1
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Sayer T, Montoya-Castillo A. Generalized quantum master equations can improve the accuracy of semiclassical predictions of multitime correlation functions. J Chem Phys 2024; 161:011101. [PMID: 38949578 DOI: 10.1063/5.0219205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2024] [Accepted: 06/12/2024] [Indexed: 07/02/2024] Open
Abstract
Multitime quantum correlation functions are central objects in physical science, offering a direct link between the experimental observables and the dynamics of an underlying model. While experiments such as 2D spectroscopy and quantum control can now measure such quantities, the accurate simulation of such responses remains computationally expensive and sometimes impossible, depending on the system's complexity. A natural tool to employ is the generalized quantum master equation (GQME), which can offer computational savings by extending reference dynamics at a comparatively trivial cost. However, dynamical methods that can tackle chemical systems with atomistic resolution, such as those in the semiclassical hierarchy, often suffer from poor accuracy, limiting the credence one might lend to their results. By combining work on the accuracy-boosting formulation of semiclassical memory kernels with recent work on the multitime GQME, here we show for the first time that one can exploit a multitime semiclassical GQME to dramatically improve both the accuracy of coarse mean-field Ehrenfest dynamics and obtain orders of magnitude efficiency gains.
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Affiliation(s)
- Thomas Sayer
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, USA
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2
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Kim CW, Franco I. General framework for quantifying dissipation pathways in open quantum systems. II. Numerical validation and the role of non-Markovianity. J Chem Phys 2024; 160:214112. [PMID: 38833365 DOI: 10.1063/5.0202862] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2024] [Accepted: 05/13/2024] [Indexed: 06/06/2024] Open
Abstract
In the previous paper [C. W. Kim and I. Franco, J. Chem. Phys. 160, 214111-1-214111-13 (2024)], we developed a theory called MQME-D, which allows us to decompose the overall energy dissipation process in open quantum system dynamics into contributions by individual components of the bath when the subsystem dynamics is governed by a Markovian quantum master equation (MQME). Here, we contrast the predictions of MQME-D against the numerically exact results obtained by combining hierarchical equations of motion (HEOM) with a recently reported protocol for monitoring the statistics of the bath. Overall, MQME-D accurately captures the contributions of specific bath components to the overall dissipation while greatly reducing the computational cost compared to exact computations using HEOM. The computations show that MQME-D exhibits errors originating from its inherent Markov approximation. We demonstrate that its accuracy can be significantly increased by incorporating non-Markovianity by exploiting time scale separations (TSS) in different components of the bath. Our work demonstrates that MQME-D combined with TSS can be reliably used to understand how energy is dissipated in realistic open quantum system dynamics.
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Affiliation(s)
- Chang Woo Kim
- Department of Chemistry, Chonnam National University, Gwangju 61186, South Korea
| | - Ignacio Franco
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
- Department of Physics, University of Rochester, Rochester, New York 14627, USA
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3
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Kang M, Nuomin H, Chowdhury SN, Yuly JL, Sun K, Whitlow J, Valdiviezo J, Zhang Z, Zhang P, Beratan DN, Brown KR. Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dynamics. Nat Rev Chem 2024; 8:340-358. [PMID: 38641733 DOI: 10.1038/s41570-024-00595-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 03/07/2024] [Indexed: 04/21/2024]
Abstract
Simulating the quantum dynamics of molecules in the condensed phase represents a longstanding challenge in chemistry. Trapped-ion quantum systems may serve as a platform for the analog-quantum simulation of chemical dynamics that is beyond the reach of current classical-digital simulation. To identify a 'quantum advantage' for these simulations, performance analysis of both analog-quantum simulation on noisy hardware and classical-digital algorithms is needed. In this Review, we make a comparison between a noisy analog trapped-ion simulator and a few choice classical-digital methods on simulating the dynamics of a model molecular Hamiltonian with linear vibronic coupling. We describe several simple Hamiltonians that are commonly used to model molecular systems, which can be simulated with existing or emerging trapped-ion hardware. These Hamiltonians may serve as stepping stones towards the use of trapped-ion simulators for systems beyond the reach of classical-digital methods. Finally, we identify dynamical regimes in which classical-digital simulations seem to have the weakest performance with respect to analog-quantum simulations. These regimes may provide the lowest hanging fruit to make the most of potential quantum advantages.
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Affiliation(s)
- Mingyu Kang
- Duke Quantum Center, Duke University, Durham, NC, USA.
- Department of Physics, Duke University, Durham, NC, USA.
| | - Hanggai Nuomin
- Department of Chemistry, Duke University, Durham, NC, USA
| | | | - Jonathon L Yuly
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA
| | - Ke Sun
- Duke Quantum Center, Duke University, Durham, NC, USA
- Department of Physics, Duke University, Durham, NC, USA
| | - Jacob Whitlow
- Duke Quantum Center, Duke University, Durham, NC, USA
- Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA
| | - Jesús Valdiviezo
- Kenneth S. Pitzer Theory Center, University of California, Berkeley, CA, USA
- Department of Chemistry, University of California, Berkeley, CA, USA
- Departamento de Ciencias, Sección Química, Pontificia Universidad Católica del Perú, Lima, Peru
| | - Zhendian Zhang
- Department of Chemistry, Duke University, Durham, NC, USA
| | - Peng Zhang
- Department of Chemistry, Duke University, Durham, NC, USA
| | - David N Beratan
- Department of Physics, Duke University, Durham, NC, USA.
- Department of Chemistry, Duke University, Durham, NC, USA.
- Department of Biochemistry, Duke University, Durham, NC, USA.
| | - Kenneth R Brown
- Duke Quantum Center, Duke University, Durham, NC, USA.
- Department of Physics, Duke University, Durham, NC, USA.
- Department of Chemistry, Duke University, Durham, NC, USA.
- Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA.
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4
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Ture TM, Jang SJ. Simple and General Unitarity Conserving Numerical Real-Time Propagators of the Time-Dependent Schrödinger Equation Based on Magnus Expansion. J Phys Chem A 2024; 128:2871-2882. [PMID: 38564477 DOI: 10.1021/acs.jpca.3c07866] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/04/2024]
Abstract
Magnus expansion (ME) provides a general way to expand the real-time propagator of a time-dependent Hamiltonian within the exponential such that the unitarity is satisfied at any order. We use this property and explicit integration of Lagrange interpolation formulas for the time-dependent Hamiltonian within each time interval and derive approximations that preserve unitarity for the differential time evolution operators of general time-dependent Hamiltonians. The resulting second-order approximation is the same as using the average of Hamiltonians for two end points of time. We identify three fourth-order approximations involving commutators of Hamiltonians at different times and also derive a sixth-order expression. A test of these approximations along with other available expressions for a two-state time-dependent Hamiltonian with sinusoidal time dependences provides information on the relative performance of these approximations and suggests that the derived expressions can serve as useful numerical tools for time evolution in time-resolved spectroscopy, quantum control, quantum sensing, real-time ab initio quantum dynamics, and open system quantum dynamics.
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Affiliation(s)
- Taner M Ture
- Department of Chemistry and Biochemistry, Queens College, City University of New York, 65-30 Kissena Boulevard, Queens, New York 11367, United States
- PhD Program in Chemistry, Graduate Center of the City University of New York, New York, New York 10016, United States
| | - Seogjoo J Jang
- Department of Chemistry and Biochemistry, Queens College, City University of New York, 65-30 Kissena Boulevard, Queens, New York 11367, United States
- PhD Programs in Chemistry and Physics, Graduate Center of the City University of New York, New York, New York 10016, United States
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5
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Atsango AO, Montoya-Castillo A, Markland TE. An accurate and efficient Ehrenfest dynamics approach for calculating linear and nonlinear electronic spectra. J Chem Phys 2023; 158:074107. [PMID: 36813724 DOI: 10.1063/5.0138671] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
Linear and nonlinear electronic spectra provide an important tool to probe the absorption and transfer of electronic energy. Here, we introduce a pure state Ehrenfest approach to obtain accurate linear and nonlinear spectra that is applicable to systems with large numbers of excited states and complex chemical environments. We achieve this by representing the initial conditions as sums of pure states and unfolding multi-time correlation functions into the Schrödinger picture. By doing this, we show that one can obtain significant improvements in accuracy over the previously used projected Ehrenfest approach and that these benefits are particularly pronounced in cases where the initial condition is a coherence between excited states. While such initial conditions do not arise when calculating linear electronic spectra, they play a vital role in capturing multidimensional spectroscopies. We demonstrate the performance of our method by showing that it is able to quantitatively capture the exact linear, 2D electronic spectroscopy, and pump-probe spectra for a Frenkel exciton model in slow bath regimes and is even able to reproduce the main spectral features in fast bath regimes.
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Affiliation(s)
- Austin O Atsango
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | | | - Thomas E Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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6
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Sayer T, Montoya-Castillo A. Compact and complete description of non-Markovian dynamics. J Chem Phys 2023; 158:014105. [PMID: 36610963 DOI: 10.1063/5.0132614] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
Generalized master equations provide a theoretically rigorous framework to capture the dynamics of processes ranging from energy harvesting in plants and photovoltaic devices to qubit decoherence in quantum technologies and even protein folding. At their center is the concept of memory. The explicit time-nonlocal description of memory is both protracted and elaborate. When physical intuition is at a premium, one would desire a more compact, yet complete, description. Here, we demonstrate how and when the time-convolutionless formalism constitutes such a description. In particular, by focusing on the dissipative dynamics of the spin-boson and Frenkel exciton models, we show how to: easily construct the time-local generator from reference reduced dynamics, elucidate the dependence of its existence on the system parameters and the choice of reduced observables, identify the physical origin of its apparent divergences, and offer analysis tools to diagnose their severity and circumvent their deleterious effects. We demonstrate that, when applicable, the time-local approach requires as little information as the more commonly used time-nonlocal scheme, with the important advantages of providing a more compact description, greater algorithmic simplicity, and physical interpretability. We conclude by introducing the discrete-time analog and a straightforward protocol to employ it in cases where the reference dynamics have limited resolution. The insights we present here offer the potential for extending the reach of dynamical methods, reducing both their cost and conceptual complexity.
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Affiliation(s)
- Thomas Sayer
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, USA
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7
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Becker T, Schnell A, Thingna J. Canonically Consistent Quantum Master Equation. PHYSICAL REVIEW LETTERS 2022; 129:200403. [PMID: 36461992 DOI: 10.1103/physrevlett.129.200403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2022] [Revised: 08/01/2022] [Accepted: 10/11/2022] [Indexed: 06/17/2023]
Abstract
We put forth a new class of quantum master equations that correctly reproduce the asymptotic state of an open quantum system beyond the infinitesimally weak system-bath coupling limit. Our method is based on incorporating the knowledge of the reduced steady state into its dynamics. The correction not only steers the reduced system toward a correct steady state but also improves the accuracy of the dynamics, thereby refining the archetypal Born-Markov weak-coupling second-order master equations. In case of equilibrium, we use the exact mean-force Gibbs state to correct the Redfield quantum master equation. By benchmarking it with the exact solution of the damped harmonic oscillator, we show that our method also helps correct the long-standing issue of positivity violation, albeit without complete positivity. Our method of a canonically consistent quantum master equation opens a new perspective in the theory of open quantum systems leading to a reduced density matrix accurate beyond the commonly used Redfield and Lindblad equations, while retaining the same conceptual and numerical complexity.
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Affiliation(s)
- Tobias Becker
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - Alexander Schnell
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - Juzar Thingna
- Department of Physics and Applied Physics, University of Massachusetts, Lowell, Massachusetts 01854, USA
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea
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8
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Dodin A, Provazza J, Coker DF, Willard AP. Trajectory Ensemble Methods Provide Single-Molecule Statistics for Quantum Dynamical Systems. J Chem Theory Comput 2022; 18:2047-2061. [PMID: 35230105 DOI: 10.1021/acs.jctc.1c00477] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The emergence of experiments capable of probing quantum dynamics at the single-molecule level requires the development of new theoretical tools capable of simulating and analyzing these dynamics beyond an ensemble-averaged description. In this article, we present an efficient method for sampling and simulating the dynamics of the individual quantum systems that make up an ensemble and apply it to study the nonequilibrium dynamics of the ubiquitous spin-boson model. We generate an ensemble of single-system trajectories, and we analyze this trajectory ensemble using tools from classical statistical mechanics. Our results demonstrate that the dynamics of quantum coherence is highly heterogeneous at the single-system level due to variations in the initial bath configuration, which significantly affects the transient exchange of coherence between the system and its bath. We observe that single systems tend to retain coherence over time scales longer than that of the ensemble. We also compute a novel thermodynamic entanglement entropy that quantifies a thermodynamic driving force favoring system-bath entanglement.
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Affiliation(s)
- Amro Dodin
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Justin Provazza
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States.,Department of Chemistry, Boston University, Boston, Massachusetts 02215, United States
| | - David F Coker
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, United States
| | - Adam P Willard
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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9
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Schlimgen AW, Head-Marsden K, Sager LM, Narang P, Mazziotti DA. Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators. PHYSICAL REVIEW LETTERS 2021; 127:270503. [PMID: 35061424 DOI: 10.1103/physrevlett.127.270503] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2021] [Accepted: 12/03/2021] [Indexed: 06/14/2023]
Abstract
Electron transport in realistic physical and chemical systems often involves the nontrivial exchange of energy with a large environment, requiring the definition and treatment of open quantum systems. Because the time evolution of an open quantum system employs a nonunitary operator, the simulation of open quantum systems presents a challenge for universal quantum computers constructed from only unitary operators or gates. Here, we present a general algorithm for implementing the action of any nonunitary operator on an arbitrary state on a quantum device. We show that any quantum operator can be exactly decomposed as a linear combination of at most four unitary operators. We demonstrate this method on a two-level system in both zero and finite temperature amplitude damping channels. The results are in agreement with classical calculations, showing promise in simulating nonunitary operations on intermediate-term and future quantum devices.
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Affiliation(s)
- Anthony W Schlimgen
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - Kade Head-Marsden
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - LeeAnn M Sager
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - Prineha Narang
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - David A Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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10
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Becker T, Wu LN, Eckardt A. Lindbladian approximation beyond ultraweak coupling. Phys Rev E 2021; 104:014110. [PMID: 34412241 DOI: 10.1103/physreve.104.014110] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2020] [Accepted: 06/08/2021] [Indexed: 11/07/2022]
Abstract
Away from equilibrium, the properties of open quantum systems depend on the details of their environment. A microscopic derivation of a master equation (ME) is therefore crucial. Of particular interest are Lindblad-type equations, not only because they provide the most general class of Markovian MEs, but also since they are the starting point for efficient quantum trajectory simulations. Lindblad-type MEs are commonly derived from the Born-Markov-Redfield equation via a rotating-wave approximation (RWA). However the RWA is valid only for ultraweak system-bath coupling and often fails to accurately describe nonequilibrium processes. Here we derive an alternative Lindbladian approximation to the Redfield equation, which does not rely on ultraweak system-bath coupling. Applying it to an extended Hubbard model coupled to Ohmic baths, we show that, especially away from equilibrium, it provides a good approximation in large parameter regimes where the RWA fails.
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Affiliation(s)
- Tobias Becker
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Ling-Na Wu
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - André Eckardt
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
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11
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Arsenault EA, Schile AJ, Limmer DT, Fleming GR. Vibronic coupling in energy transfer dynamics and two-dimensional electronic-vibrational spectra. J Chem Phys 2021; 155:054201. [PMID: 34364357 DOI: 10.1063/5.0056477] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
We introduce a heterodimer model in which multiple mechanisms of vibronic coupling and their impact on energy transfer can be explicitly studied. We consider vibronic coupling that arises through either Franck-Condon activity in which each site in the heterodimer has a local electron-phonon coupling or Herzberg-Teller activity in which the transition dipole moment coupling the sites has an explicit vibrational mode-dependence. We have computed two-dimensional electronic-vibrational (2DEV) spectra for this model while varying the magnitude of these two effects and find that 2DEV spectra contain static and dynamic signatures of both types of vibronic coupling. Franck-Condon activity emerges through a change in the observed excitonic structure, while Herzberg-Teller activity is evident in the appearance of significant side-band transitions that mimic the lower-energy excitonic structure. A comparison of quantum beating patterns obtained from analysis of the simulated 2DEV spectra shows that this technique can report on the mechanism of energy transfer, elucidating a means of experimentally determining the role of specific vibronic coupling mechanisms in such processes.
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Affiliation(s)
- Eric A Arsenault
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Addison J Schile
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - David T Limmer
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Graham R Fleming
- Department of Chemistry, University of California, Berkeley, California 94720, USA
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12
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Castellanos MA, Willard AP. Designing excitonic circuits for the Deutsch-Jozsa algorithm: mitigating fidelity loss by merging gate operations. Phys Chem Chem Phys 2021; 23:15196-15208. [PMID: 34231586 DOI: 10.1039/d1cp01643a] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this manuscript, we examine design strategies for the development of excitonic circuits that are capable of performing simple 2-qubit multi-step quantum algorithms. Specifically, we compare two different strategies for designing dye-based systems that prescribe exciton evolution encoding a particular quantum algorithm. A serial strategy implements the computation as a step-by-step series of circuits, with each carrying out a single operation of the quantum algorithm, and a combined strategy implements the entire computation in a single circuit. We apply these two approaches to the well-studied Deutsch-Jozsa algorithm and evaluate circuit fidelity in an idealized system under a model harmonic bath, and also for a bath that is parameterized to reflect the thermal fluctuations of an explicit molecular environment. We find that the combined strategy tends to yield higher fidelity and that the harmonic bath approximation leads to lower fidelity than a model molecular bath. These results imply that the programming of excitonic circuits for quantum computation should favor hard-coded modules that incorporate multiple algorithmic steps and should represent the molecular nature of the circuit environment.
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Affiliation(s)
- Maria A Castellanos
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA, USA.
| | - Adam P Willard
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA, USA.
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13
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Abstract
We introduce a simple and effective method to decompose the energy dissipation in the dynamics of open quantum systems into contributions due to individual bath components. The method is based on a vibronic extension of the Förster resonance energy transfer theory that enables quantifying the energy dissipated by specific bath degrees of freedom. Its accuracy is determined by benchmarking against mixed quantum-classical simulations that reveal that the method provides a semi-quantitative frequency-dependent decomposition of the overall dissipation. The utility of the method is illustrated by using a model donor-acceptor pair interacting to a thermal harmonic bath with different coupling strengths. The method can be used to identify the key features of a bath that leads to energy dissipation as required to develop a deep understanding of the dynamics of open quantum systems and to engineer environments with desired dissipative features.
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Affiliation(s)
- Chang Woo Kim
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
| | - Ignacio Franco
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
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14
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Head-Marsden K, Flick J, Ciccarino CJ, Narang P. Quantum Information and Algorithms for Correlated Quantum Matter. Chem Rev 2020; 121:3061-3120. [PMID: 33326218 DOI: 10.1021/acs.chemrev.0c00620] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Discoveries in quantum materials, which are characterized by the strongly quantum-mechanical nature of electrons and atoms, have revealed exotic properties that arise from correlations. It is the promise of quantum materials for quantum information science superimposed with the potential of new computational quantum algorithms to discover new quantum materials that inspires this Review. We anticipate that quantum materials to be discovered and developed in the next years will transform the areas of quantum information processing including communication, storage, and computing. Simultaneously, efforts toward developing new quantum algorithmic approaches for quantum simulation and advanced calculation methods for many-body quantum systems enable major advances toward functional quantum materials and their deployment. The advent of quantum computing brings new possibilities for eliminating the exponential complexity that has stymied simulation of correlated quantum systems on high-performance classical computers. Here, we review new algorithms and computational approaches to predict and understand the behavior of correlated quantum matter. The strongly interdisciplinary nature of the topics covered necessitates a common language to integrate ideas from these fields. We aim to provide this common language while weaving together fields across electronic structure theory, quantum electrodynamics, algorithm design, and open quantum systems. Our Review is timely in presenting the state-of-the-art in the field toward algorithms with nonexponential complexity for correlated quantum matter with applications in grand-challenge problems. Looking to the future, at the intersection of quantum information science and algorithms for correlated quantum matter, we envision seminal advances in predicting many-body quantum states and describing excitonic quantum matter and large-scale entangled states, a better understanding of high-temperature superconductivity, and quantifying open quantum system dynamics.
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Affiliation(s)
- Kade Head-Marsden
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Johannes Flick
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
| | - Christopher J Ciccarino
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States.,Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Prineha Narang
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
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15
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Xie X, Zhang C, Ma H. Charge transfer via deep hole in the J51/N2200 blend. J Chem Phys 2020; 153:054705. [PMID: 32770906 DOI: 10.1063/5.0013466] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Abstract
In recently developed non-fullerene acceptor (NFA) based organic solar cells (OSCs), both the donor and acceptor parts can be excited by absorbing light photons. Therefore, both the electron transfer and hole transfer channels could occur at the donor/acceptor interface for generating free charge carriers in NFA based OSCs. However, in many molecular and DNA systems, recent studies revealed that the high charge transfer (CT) efficiency cannot be reasonably explained by a CT model with only highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of donor and acceptor molecules. In this work, taking an example of a full-polymer blend consisting of benzodithiophene-alt-benzotriazole copolymers (J51) as donor and naphthalene diimide-bithiophene (N2200) as acceptor, in which the ultrafast hole transfer has been recently reported, we investigate its CT process and examine the different roles of various frontier molecular orbitals (FMOs). Through a joint study of quantum mechanics electronic structure calculation and nonadiabatic dynamics simulation, we find that the hole transfer between HOMOs of J51 and N2200 can hardly happen, but the hole transfer from HOMO of N2200 to HOMO - 1 of J51 is much more efficient. This points out the underlying importance of the deep hole channel in the CT process and indicates that including FMOs other than HOMOs and LUMOs is highly necessary to build a robust physical model for studying the CT process in molecular optoelectronic materials.
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Affiliation(s)
- Xiaoyu Xie
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | - Chunfeng Zhang
- National Laboratory of Solid State Microstructures, School of Physics, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Haibo Ma
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
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16
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Ueno S, Tanimura Y. Modeling Intermolecular and Intramolecular Modes of Liquid Water Using Multiple Heat Baths: Machine Learning Approach. J Chem Theory Comput 2020; 16:2099-2108. [DOI: 10.1021/acs.jctc.9b01288] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Seiji Ueno
- HPC Systems Inc., Nakagyoku, Kyoto 604, Japan
- Department of Chemistry, Kyoto University, Kyoto 606-8502, Japan
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17
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Dodin A, Willard AP. State space distribution and dynamical flow for closed and open quantum systems. J Chem Phys 2019. [DOI: 10.1063/1.5100736] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Affiliation(s)
- Amro Dodin
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Adam P. Willard
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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18
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Jang SJ. Fourth order expressions for the electronic absorption lineshape of molecular excitons. J Chem Phys 2019; 151:044110. [DOI: 10.1063/1.5100986] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Seogjoo J. Jang
- Department of Chemistry and Biochemistry, Queens College, City University of New York, 65-30 Kissena Boulevard, Queens, New York 11367, USA and Ph.D. Programs in Chemistry and Physics, and Initiative for Theoretical Sciences, Graduate Center, City University of New York, 365 Fifth Avenue, New York, New York 10016, USA
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19
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Head-Marsden K, Mazziotti DA. Satisfying fermionic statistics in the modeling of non-Markovian dynamics with one-electron reduced density matrices. J Chem Phys 2019; 151:034111. [PMID: 31325953 DOI: 10.1063/1.5100143] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Treatment of Markovian, many-electron dynamics from the solution of the Lindblad equation for the 1-electron reduced density matrix requires additional constraints on the bath operators to maintain fermion statistics. Recently, we generalized Lindblad's formalism to non-Markovian dynamics through an ensemble of Lindbladian trajectories. Here we show that the fermion statistics of non-Markovian dynamics can be enforced through analogous constraints on the bath operators of each Lindbladian trajectory in the ensemble. To illustrate, we apply the non-Markovian method to three distinct systems of two fermions in three levels. While the electrons violate the fermion statistics without the constraints, correct fermion behavior is recovered with the constraints.
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Affiliation(s)
- Kade Head-Marsden
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - David A Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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20
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Schile AJ, Limmer DT. Simulating conical intersection dynamics in the condensed phase with hybrid quantum master equations. J Chem Phys 2019; 151:014106. [DOI: 10.1063/1.5106379] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Addison J. Schile
- Department of Chemistry, University of California, Berkeley, California 94720-1460, USA
- Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720-1460, USA
| | - David T. Limmer
- Department of Chemistry, University of California, Berkeley, California 94720-1460, USA
- Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720-1460, USA
- Kavli Energy NanoSciences Institute, University of California, Berkeley, California 94720-1460, USA
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21
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Wang S, Scholes GD, Hsu LY. Quantum dynamics of a molecular emitter strongly coupled with surface plasmon polaritons: A macroscopic quantum electrodynamics approach. J Chem Phys 2019; 151:014105. [DOI: 10.1063/1.5100014] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Siwei Wang
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
| | - Gregory D. Scholes
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | - Liang-Yan Hsu
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
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22
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Teh HH, Jin BY, Cheng YC. Frozen-mode small polaron quantum master equation with variational bound for excitation energy transfer in molecular aggregates. J Chem Phys 2019; 150:224110. [DOI: 10.1063/1.5096287] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Hung-Hsuan Teh
- Department of Chemistry, National Taiwan University, Taipei City 10617, Taiwan
| | - Bih-Yaw Jin
- Department of Chemistry, National Taiwan University, Taipei City 10617, Taiwan
| | - Yuan-Chung Cheng
- Department of Chemistry, National Taiwan University, Taipei City 10617, Taiwan
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23
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Dodin A, Brumer P. Light-induced processes in nature: Coherences in the establishment of the nonequilibrium steady state in model retinal isomerization. J Chem Phys 2019; 150:184304. [DOI: 10.1063/1.5092981] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Amro Dodin
- Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Paul Brumer
- Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada
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24
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Xie X, Santana-Bonilla A, Fang W, Liu C, Troisi A, Ma H. Exciton–Phonon Interaction Model for Singlet Fission in Prototypical Molecular Crystals. J Chem Theory Comput 2019; 15:3721-3729. [DOI: 10.1021/acs.jctc.9b00122] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Xiaoyu Xie
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | | | - Weihai Fang
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
- Department of Chemistry, Beijing Normal University, Beijing, 100875, China
| | - Chungen Liu
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | - Alessandro Troisi
- Department of Chemistry, University of Liverpool, Liverpool L69 3BX, United Kingdom
| | - Haibo Ma
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
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25
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Kim CW, Lee WG, Kim I, Rhee YM. Effect of Underdamped Vibration on Excitation Energy Transfer: Direct Comparison between Two Different Partitioning Schemes. J Phys Chem A 2019; 123:1186-1197. [DOI: 10.1021/acs.jpca.8b10977] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- Chang Woo Kim
- Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea
| | - Weon-Gyu Lee
- Department of Chemistry, Sungkyunkwan University, Suwon 16419, Korea
| | - Inkoo Kim
- Samsung Advanced Institute of Technology, Samsung Electronics, 130 Samsung-ro, Yeongtong-gu, Suwon 16678, Korea
| | - Young Min Rhee
- Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea
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26
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Schile AJ, Limmer DT. Studying rare nonadiabatic dynamics with transition path sampling quantum jump trajectories. J Chem Phys 2018; 149:214109. [DOI: 10.1063/1.5058281] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Addison J. Schile
- Department of Chemistry, University of California, Berkeley, California 94618, USA
- Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94618, USA
| | - David T. Limmer
- Department of Chemistry, University of California, Berkeley, California 94618, USA
- Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94618, USA
- Kavli Energy NanoSciences Institute, University of California, Berkeley, California 94618, USA
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27
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Liu YY, Yan YM, Xu M, Song K, Shi Q. Exact generator and its high order expansions in time-convolutionless generalized master equation: Applications to spin-boson model and excitation energy transfer. CHINESE J CHEM PHYS 2018. [DOI: 10.1063/1674-0068/31/cjcp1806146] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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28
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Tempelaar R, Reichman DR. Vibronic exciton theory of singlet fission. III. How vibronic coupling and thermodynamics promote rapid triplet generation in pentacene crystals. J Chem Phys 2018; 148:244701. [DOI: 10.1063/1.5031778] [Citation(s) in RCA: 55] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Roel Tempelaar
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - David R. Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
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29
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Fetherolf JH, Berkelbach TC. Linear and nonlinear spectroscopy from quantum master equations. J Chem Phys 2018; 147:244109. [PMID: 29289132 DOI: 10.1063/1.5006824] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the accuracy of the second-order time-convolutionless (TCL2) quantum master equation for the calculation of linear and nonlinear spectroscopies of multichromophore systems. We show that even for systems with non-adiabatic coupling, the TCL2 master equation predicts linear absorption spectra that are accurate over an extremely broad range of parameters and well beyond what would be expected based on the perturbative nature of the approach; non-equilibrium population dynamics calculated with TCL2 for identical parameters are significantly less accurate. For third-order (two-dimensional) spectroscopy, the importance of population dynamics and the violation of the so-called quantum regression theorem degrade the accuracy of TCL2 dynamics. To correct these failures, we combine the TCL2 approach with a classical ensemble sampling of slow microscopic bath degrees of freedom, leading to an efficient hybrid quantum-classical scheme that displays excellent accuracy over a wide range of parameters. In the spectroscopic setting, the success of such a hybrid scheme can be understood through its separate treatment of homogeneous and inhomogeneous broadening. Importantly, the presented approach has the computational scaling of TCL2, with the modest addition of an embarrassingly parallel prefactor associated with ensemble sampling. The presented approach can be understood as a generalized inhomogeneous cumulant expansion technique, capable of treating multilevel systems with non-adiabatic dynamics.
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Affiliation(s)
- Jonathan H Fetherolf
- Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
| | - Timothy C Berkelbach
- Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
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30
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Chen HT, Cohen G, Reichman DR. Inchworm Monte Carlo for exact non-adiabatic dynamics. II. Benchmarks and comparison with established methods. J Chem Phys 2017; 146:054106. [DOI: 10.1063/1.4974329] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Hsing-Ta Chen
- Department of Chemistry, Columbia University, New York, New York 10027, USA
- The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
| | - Guy Cohen
- The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
- School of Chemistry, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
| | - David R. Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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31
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Montoya-Castillo A, Reichman DR. Path integral approach to the Wigner representation of canonical density operators for discrete systems coupled to harmonic baths. J Chem Phys 2017; 146:024107. [DOI: 10.1063/1.4973646] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - David R. Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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32
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Chen HT, Berkelbach TC, Reichman DR. On the accuracy of the Padé-resummed master equation approach to dissipative quantum dynamics. J Chem Phys 2016; 144:154106. [DOI: 10.1063/1.4946809] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Hsing-Ta Chen
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - Timothy C. Berkelbach
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
| | - David R. Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
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