1
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Makri N. Discrete Generalized Quantum Master Equations. J Chem Theory Comput 2025; 21:5037-5048. [PMID: 40326041 DOI: 10.1021/acs.jctc.5c00396] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/07/2025]
Abstract
Several derivative and integral approximations are explored for discretizing the Nakajima-Zwanzig generalized quantum master equation (NZ-QME or GQME) to obtain discrete quantum master equation (DQME) hierarchies and relations between discrete memory kernel and reduced density matrix (RDM) elements. It is shown that the simplest forward-difference approximation does not allow the reliable determination of the discrete kernel elements, even in the infinitesimal time-step limit, and that discrete kernels obtained in earlier work are flawed, although the procedure can be remedied. The various approximations give rise to DQMEs that differ in structure and in the RDM-kernel relationships. It is shown that the use of a more accurate discretization based on the midpoint derivative and midpoint integral approximations leads to a DQME that exhibits endpoint effects, which reflect the weaker impact of the bath on the RDM during the first time step and which parallel those encountered in the small matrix decomposition of the path integral (SMatPI) with a symmetric factorization of the short-time propagator. The features of the DQME hierarchies and RDM-kernel relations are illustrated through analytical examples involving a simple integrodifferential equation and a scalar GQME model, as well as numerical results for a two-level system (TLS) coupled to a harmonic bath.
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Affiliation(s)
- Nancy Makri
- Department of Chemistry, Department of Physics, and Illinois Quantum Information Science and Technology Center, University of Illinois, Urbana, Illinois 61801, United States
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2
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Seneviratne A, Walters PL, Wang F. Quantum algorithm for the simulation of non-Markovian quantum dynamics using Feynman-Vernon influence functional. J Chem Phys 2025; 162:194101. [PMID: 40371828 DOI: 10.1063/5.0258227] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2025] [Accepted: 04/28/2025] [Indexed: 05/16/2025] Open
Abstract
In this work, we developed a quantum algorithm for the simulation of non-Markovian quantum dynamics based on the Feynman-Vernon's path integral formulation. The algorithm performs the full path sum and proves to be polynomial either in time or in space, compared to the same classical algorithm, which is exponential in time. In addition, the algorithm has no classical overhead and is equally applicable regardless of whether the temporal entanglement due to non-Markovianity is low or high, making it a unified framework for simulating non-Markovian dynamics in open quantum systems.
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Affiliation(s)
- Avin Seneviratne
- Department of Physics and Astronomy, George Mason University, 4400 University Drive, Fairfax, Virginia 22030, USA
| | - Peter L Walters
- Department of Chemistry and Biochemistry, George Mason University, 4400 University Drive, Fairfax, Virginia 22030, USA
| | - Fei Wang
- Department of Chemistry and Biochemistry, George Mason University, 4400 University Drive, Fairfax, Virginia 22030, USA
- Quantum Science and Engineering Center, George Mason University, 4400 University Drive, Fairfax, Virginia 22030, USA
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3
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Uthailiang T, Suntijitrungruang O, Issarakul P, Pongkitiwanichakul P, Boonchui S. Investigation of quantum trajectories in photosynthetic light harvesting through a quantum stochastic approach. Sci Rep 2025; 15:5220. [PMID: 39939706 PMCID: PMC11822076 DOI: 10.1038/s41598-025-89474-3] [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: 09/17/2024] [Accepted: 02/05/2025] [Indexed: 02/14/2025] Open
Abstract
In natural photosynthesis systems, pigment-protein complexes harvest the photon from sunlight with near-unity quantum efficiency. These complexes show incredible properties that cannot be merely extrapolated from knowledge of their composition. Additionally, the environment perturbing the light-harvesting process significantly affects the mechanism of photosynthesis. This research investigates the photosystem II reaction center (PSII RC) from a new perspective which considers the restricted path of the exciton transfer, in the photosynthesis system, as a quantum trajectory picture with the quantum continuous measurement. In this work, the corridor path of exciton transfer dynamics satisfies the equation of motion, as the spin dynamics, which consists of precession, relaxation, and random force rapidly fluctuating spin splitting arising from the bath. Moreover, the width of the corridor is an important factor for restricting path dynamics resulting in the localization and decoherence phenomenon. Our method is to analyze exciton transfer dynamics through paths on the Bloch sphere, in order to investigate the propagating states in accordance with the weight functional which depends on the coupling parameter between the system and environment as the phonon bath. Our results show that the paths outside the width of the corridor have a considerably lower weight functional and decoherence functional than those inside the width. Therefore, the degrees of localization, the weight functional, and the decoherence functional are related. Furthermore, the simulation reveals three characteristics of exciton transfer: gradual transfer, no transfer, and rapid transfer, relying significantly on the coupling between the system and phonons.
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Affiliation(s)
- Teerapat Uthailiang
- Department of Physics, Faculty of Science, Kasetsart University, Bangkok, 10900, Thailand
| | | | - Purin Issarakul
- Department of Physics, Faculty of Science, Kasetsart University, Bangkok, 10900, Thailand
| | | | - S Boonchui
- Department of Physics, Faculty of Science, Kasetsart University, Bangkok, 10900, Thailand.
- Center of Rubber and Polymer Materials in Agriculture and Industry (RPM), Faculty of Science, Kasetsart University, Bangkok, 10900, Thailand.
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4
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Walters P, Sherazi MU, Wang F. Variational Quantum Algorithm for Non-Markovian Quantum Dynamics Using an Ensemble of Ehrenfest Trajectories. J Phys Chem Lett 2025; 16:1001-1006. [PMID: 39840760 PMCID: PMC11789130 DOI: 10.1021/acs.jpclett.4c03431] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2024] [Revised: 01/08/2025] [Accepted: 01/16/2025] [Indexed: 01/23/2025]
Abstract
The simulation of non-Markovian quantum dynamics plays an important role in the understanding of charge and exciton dynamics in the condensed phase environment, yet such a simulation remains computationally expensive on classical computers. In this work, we develop a variational quantum algorithm that is capable of simulating non-Markovian quantum dynamics on quantum computers. The algorithm captures the non-Markovian effect by employing the Ehrenfest trajectories and Monte Carlo sampling of their thermal distribution. We test the algorithm with the spin-boson model on the quantum simulator, and the results match quantitatively with the exact ones. The algorithm naturally fits into the parallel computing platform of the NISQ devices and can be extended to anharmonic system-bath interactions and multistate systems.
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Affiliation(s)
- Peter
L. Walters
- Department
of Chemistry and Biochemistry, George Mason
University, Fairfax, Virginia 22030, United States
| | - Mohammad U. Sherazi
- Department
of Physics and Astronomy, George Mason University, Fairfax, Virginia 22030, United States
| | - Fei Wang
- Department
of Chemistry and Biochemistry, George Mason
University, Fairfax, Virginia 22030, United States
- Quantum
Science and Engineering Center, George Mason
University, Fairfax, Virginia 22030, United States
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5
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Schultz JD, Yuly JL, Arsenault EA, Parker K, Chowdhury SN, Dani R, Kundu S, Nuomin H, Zhang Z, Valdiviezo J, Zhang P, Orcutt K, Jang SJ, Fleming GR, Makri N, Ogilvie JP, Therien MJ, Wasielewski MR, Beratan DN. Coherence in Chemistry: Foundations and Frontiers. Chem Rev 2024; 124:11641-11766. [PMID: 39441172 DOI: 10.1021/acs.chemrev.3c00643] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2024]
Abstract
Coherence refers to correlations in waves. Because matter has a wave-particle nature, it is unsurprising that coherence has deep connections with the most contemporary issues in chemistry research (e.g., energy harvesting, femtosecond spectroscopy, molecular qubits and more). But what does the word "coherence" really mean in the context of molecules and other quantum systems? We provide a review of key concepts, definitions, and methodologies, surrounding coherence phenomena in chemistry, and we describe how the terms "coherence" and "quantum coherence" refer to many different phenomena in chemistry. Moreover, we show how these notions are related to the concept of an interference pattern. Coherence phenomena are indeed complex, and ambiguous definitions may spawn confusion. By describing the many definitions and contexts for coherence in the molecular sciences, we aim to enhance understanding and communication in this broad and active area of chemistry.
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Affiliation(s)
- Jonathan D Schultz
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | - Jonathon L Yuly
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08540, United States
- Department of Physics, Duke University, Durham, North Carolina 27708, United States
| | - Eric A Arsenault
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, United States
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Kelsey Parker
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Sutirtha N Chowdhury
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Reshmi Dani
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, United States
| | - Sohang Kundu
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, United States
| | - Hanggai Nuomin
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Zhendian Zhang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Jesús Valdiviezo
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
- Department of Biological Chemistry and Molecular Pharmacology, Harvard Medical School, Boston, Massachusetts 02115, United States
- Department of Cancer Biology, Dana-Farber Cancer Institute, Boston, Massachusetts 02215, United States
- Sección Química, Departamento de Ciencias, Pontificia Universidad Católica del Perú, San Miguel, Lima 15088, Peru
| | - Peng Zhang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Kaydren Orcutt
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, United States
- Molecular Biophysics and Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Bioproducts Research Unit, Western Regional Research Center, Agricultural Research Service, United States Department of Agriculture, 800 Buchanan Street, Albany, California 94710, United States
| | - Seogjoo J Jang
- Department of Chemistry and Biochemistry, Queens College, City University of New York, Queens, New York 11367, United States
- Chemistry and Physics PhD programs, Graduate Center, City University of New York, New York, New York 10016, United States
| | - Graham R Fleming
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, United States
| | - Nancy Makri
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, United States
- Department of Physics, University of Illinois, Urbana, Illinois 61801, United States
- Illinois Quantum Information Science and Technology Center, University of Illinois, Urbana, Illinois 61801, United States
| | - Jennifer P Ogilvie
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Michael J Therien
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Michael R Wasielewski
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | - David N Beratan
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
- Department of Physics, Duke University, Durham, North Carolina 27708, United States
- Department of Biochemistry, Duke University, Durham, North Carolina 27710, United States
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6
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Malpathak S, Ananth N. Semiclassical dynamics in Wigner phase space II: Nonadiabatic hybrid Wigner dynamics. J Chem Phys 2024; 161:094110. [PMID: 39234964 DOI: 10.1063/5.0223187] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2024] [Accepted: 08/12/2024] [Indexed: 09/06/2024] Open
Abstract
We present an approximate semiclassical (SC) framework for mixed quantized dynamics in Wigner phase space in a two-part series. In the first article, we introduced the Adiabatic Hybrid Wigner Dynamics (AHWD) method that allows for a few important "system" degrees of freedom to be quantized using high-level double Herman-Kluk SC theory while describing the rest (the "bath") using classical-limit linearized SC theory. In this second article, we extend our hybrid Wigner dynamics to nonadiabatic processes. The resulting Nonadiabatic Hybrid Wigner Dynamics (NHWD) has two variants that differ in the choice of degrees of freedom to be quantized. Specifically, we introduce NHWD(E) where only the electronic state variables are quantized and the NHWD(V) where both electronic state variables and a handful of strongly coupled nuclear modes are quantized. We show that while NHWD(E) proves accurate for a wide range of scattering models and spin-boson models, systems where a few nuclear modes are strongly coupled to electronic states require NHWD(V) to accurately capture the long-time dynamics. Taken together, we show that AHWD and NHWD represent a new framework for SC simulations of high-dimensional systems with significant quantum effects.
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Affiliation(s)
- Shreyas Malpathak
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
| | - Nandini Ananth
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
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7
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Liu L, Ren J, Fang W. Improved memory truncation scheme for quasi-adiabatic propagator path integral via influence functional renormalization. J Chem Phys 2024; 161:084101. [PMID: 39171703 DOI: 10.1063/5.0221916] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2024] [Accepted: 08/05/2024] [Indexed: 08/23/2024] Open
Abstract
Accurately simulating non-Markovian quantum dynamics in system-bath coupled problems remains challenging. In this work, we present a novel memory truncation scheme for the iterative quasi-adiabatic propagator path integral (iQuAPI) method to improve accuracy. Conventional memory truncation in iQuAPI discards all influence functional beyond a certain time interval, which is not effective for problems with a long memory time. Our proposed scheme selectively retains the most significant parts of the influence functional using the density matrix renormalization group algorithm. We validate the effectiveness of our scheme through simulations of the spin-boson model across various parameter sets, demonstrating faster convergence and improved accuracy compared to the conventional scheme. Our findings suggest that the new memory truncation scheme significantly advances the capabilities of iQuAPI for problems with a long memory time.
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Affiliation(s)
- Limin Liu
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, 100875 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
| | - Weihai Fang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, 100875 Beijing, People's Republic of China
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8
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Cygorek M, Gauger EM. ACE: A general-purpose non-Markovian open quantum systems simulation toolkit based on process tensors. J Chem Phys 2024; 161:074111. [PMID: 39158046 DOI: 10.1063/5.0221182] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2024] [Accepted: 08/01/2024] [Indexed: 08/20/2024] Open
Abstract
We describe a general-purpose computational toolkit for simulating open quantum systems, which provides numerically exact solutions for composites of zero-dimensional quantum systems that may be strongly coupled to multiple, quite general non-Markovian environments. It is based on process tensor matrix product operators (PT-MPOs), which efficiently encapsulate environment influences. The code features implementations of several PT-MPO algorithms, in particular Automated Compression of Environments for general environments comprised of independent modes as well as schemes for generalized spin boson models. The latter includes a divide-and-conquer scheme for periodic PT-MPOs, which enable million time step simulations for realistic models. PT-MPOs can be precalculated and reused for efficiently probing different time-dependent system Hamiltonians. They can also be stacked together and combined to provide numerically complete solutions of small networks of open quantum systems. The code is written in C++ and is fully controllable by configuration files, for which we have developed a versatile and compact human-readable format.
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Affiliation(s)
- Moritz Cygorek
- Condensed Matter Theory, Department of Physics, TU Dortmund, 44221 Dortmund, Germany
- SUPA, Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Erik M Gauger
- SUPA, Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
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9
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Walters PL, Tsakanikas J, Wang F. An ensemble variational quantum algorithm for non-Markovian quantum dynamics. Phys Chem Chem Phys 2024. [PMID: 39034756 DOI: 10.1039/d4cp01669f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/23/2024]
Abstract
Many physical and chemical processes in a condensed phase environment exhibit non-Markovian quantum dynamics. As such simulations are challenging on classical computers, we developed a variational quantum algorithm that is capable of simulating non-Markovian dynamics on noisy intermediate-scale quantum (NISQ) devices. We used a quantum system linearly coupled to its harmonic bath as the model Hamiltonian. The non-Markovianity is captured by introducing auxiliary variables from the bath trajectories. With Monte Carlo sampling of the bath degrees of freedom, finite temperature dynamics is produced. We validated the algorithm on a simulator and demonstrated its performance on an IBM quantum device. The framework developed naturally adapts to any anharmonic bath with non-linear coupling to the system, and is also well suited for simulating spin chain dynamics in a dissipative environment.
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Affiliation(s)
- Peter L Walters
- Department of Chemistry and Biochemistry, George Mason University, Fairfax, Virginia 22030, USA.
| | - Joachim Tsakanikas
- Department of Physics and Astronomy, George Mason University, Fairfax, Virginia 22030, USA
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
| | - Fei Wang
- Department of Chemistry and Biochemistry, George Mason University, Fairfax, Virginia 22030, USA.
- Quantum Science and Engineering Center, George Mason University, Fairfax, Virginia 22030, USA
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10
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Dietert RR, Dietert JM. Examining Sound, Light, and Vibrations as Tools to Manage Microbes and Support Holobionts, Ecosystems, and Technologies. Microorganisms 2024; 12:905. [PMID: 38792734 PMCID: PMC11123986 DOI: 10.3390/microorganisms12050905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2024] [Revised: 04/27/2024] [Accepted: 04/28/2024] [Indexed: 05/26/2024] Open
Abstract
The vast array of interconnected microorganisms across Earth's ecosystems and within holobionts has been called the "Internet of Microbes." Bacteria and archaea are masters of energy and information collection, storage, transformation, and dissemination using both "wired" and wireless (at a distance) functions. Specific tools affecting microbial energy and information functions offer effective strategies for managing microbial populations within, between, and beyond holobionts. This narrative review focuses on microbial management using a subset of physical modifiers of microbes: sound and light (as well as related vibrations). These are examined as follows: (1) as tools for managing microbial populations, (2) as tools to support new technologies, (3) as tools for healing humans and other holobionts, and (4) as potential safety dangers for microbial populations and their holobionts. Given microbial sensitivity to sound, light, and vibrations, it is critical that we assign a higher priority to the effects of these physical factors on microbial populations and microbe-laden holobionts. We conclude that specific sound, light, and/or vibrational conditions are significant therapeutic tools that can help support useful microbial populations and help to address the ongoing challenges of holobiont disease. We also caution that inappropriate sound, light, and/or vibration exposure can represent significant hazards that require greater recognition.
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Affiliation(s)
- Rodney R. Dietert
- Department of Microbiology and Immunology, Cornell University, Ithaca, NY 14853, USA
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11
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Zhang C, Kundu S, Makri N, Gruebele M, Wolynes PG. Quantum information scrambling and chemical reactions. Proc Natl Acad Sci U S A 2024; 121:e2321668121. [PMID: 38557180 PMCID: PMC11009637 DOI: 10.1073/pnas.2321668121] [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: 12/08/2023] [Accepted: 02/22/2024] [Indexed: 04/04/2024] Open
Abstract
The ultimate regularity of quantum mechanics creates a tension with the assumption of classical chaos used in many of our pictures of chemical reaction dynamics. Out-of-time-order correlators (OTOCs) provide a quantum analog to the Lyapunov exponents that characterize classical chaotic motion. Maldacena, Shenker, and Stanford have suggested a fundamental quantum bound for the rate of information scrambling, which resembles a limit suggested by Herzfeld for chemical reaction rates. Here, we use OTOCs to study model reactions based on a double-well reaction coordinate coupled to anharmonic oscillators or to a continuum oscillator bath. Upon cooling, as one enters the tunneling regime where the reaction rate does not strongly depend on temperature, the quantum Lyapunov exponent can approach the scrambling bound and the effective reaction rate obtained from a population correlation function can approach the Herzfeld limit on reaction rates: Tunneling increases scrambling by expanding the state space available to the system. The coupling of a dissipative continuum bath to the reaction coordinate reduces the scrambling rate obtained from the early-time OTOC, thus making the scrambling bound harder to reach, in the same way that friction is known to lower the temperature at which thermally activated barrier crossing goes over to the low-temperature activationless tunneling regime. Thus, chemical reactions entering the tunneling regime can be information scramblers as powerful as the black holes to which the quantum Lyapunov exponent bound has usually been applied.
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Affiliation(s)
- Chenghao Zhang
- Department of Physics, University of Illinois Urbana-Champaign, IL61801
| | - Sohang Kundu
- Department of Chemistry, University of Illinois Urbana-Champaign, IL61801
| | - Nancy Makri
- Department of Physics, University of Illinois Urbana-Champaign, IL61801
- Department of Chemistry, University of Illinois Urbana-Champaign, IL61801
| | - Martin Gruebele
- Department of Physics, University of Illinois Urbana-Champaign, IL61801
- Department of Chemistry, University of Illinois Urbana-Champaign, IL61801
- Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, IL61801
- Carle-Illinois College of Medicine, University of Illinois at Urbana-Champaign, IL61801
| | - Peter G. Wolynes
- Department of Chemistry, Rice University, Houston, TX77251
- Department Physics, Rice University, Houston, TX77251
- Center for Theoretical Biological Physics, Rice University, Houston, TX77251
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12
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Makri N. Kink Sum for Long-Memory Small Matrix Path Integral Dynamics. J Phys Chem B 2024. [PMID: 38437738 DOI: 10.1021/acs.jpcb.3c08282] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/06/2024]
Abstract
The small matrix decomposition of the real-time path integral (SMatPI) allows for numerically exact and efficient propagation of the reduced density matrix (RDM) for system-bath Hamiltonians. Its high efficiency lies in the small size of the SMatPI matrices employed in the iterative algorithm, whose size is equal to that of the full RDM. By avoiding the storage and multiplication of large tensors, the SMatPI algorithm is applicable in multistate systems under a variety of conditions. The main computational effort is the evaluation of path sums within the entangled memory length to construct the SMatPI matrices. A number of methods are available for this task, each with its own favorable parameter regime, but calculations with strong system-bath coupling and long memory at low temperatures remain out of reach. The present paper evaluates the path sums by binning the paths (in forward time only) based on their amplitudes, which depend on the number and type of kinks they contain. The algorithm is very efficient, leading to a dramatic acceleration of path sums and significantly extending the accessible memory length in the most challenging regimes.
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Affiliation(s)
- Nancy Makri
- Departments of Chemistry and Physics, University of Illinois, 505 S. Mathews Avenue, Urbana, Illinois 61801, United States
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13
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Seneviratne A, Walters PL, Wang F. Exact Non-Markovian Quantum Dynamics on the NISQ Device Using Kraus Operators. ACS OMEGA 2024; 9:9666-9675. [PMID: 38434817 PMCID: PMC10906042 DOI: 10.1021/acsomega.3c09720] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/05/2023] [Revised: 01/18/2024] [Accepted: 01/23/2024] [Indexed: 03/05/2024]
Abstract
The theory of open quantum systems has many applications ranging from simulating quantum dynamics in condensed phases to better understanding quantum-enabled technologies. At the center of theoretical chemistry are the developments of methodologies and computational tools for simulating charge and excitation energy transfer in solutions, biomolecules, and molecular aggregates. As a variety of these processes display non-Markovian behavior, classical computer simulation can be challenging due to exponential scaling with existing methods. With quantum computers holding the promise of efficient quantum simulations, in this paper, we present a new quantum algorithm based on Kraus operators that capture the exact non-Markovian effect at a finite temperature. The implementation of the Kraus operators on the quantum machine uses a combination of singular value decomposition (SVD) and optimal Walsh operators that result in shallow circuits. We demonstrate the feasibility of the algorithm by simulating the spin-boson dynamics and the exciton transfer in the Fenna-Matthews-Olson (FMO) complex. The NISQ results show very good agreement with the exact ones.
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Affiliation(s)
- Avin Seneviratne
- Department
of Physics and Astronomy, George Mason University, 4400 University Drive, Fairfax, Virginia 22030, United States
| | - Peter L. Walters
- Department
of Chemistry and Biochemistry, George Mason
University, 4400 University
Drive, Fairfax, Virginia 22030, United States
| | - Fei Wang
- Department
of Chemistry and Biochemistry, George Mason
University, 4400 University
Drive, Fairfax, Virginia 22030, United States
- Quantum
Science and Engineering Center, George Mason
University, 4400 University
Drive, Fairfax, Virginia 22030, United States
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14
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Bose A, Walters PL. Impact of Spatial Inhomogeneity on Excitation Energy Transport in the Fenna-Matthews-Olson Complex. J Phys Chem B 2023; 127:7663-7673. [PMID: 37647510 DOI: 10.1021/acs.jpcb.3c03062] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
Abstract
The dynamics of the excitation energy transfer (EET) in photosynthetic complexes is an interesting question both from the perspective of fundamental understanding and the research in artificial photosynthesis. Over the past decade, very accurate spectral densities have been developed to capture spatial inhomogeneities in the Fenna-Matthews-Olson (FMO) complex. However, challenges persist in numerically simulating these systems, both in terms of parameterizing them and following their dynamics over long periods of time because of long non-Markovian memories. We investigate the dynamics of FMO with the exact treatment of various theoretical spectral densities using the new tensor network path integral-based methods, which are uniquely capable of addressing the difficulty of long memory length and incoherent Förster theory. It is also important to be able to analyze the pathway of EET flow, which can be difficult to identify given the non-trivial structure of connections between bacteriochlorophyll molecules in FMO. We use the recently introduced ideas of relating coherence to population derivatives to analyze the transport process and reveal some new routes of transport. The combination of exact and approximate methods sheds light on the role of coherences in affecting the fine details of the transport and promises to be a powerful toolbox for future exploration of other open systems with quantum transport.
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Affiliation(s)
- Amartya Bose
- Department of Chemical Sciences, Tata Institute of Fundamental Research, Mumbai 400005, India
| | - Peter L Walters
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Miller Institute for Basic Research in Science, University of California Berkeley, Berkeley, California 94720, United States
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15
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Dani R, Kundu S, Makri N. Coherence Maps and Flow of Excitation Energy in the Bacterial Light Harvesting Complex 2. J Phys Chem Lett 2023; 14:3835-3843. [PMID: 37067041 DOI: 10.1021/acs.jpclett.3c00670] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/19/2023]
Abstract
We present and analyze coherence maps [ J. Phys. Chem. B 2022, 126, 9361-9375] to investigate the quantum coherences that are created, sustained, and damped by vibrational modes during the transfer of excitation energy from the B800 (outer) to the B850 (inner) ring of the light harvesting complex 2 (LH2) of purple bacteria with a variety of initial conditions. The reduced density matrix of the 24-pigment complex, where the ground and excited electronic states of each bacteriochlorophyll are explicitly coupled to 50 intramolecular vibrations at room temperature, is obtained from fully quantum-mechanical small matrix path integral (SMatPI) calculations. The coherence maps show a very rapid localization within the outer ring, accompanied by the formation of inter-ring quantum superpositions that evolve to a partial quantum delocalization at equilibrium, and quantify in state-to-state detail the flow of energy within the complex.
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Affiliation(s)
- Reshmi Dani
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, United States
| | - Sohang Kundu
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, United States
| | - Nancy Makri
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, United States
- Department of Physics, University of Illinois, Urbana, Illinois 61801, United States
- Illinois Quantum Information Science and Technology Center, University of Illinois, Urbana, Illinois 61801, United States
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