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Provazza J, Gunst K, Zhai H, Chan GKL, Shiozaki T, Rubin NC, White AF. Fast Emulation of Fermionic Circuits with Matrix Product States. J Chem Theory Comput 2024; 20:3719-3728. [PMID: 38661337 DOI: 10.1021/acs.jctc.4c00200] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/26/2024]
Abstract
We describe a matrix product state (MPS) extension for the Fermionic Quantum Emulator (FQE) software library. We discuss the theory behind symmetry-adapted MPSs for approximating many-body wave functions of spin-1/2 Fermions, and we present an open-source, MPS-enabled implementation of the FQE interface (MPS-FQE). The software uses the open-source pyblock3 and block2 libraries for most elementary tensor operations, and it can largely be used as a drop-in replacement for FQE that allows for more efficient but approximate emulation of larger Fermionic circuits. Finally, we show several applications relevant to both near-term and fault-tolerant quantum algorithms where approximate emulation of larger systems is expected to be useful: characterization of state preparation strategies for quantum phase estimation, the testing of different variational quantum eigensolver ansätze, the numerical evaluation of Trotter errors, and the simulation of general quantum dynamics problems. In all these examples, approximate emulation with MPS-FQE allows us to treat systems that are significantly larger than those accessible with a full statevector emulator.
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Affiliation(s)
- Justin Provazza
- Quantum Simulation Technologies Inc., Boston, Massachusetts 02135, United States
| | - Klaas Gunst
- Quantum Simulation Technologies Inc., Boston, Massachusetts 02135, United States
| | - Huanchen Zhai
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Garnet K-L Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Toru Shiozaki
- Quantum Simulation Technologies Inc., Boston, Massachusetts 02135, United States
| | - Nicholas C Rubin
- Google Quantum AI, Mountain View, California 94043, United States
| | - Alec F White
- Quantum Simulation Technologies Inc., Boston, Massachusetts 02135, United States
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2
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Wang Y, Ren J, Shuai Z. Minimizing non-radiative decay in molecular aggregates through control of excitonic coupling. Nat Commun 2023; 14:5056. [PMID: 37598183 PMCID: PMC10439946 DOI: 10.1038/s41467-023-40716-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2022] [Accepted: 08/03/2023] [Indexed: 08/21/2023] Open
Abstract
The widely known "Energy Gap Law" (EGL) predicts a monotonically exponential increase in the non-radiative decay rate (knr) as the energy gap narrows, which hinders the development of near-infrared (NIR) emissive molecular materials. Recently, several experiments proposed that the exciton delocalization in molecular aggregates could counteract EGL to facilitate NIR emission. In this work, the nearly exact time-dependent density matrix renormalization group (TD-DMRG) method is developed to evaluate the non-radiative decay rate for exciton-phonon coupled molecular aggregates. Systematical numerical simulations show, by increasing the excitonic coupling, knr will first decrease, then reach a minimum, and finally start to increase to follow EGL, which is an overall result of two opposite effects of a smaller energy gap and a smaller effective electron-phonon coupling. This anomalous non-monotonic behavior is found robust in a number of models, including dimer, one-dimensional chain, and two-dimensional square lattice. The optimal excitonic coupling strength that gives the minimum knr is about half of the monomer reorganization energy and is also influenced by system size, dimensionality, and temperature.
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Affiliation(s)
- Yuanheng Wang
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, 100084, Beijing, People's Republic of China
| | - Jiajun Ren
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, 100875, Beijing, People's Republic of China.
| | - Zhigang Shuai
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, 100084, Beijing, People's Republic of China.
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, 518172, People's Republic of China.
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3
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Li W, Ren J, Yang H, Shuai Z. On the fly swapping algorithm for ordering of degrees of freedom in density matrix renormalization group. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:254003. [PMID: 35378514 DOI: 10.1088/1361-648x/ac640e] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2022] [Accepted: 04/04/2022] [Indexed: 06/14/2023]
Abstract
Density matrix renormalization group (DMRG) and its time-dependent variants have found widespread applications in quantum chemistry, includingab initioelectronic structure of complex bio-molecules, spectroscopy for molecular aggregates, and charge transport in bulk organic semiconductors. The underlying wavefunction ansatz for DMRG, matrix product state (MPS), requires mapping degrees of freedom (DOF) into a one-dimensional topology. DOF ordering becomes a crucial factor for DMRG accuracy. In this work, we propose swapping neighboring DOFs during the DMRG sweeps for DOF ordering, which we term 'on the fly swapping' (OFS) algorithm. We show that OFS is universal for both static and time-dependent DMRG with minimum computational overhead. Examples are given for one dimensional antiferromagnetic Heisenberg model,ab initioelectronic structure of N2molecule, and the S1/S2internal conversion dynamics of pyrazine molecule. It is found that OFS can indeed improve accuracy by finding better DOF ordering in all cases.
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Affiliation(s)
- Weitang Li
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing, People's Republic of China
| | - Jiajun Ren
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing, People's Republic of China
| | - Hengrui Yang
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing, People's Republic of China
| | - Zhigang Shuai
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing, People's Republic of China
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Ren J, Li W, Jiang T, Wang Y, Shuai Z. Time‐dependent density matrix renormalization group method for quantum dynamics in complex systems. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1614] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Jiajun Ren
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry Tsinghua University Beijing People's Republic of China
| | - Weitang Li
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry Tsinghua University Beijing People's Republic of China
| | - Tong Jiang
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry Tsinghua University Beijing People's Republic of China
| | - Yuanheng Wang
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry Tsinghua University Beijing People's Republic of China
| | - Zhigang Shuai
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry Tsinghua University Beijing People's Republic of China
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Abstract
We introduce DMRG[FEAST], a new method for optimizing excited-state many-body wave functions with the density matrix renormalization group (DMRG) algorithm. Our approach applies the FEAST algorithm, originally designed for large-scale diagonalization problems, to matrix product state wave functions. We show that DMRG[FEAST] enables the stable optimization of both low- and high-energy eigenstates, therefore overcoming the limitations of state-of-the-art excited-state DMRG algorithms. We demonstrate the reliability of DMRG[FEAST] by calculating anharmonic vibrational excitation energies of molecules with up to 30 fully coupled degrees of freedom.
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Affiliation(s)
- Alberto Baiardi
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Anna Klára Kelemen
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Markus Reiher
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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Li W, Ma H, Li S, Ma J. Computational and data driven molecular material design assisted by low scaling quantum mechanics calculations and machine learning. Chem Sci 2021; 12:14987-15006. [PMID: 34909141 PMCID: PMC8612375 DOI: 10.1039/d1sc02574k] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2021] [Accepted: 10/12/2021] [Indexed: 12/11/2022] Open
Abstract
Electronic structure methods based on quantum mechanics (QM) are widely employed in the computational predictions of the molecular properties and optoelectronic properties of molecular materials. The computational costs of these QM methods, ranging from density functional theory (DFT) or time-dependent DFT (TDDFT) to wave-function theory (WFT), usually increase sharply with the system size, causing the curse of dimensionality and hindering the QM calculations for large sized systems such as long polymer oligomers and complex molecular aggregates. In such cases, in recent years low scaling QM methods and machine learning (ML) techniques have been adopted to reduce the computational costs and thus assist computational and data driven molecular material design. In this review, we illustrated low scaling ground-state and excited-state QM approaches and their applications to long oligomers, self-assembled supramolecular complexes, stimuli-responsive materials, mechanically interlocked molecules, and excited state processes in molecular aggregates. Variable electrostatic parameters were also introduced in the modified force fields with the polarization model. On the basis of QM computational or experimental datasets, several ML algorithms, including explainable models, deep learning, and on-line learning methods, have been employed to predict the molecular energies, forces, electronic structure properties, and optical or electrical properties of materials. It can be conceived that low scaling algorithms with periodic boundary conditions are expected to be further applicable to functional materials, perhaps in combination with machine learning to fast predict the lattice energy, crystal structures, and spectroscopic properties of periodic functional materials.
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Affiliation(s)
- Wei Li
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University Nanjing 210023 China
| | - Haibo Ma
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University Nanjing 210023 China
- Jiangsu Key Laboratory of Advanced Organic Materials, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University Nanjing 210023 China
| | - Shuhua Li
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University Nanjing 210023 China
| | - Jing Ma
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University Nanjing 210023 China
- Jiangsu Key Laboratory of Advanced Organic Materials, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University Nanjing 210023 China
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Karlsson D, van Leeuwen R, Pavlyukh Y, Perfetto E, Stefanucci G. Fast Green's Function Method for Ultrafast Electron-Boson Dynamics. PHYSICAL REVIEW LETTERS 2021; 127:036402. [PMID: 34328754 DOI: 10.1103/physrevlett.127.036402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2020] [Revised: 03/29/2021] [Accepted: 05/20/2021] [Indexed: 06/13/2023]
Abstract
The interaction of electrons with quantized phonons and photons underlies the ultrafast dynamics of systems ranging from molecules to solids, and it gives rise to a plethora of physical phenomena experimentally accessible using time-resolved techniques. Green's function methods offer an invaluable interpretation tool since scattering mechanisms of growing complexity can be selectively incorporated in the theory. Currently, however, real-time Green's function simulations are either prohibitively expensive due to the cubic scaling with the propagation time or do neglect the feedback of electrons on the bosons, thus violating energy conservation. We put forward a computationally efficient Green's function scheme which overcomes both limitations. The numerical effort scales linearly with the propagation time while the simultaneous dressing of electrons and bosons guarantees the fulfillment of all fundamental conservation laws. We present a real-time study of the phonon-driven relaxation dynamics in an optically excited narrow band-gap insulator, highlighting the nonthermal behavior of the phononic degrees of freedom. Our formulation paves the way to first-principles simulations of electron-boson systems with unprecedented long propagation times.
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Affiliation(s)
- Daniel Karlsson
- Department of Physics, Nanoscience Center, University of Jyväskylä, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - Robert van Leeuwen
- Department of Physics, Nanoscience Center, University of Jyväskylä, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - Yaroslav Pavlyukh
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06120 Halle, Germany
- Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - Enrico Perfetto
- Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
- INFN, Sezione di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - Gianluca Stefanucci
- Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
- INFN, Sezione di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
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Li W, Ren J, Shuai Z. Numerical assessment for accuracy and GPU acceleration of TD-DMRG time evolution schemes. J Chem Phys 2020; 152:024127. [PMID: 31941314 DOI: 10.1063/1.5135363] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
The time dependent density matrix renormalization group (TD-DMRG) has become one of the cutting edge methods of quantum dynamics for complex systems. In this paper, we comparatively study the accuracy of three time evolution schemes in the TD-DMRG, the global propagation and compression method with the Runge-Kutta algorithm (P&C-RK), the time dependent variational principle based methods with the matrix unfolding algorithm (TDVP-MU), and with the projector-splitting algorithm (TDVP-PS), by performing benchmarks on the exciton dynamics of the Fenna-Matthews-Olson complex. We show that TDVP-MU and TDVP-PS yield the same result when the time step size is converged and they are more accurate than P&C-RK4, while TDVP-PS tolerates a larger time step size than TDVP-MU. We further adopt the graphical processing units to accelerate the heavy tensor contractions in the TD-DMRG, and it is able to speed up the TDVP-MU and TDVP-PS schemes by up to 73 times.
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Affiliation(s)
- Weitang Li
- MOE Key Laboratory of Organic Optoelectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, People's Republic of China
| | - Jiajun Ren
- MOE Key Laboratory of Organic Optoelectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, People's Republic of China
| | - Zhigang Shuai
- MOE Key Laboratory of Organic Optoelectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, People's Republic of China
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9
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Xie X, Liu Y, Yao Y, Schollwöck U, Liu C, Ma H. Time-dependent density matrix renormalization group quantum dynamics for realistic chemical systems. J Chem Phys 2019; 151:224101. [DOI: 10.1063/1.5125945] [Citation(s) in RCA: 34] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Xiaoyu Xie
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | - Yuyang Liu
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | - Yao Yao
- Department of Physics and State Key Laboratory of Luminescent Materials and Devices, South China University of Technology, Guangzhou 510640, China
| | - Ulrich Schollwöck
- Department of Physics, Arnold Sommerfeld Center for Theoretical Physics (ASC), Fakultät für Physik, Ludwig-Maximilians-Universität München, München D-80333, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, München D-80799, Germany
| | - Chungen Liu
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | - Haibo Ma
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
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10
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Baiardi A, Stein CJ, Barone V, Reiher M. Optimization of highly excited matrix product states with an application to vibrational spectroscopy. J Chem Phys 2019; 150:094113. [DOI: 10.1063/1.5068747] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Alberto Baiardi
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Christopher J. Stein
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Vincenzo Barone
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Markus Reiher
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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11
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Yao Y, Sun KW, Luo Z, Ma H. Full Quantum Dynamics Simulation of a Realistic Molecular System Using the Adaptive Time-Dependent Density Matrix Renormalization Group Method. J Phys Chem Lett 2018; 9:413-419. [PMID: 29298068 DOI: 10.1021/acs.jpclett.7b03224] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The accurate theoretical interpretation of ultrafast time-resolved spectroscopy experiments relies on full quantum dynamics simulations for the investigated system, which is nevertheless computationally prohibitive for realistic molecular systems with a large number of electronic and/or vibrational degrees of freedom. In this work, we propose a unitary transformation approach for realistic vibronic Hamiltonians, which can be coped with using the adaptive time-dependent density matrix renormalization group (t-DMRG) method to efficiently evolve the nonadiabatic dynamics of a large molecular system. We demonstrate the accuracy and efficiency of this approach with an example of simulating the exciton dissociation process within an oligothiophene/fullerene heterojunction, indicating that t-DMRG can be a promising method for full quantum dynamics simulation in large chemical systems. Moreover, it is also shown that the proper vibronic features in the ultrafast electronic process can be obtained by simulating the two-dimensional (2D) electronic spectrum by virtue of the high computational efficiency of the t-DMRG method.
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Affiliation(s)
- Yao Yao
- Department of Physics and State Key Laboratory of Luminescent Materials and Devices, South China University of Technology , Guangzhou 510640, China
| | - Ke-Wei Sun
- School of Science, Hangzhou Dianzi University , Hangzhou 310018, China
| | - Zhen Luo
- Key Laboratory of Mesoscopic Chemistry of MOE, School of Chemistry and Chemical Engineering, Nanjing University , Nanjing 210023, China
| | - Haibo Ma
- Key Laboratory of Mesoscopic Chemistry of MOE, School of Chemistry and Chemical Engineering, Nanjing University , Nanjing 210023, China
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