. Metal-Insulator Transition of Solid Hydrogen by the Antisymmetric Shadow Wave Function. ACTA ACUST UNITED AC 2018. [DOI: 10.1515/zna-2018-0180] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Abstract
We revisit the pressure-induced molecular-atomic metal-insulator transition of solid hydrogen by means of variational quantum Monte Carlo simulations based on the antisymmetric shadow wave function. For the purpose of facilitating the study of the electronic structure of large-scale fermionic systems, the shadow wave function formalism is extended by a series of technical advancements as implemented in our HswfQMC code. Among others, these improvements include a revised optimization method for the employed shadow wave function and an enhanced treatment of periodic systems with long-range interactions. It is found that the superior accuracy of the antisymmetric shadow wave function results in a significantly increased transition pressure with respect to previous theoretical estimates.
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Affiliation(s)
- Francesco Calcavecchia
- LPMMC, UMR 5493 of CNRS , Université Grenoble Alpes , 38042 Grenoble , France
- Institute of Physics , Johannes Gutenberg University , Staudingerweg 7 , D-55128 Mainz , Germany
- Graduate School of Excellence Materials Science in Mainz , Staudingerweg 9 , D-55128 Mainz , Germany
| | - Thomas D. Kühne
- Dynamics of Condensed Matter, Department of Chemistry , University of Paderborn , Warburger Str. 100 , D-33098 Paderborn , Germany
- Paderborn Center for Parallel Computing , University of Paderborn , Warburger Str. 100 , D-33098 Paderborn , Germany
- Center for Sustainable Systems Design , University of Paderborn , Warburger Str. 100 , D-33098 Paderborn , Germany
- Institute for Lightweight Design , University of Paderborn , Warburger Str. 100 , D-33098 Paderborn , Germany
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36
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Krogel JT, Reboredo FA. Kinetic energy classification and smoothing for compact B-spline basis sets in quantum Monte Carlo. J Chem Phys 2018; 148:044110. [PMID: 29390850 DOI: 10.1063/1.4994817] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Quantum Monte Carlo calculations of defect properties of transition metal oxides have become feasible in recent years due to increases in computing power. As the system size has grown, availability of on-node memory has become a limiting factor. Saving memory while minimizing computational cost is now a priority. The main growth in memory demand stems from the B-spline representation of the single particle orbitals, especially for heavier elements such as transition metals where semi-core states are present. Despite the associated memory costs, splines are computationally efficient. In this work, we explore alternatives to reduce the memory usage of splined orbitals without significantly affecting numerical fidelity or computational efficiency. We make use of the kinetic energy operator to both classify and smooth the occupied set of orbitals prior to splining. By using a partitioning scheme based on the per-orbital kinetic energy distributions, we show that memory savings of about 50% is possible for select transition metal oxide systems. For production supercells of practical interest, our scheme incurs a performance penalty of less than 5%.
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Affiliation(s)
- Jaron T Krogel
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Fernando A Reboredo
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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Ruggeri M, Moroni S, Holzmann M. Nonlinear Network Description for Many-Body Quantum Systems in Continuous Space. PHYSICAL REVIEW LETTERS 2018; 120:205302. [PMID: 29864292 DOI: 10.1103/physrevlett.120.205302] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2017] [Indexed: 06/08/2023]
Abstract
We show that the recently introduced iterative backflow wave function can be interpreted as a general neural network in continuum space with nonlinear functions in the hidden units. Using this wave function in variational Monte Carlo simulations of liquid ^{4}He in two and three dimensions, we typically find a tenfold increase in accuracy over currently used wave functions. Furthermore, subsequent stages of the iteration procedure define a set of increasingly good wave functions, each with its own variational energy and variance of the local energy: extrapolation to zero variance gives energies in close agreement with the exact values. For two dimensional ^{4}He, we also show that the iterative backflow wave function can describe both the liquid and the solid phase with the same functional form-a feature shared with the shadow wave function, but now joined by much higher accuracy. We also achieve significant progress for liquid ^{3}He in three dimensions, improving previous variational and fixed-node energies.
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Affiliation(s)
- Michele Ruggeri
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
| | - Saverio Moroni
- DEMOCRITOS National Simulation Center, Istituto Officina dei Materiali del CNR and SISSA, Via Bonomea 265, I-34136 Trieste, Italy
| | - Markus Holzmann
- Univ. Grenoble Alpes, CNRS, LPMMC, 3800 Grenoble, France
- Institut Laue Langevin, BP 156, F-38042 Grenoble Cedex 9, France
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López Ríos P, Perali A, Needs RJ, Neilson D. Evidence from Quantum Monte Carlo Simulations of Large-Gap Superfluidity and BCS-BEC Crossover in Double Electron-Hole Layers. PHYSICAL REVIEW LETTERS 2018; 120:177701. [PMID: 29756819 DOI: 10.1103/physrevlett.120.177701] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2017] [Indexed: 06/08/2023]
Abstract
We report quantum Monte Carlo evidence of the existence of large gap superfluidity in electron-hole double layers over wide density ranges. The superfluid parameters evolve from normal state to BEC with decreasing density, with the BCS state restricted to a tiny range of densities due to the strong screening of Coulomb interactions, which causes the gap to rapidly become large near the onset of superfluidity. The superfluid properties exhibit similarities to ultracold fermions and iron-based superconductors, suggesting an underlying universal behavior of BCS-BEC crossovers in pairing systems.
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Affiliation(s)
- Pablo López Ríos
- Max-Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
- Theory of Condensed Matter Group, Cavendish Laboratory, 19 J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Andrea Perali
- School of Pharmacy, Physics Unit, University of Camerino, 62032 Camerino (MC), Italy
| | - Richard J Needs
- Theory of Condensed Matter Group, Cavendish Laboratory, 19 J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - David Neilson
- School of Science and Technology, Physics Division, University of Camerino, 62032 Camerino (MC), Italy
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium
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Dzubak AL, Mitra C, Chance M, Kuhn S, Jellison GE, Sefat AS, Krogel JT, Reboredo FA. MnNiO3 revisited with modern theoretical and experimental methods. J Chem Phys 2017; 147:174703. [DOI: 10.1063/1.5000847] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Affiliation(s)
- Allison L. Dzubak
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Chandrima Mitra
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Michael Chance
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Stephen Kuhn
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Gerald E. Jellison
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Athena S. Sefat
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Jaron T. Krogel
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Fernando A. Reboredo
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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Lutsyshyn Y. Weakly parametrized Jastrow ansatz for a strongly correlated Bose system. J Chem Phys 2017; 146:124102. [PMID: 28388103 DOI: 10.1063/1.4978707] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
We consider the Jastrow pair-product wavefunction for strongly correlated Bose systems, in our case liquid helium-4. An ansatz is proposed for the pair factors which consist of a numeric solution to a modified and parametrized pair scattering equation. We consider a number of such simple one-variable parametrizations. Additionally, we allow for a parametrizeable cutoff of the pair factors and for the addition of a long-range phonon tail. This approach results in many-body wavefunctions that have between just one and three variational parameters. Calculation of observables is carried with the variational Monte Carlo method. We find that such a simple parametrization is sufficient to produce results that are comparable in quality to the best available two-body factors for helium. For the two-parameter wavefunction, we find variational energies of -6.04 K per particle for a system of one thousand particles. It is also shown that short-range two-body correlations are reproduced in good detail by the two- and three-parameter functions.
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41
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Carleo G, Troyer M. Solving the quantum many-body problem with artificial neural networks. Science 2017; 355:602-606. [DOI: 10.1126/science.aag2302] [Citation(s) in RCA: 963] [Impact Index Per Article: 137.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2016] [Accepted: 01/12/2017] [Indexed: 11/03/2022]
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Wagner LK, Ceperley DM. Discovering correlated fermions using quantum Monte Carlo. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:094501. [PMID: 27518859 DOI: 10.1088/0034-4885/79/9/094501] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
It has become increasingly feasible to use quantum Monte Carlo (QMC) methods to study correlated fermion systems for realistic Hamiltonians. We give a summary of these techniques targeted at researchers in the field of correlated electrons, focusing on the fundamentals, capabilities, and current status of this technique. The QMC methods often offer the highest accuracy solutions available for systems in the continuum, and, since they address the many-body problem directly, the simulations can be analyzed to obtain insight into the nature of correlated quantum behavior.
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Affiliation(s)
- Lucas K Wagner
- Department of Physics, University of Illinois at Urbana-Champaign, Champaign, IL, USA
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Kamibayashi Y, Miura S. Variational path integral molecular dynamics and hybrid Monte Carlo algorithms using a fourth order propagator with applications to molecular systems. J Chem Phys 2016; 145:074114. [DOI: 10.1063/1.4961149] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Affiliation(s)
- Yuki Kamibayashi
- Graduate School of Natural Science and Technology, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan
| | - Shinichi Miura
- Graduate School of Natural Science and Technology, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan
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Calcavecchia F, Holzmann M. Fermion sign problem in imaginary-time projection continuum quantum Monte Carlo with local interaction. Phys Rev E 2016; 93:043321. [PMID: 27176442 DOI: 10.1103/physreve.93.043321] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2016] [Indexed: 06/05/2023]
Abstract
We use the shadow wave function formalism as a convenient model to study the fermion sign problem affecting all projector quantum Monte Carlo methods in continuum space. We demonstrate that the efficiency of imaginary-time projection algorithms decays exponentially with increasing number of particles and/or imaginary-time propagation. Moreover, we derive an analytical expression that connects the localization of the system with the magnitude of the sign problem, illustrating this behavior through numerical results. Finally, we discuss the computational complexity of the fermion sign problem and methods for alleviating its severity.
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Affiliation(s)
- Francesco Calcavecchia
- LPMMC, UMR 5493 of CNRS, Université Grenoble Alpes, 38042 Grenoble, France; Institute of Physics, Johannes Gutenberg University, Staudingerweg 7, D-55128 Mainz, Germany; and Graduate School of Excellence Materials Science in Mainz, Staudingerweg 9, D-55128 Mainz, Germany
| | - Markus Holzmann
- LPMMC, UMR 5493 of CNRS, Université Grenoble Alpes, 38042 Grenoble, France and Institut Laue Langevin, BP 156, F-38042 Grenoble Cedex 9, France
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45
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Toulouse J, Assaraf R, Umrigar CJ. Introduction to the Variational and Diffusion Monte Carlo Methods. ADVANCES IN QUANTUM CHEMISTRY 2016. [DOI: 10.1016/bs.aiq.2015.07.003] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/03/2022]
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47
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Luo Y, Zen A, Sorella S. Ab initio molecular dynamics with noisy forces: Validating the quantum Monte Carlo approach with benchmark calculations of molecular vibrational properties. J Chem Phys 2014; 141:194112. [DOI: 10.1063/1.4901430] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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48
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Calcavecchia F, Pederiva F, Kalos MH, Kühne TD. Sign problem of the fermionic shadow wave function. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:053304. [PMID: 25493901 DOI: 10.1103/physreve.90.053304] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2014] [Indexed: 06/04/2023]
Abstract
We present a whole series of methods to alleviate the sign problem of the fermionic shadow wave function in the context of variational Monte Carlo. The effectiveness of our techniques is demonstrated on liquid ^{3}He. We found that although the variance is reduced, the gain in efficiency is restricted by the increased computational cost. Yet, this development not only extends the scope of the fermionic shadow wave function, but also facilitates highly accurate quantum Monte Carlo simulations previously thought not feasible.
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Affiliation(s)
- Francesco Calcavecchia
- Institute of Physics, Johannes Gutenberg-University, Staudingerweg 7, D-55128 Mainz, Germany and Graduate School Materials Science in Mainz, Staudingerweg 9, D-55128 Mainz, Germany
| | - Francesco Pederiva
- Dipartimento di Fisica, University of Trento, via Sommarive 14, I-38050 Povo, Trento, Italy and INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Malvin H Kalos
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Thomas D Kühne
- Institute of Physical Chemistry and Center for Computational Sciences, Johannes Gutenberg University Mainz, Staudinger Weg 7, D-55128 Mainz, Germany and Department of Chemistry, University of Paderborn, Warburger Strasse 100, D-33098 Paderborn, Germany
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Ochi M, Sodeyama K, Tsuneyuki S. Optimization of the Jastrow factor using the random-phase approximation and a similarity-transformed Hamiltonian: Application to band-structure calculation for some semiconductors and insulators. J Chem Phys 2014; 140:074112. [DOI: 10.1063/1.4865500] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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