1
|
Liu Y, Meitei OR, Chin ZE, Dutt A, Tao M, Chuang IL, Van Voorhis T. Bootstrap Embedding on a Quantum Computer. J Chem Theory Comput 2023; 19:2230-2247. [PMID: 37001026 DOI: 10.1021/acs.jctc.3c00012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/03/2023]
Abstract
We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian governing fragments of the total system, in such a way that fragment solutions can harness the capabilities of quantum computers. By employing state-of-art quantum subroutines including the quantum SWAP test and quantum amplitude amplification, we show how a quadratic speedup can be obtained over the classical algorithm, in principle. Utilization of quantum computation also allows the algorithm to match─at little additional computational cost─full density matrices at fragment boundaries, instead of being limited to 1-RDMs. Current quantum computers are small, but quantum bootstrap embedding provides a potentially generalizable strategy for harnessing such small machines through quantum fragment matching.
Collapse
Affiliation(s)
- Yuan Liu
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Oinam R. Meitei
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Zachary E. Chin
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Arkopal Dutt
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Max Tao
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Isaac L. Chuang
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| |
Collapse
|
2
|
Faulstich FM, Kim R, Cui ZH, Wen Z, Kin-Lic Chan G, Lin L. Pure State v-Representability of Density Matrix Embedding Theory. J Chem Theory Comput 2022; 18:851-864. [PMID: 35084855 DOI: 10.1021/acs.jctc.1c01061] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Density matrix embedding theory (DMET) formally requires the matching of density matrix blocks obtained from high-level and low-level theories, but this is sometimes not achievable in practical calculations. In such a case, the global band gap of the low-level theory vanishes, and this can require additional numerical considerations. We find that both the violation of the exact matching condition and the vanishing low-level gap are related to the assumption that the high-level density matrix blocks are noninteracting pure-state v-representable (NI-PS-V), which assumes that the low-level density matrix is constructed following the Aufbau principle. To relax the NI-PS-V condition, we develop an augmented Lagrangian method to match the density matrix blocks without referring to the Aufbau principle. Numerical results for the 2D Hubbard and hydrogen model systems indicate that, in some challenging scenarios, the relaxation of the Aufbau principle directly leads to exact matching of the density matrix blocks, which also yields improved accuracy.
Collapse
Affiliation(s)
- Fabian M Faulstich
- Department of Mathematics, University of California, Berkeley, California 94720, United States
| | - Raehyun Kim
- Department of Mathematics, University of California, Berkeley, California 94720, United States
| | - Zhi-Hao Cui
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Zaiwen Wen
- Beijing International Center for Mathematical Research, BICMR, Peking University, Beijing 100871, China
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Lin Lin
- Department of Mathematics, University of California, Berkeley, California 94720, United States.,Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| |
Collapse
|
3
|
Cheng Y, Xie Z, Ma H. Post-Density Matrix Renormalization Group Methods for Describing Dynamic Electron Correlation with Large Active Spaces. J Phys Chem Lett 2022; 13:904-915. [PMID: 35049302 DOI: 10.1021/acs.jpclett.1c04078] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The ab initio density matrix renormalization group (DMRG) method has been well-established and has become one of the most accurate numerical methods for the precise electronic structure solution of large active spaces. In the past few years, to capture the missing dynamic correlation, various post-DMRG approaches have been proposed through the combination of DMRG and multireference quantum chemical methods or density functional theory. With this in mind, this work provides a brief overview of ab initio DMRG principles and the new developments within post-DMRG methods. For clarity, post-DMRG methods are classified into two main categories depending on whether high-order n-electron reduced density matrices are used, and their merits and disadvantages are properly discussed. Finally, we conclude by discussing unsolved bottlenecks and giving development perspectives of post-DMRG approaches, which are expected to yield quantitative descriptions of complex electronic structures in large strongly correlated molecules and materials.
Collapse
Affiliation(s)
- Yifan Cheng
- School of Chemistry and Chemical Engineering, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University, Nanjing 210023, China
| | - Zhaoxuan Xie
- School of Chemistry and Chemical Engineering, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University, Nanjing 210023, China
| | - Haibo Ma
- School of Chemistry and Chemical Engineering, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University, Nanjing 210023, China
- Chemistry and Biomedicine Innovation Center (ChemBIC), Nanjing University, Nanjing 210023, China
| |
Collapse
|
4
|
Wang K, Xie Z, Luo Z, Ma H. Low-Scaling Excited State Calculation Using the Block Interaction Product State. J Phys Chem Lett 2022; 13:462-470. [PMID: 35015548 DOI: 10.1021/acs.jpclett.1c03445] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
We develop an automatic and efficient scheme for the accurate construction of the bases for excitonic models, which can enable "black-box" excited state structure calculations for large molecular systems. These new and optimized bases, which are named the block interaction product state (BIPS), can be expressed as the direct products of the local states for each chromophore. Each chromophore's local states are selected by diagonalization of its reduced density matrix, which is obtained by quantum chemical calculation of the small subsystem composed of the chromophore and its nearest neighbors. We implemented the BIPS framework with fragment-based calculations considering two- and three-body interactions. Test calculations for eight different molecular aggregates demonstrate that this framework provides an accurate description of not only the excitation energies but also the first-order wave function properties (dipole moment and transition dipole moment) of the low-lying excited states at a low-scaling computational cost.
Collapse
Affiliation(s)
- Ke Wang
- School of Chemistry and Chemical Engineering, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University, Nanjing 210023, China
| | - Zhaoxuan Xie
- School of Chemistry and Chemical Engineering, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University, Nanjing 210023, China
| | - Zhen Luo
- School of Chemistry and Chemical Engineering, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University, Nanjing 210023, China
| | - Haibo Ma
- School of Chemistry and Chemical Engineering, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University, Nanjing 210023, China
| |
Collapse
|