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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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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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3
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Abstract
The quantum-classical path integral (QCPI) is a rigorous formulation of nonadiabatic dynamics, where the dynamical interaction between a quantum system and its environment is captured consistently through classical trajectories driven by forces along quantum paths of the system. In this Letter, we develop a small matrix decomposition (SMatQCPI) that eliminates the tensor storage requirements of the iterative QCPI algorithm. In the case of a system coupled to a harmonic bath, SMatQCPI provides fully quantum mechanical propagation, which also reduces the computational cost to that of a single QCPI step. Further, the SMatQCPI matrices only need to account for quantum contributions to decoherence, allowing high efficiency in challenging regimes of incoherent dynamics. Overall, this new composite algorithm combines the best features of two powerful path integral formulations and offers a versatile tool for simulating condensed phase quantum dynamics.
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Affiliation(s)
- 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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Kundu S, Makri N. Intramolecular Vibrations in Excitation Energy Transfer: Insights from Real-Time Path Integral Calculations. Annu Rev Phys Chem 2022; 73:349-375. [PMID: 35081322 DOI: 10.1146/annurev-physchem-090419-120202] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Excitation energy transfer (EET) is fundamental to many processes in chemical and biological systems and carries significant implications for the design of materials suitable for efficient solar energy harvest and transport. This review discusses the role of intramolecular vibrations on the dynamics of EET in nonbonded molecular aggregates of bacteriochlorophyll, a perylene bisimide, and a model system, based on insights obtained from fully quantum mechanical real-time path integral results for a Frenkel exciton Hamiltonian that includes all vibrational modes of each molecular unit at finite temperature. Generic trends, as well as features specific to the vibrational characteristics of the molecules, are identified. Weak exciton-vibration (EV) interaction leads to compact, near-Gaussian densities on each electronic state, whose peak follows primarily a classical trajectory on a torus, while noncompact densities and nonlinear peak evolution are observed with strong EV coupling. Interaction with many intramolecular modes and increasing aggregate size smear, shift, and damp these dynamical features. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
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Affiliation(s)
- Sohang Kundu
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA;
| | - Nancy Makri
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA; .,Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA
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Chatterjee S, Makri N. Density matrix and purity evolution in dissipative two-level systems: I. Theory and path integral results for tunneling dynamics. Phys Chem Chem Phys 2021; 23:5113-5124. [PMID: 33623944 DOI: 10.1039/d0cp05527a] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
The time evolution of the purity (the trace of the square of the reduced density matrix) and von Neumann entropy in a symmetric two-level system coupled to a dissipative harmonic bath is investigated through analytical arguments and accurate path integral calculations on simple models and the singly excited bacteriochlorophyll dimer. A simple theoretical analysis establishes bounds and limiting behaviors. The contributions to purity from a purely incoherent term obtained from the diagonal elements of the reduced density matrix, a term associated with the difference of the two eigenstate populations, and a third term related to the square of the time derivative of a site population, are discussed in various regimes. In the case of tunneling dynamics from a localized initial condition, the complex interplay among these contributions leads to the recovery of purity under low-temperature, weakly dissipative conditions. Memory effects from the bath are found to play a critical role to the dynamics of purity. It is shown that the strictly quantum mechanical decoherence process associated with spontaneous phonon emission is responsible for the long-time recovery of purity. These analytical and numerical results show clearly that the loss of quantum coherence during the evolution toward equilibrium does not necessarily imply the decay of purity, and that the time scales relevant to these two processes may be entirely different.
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Affiliation(s)
| | - Nancy Makri
- Department of Chemistry, University of Illinois, Urbana, IL 61801, USA. and Department of Physics, University of Illinois, Urbana, IL 61801, USA
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Nava M, Makri N. Quantum-Classical Path Integral Simulation of Excess Proton Dynamics in a Water Dimer Embedded in the Gramicidin Channel. J Chem Theory Comput 2021; 17:627-638. [PMID: 33494606 DOI: 10.1021/acs.jctc.0c01012] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We use the quantum-classical path integral (QCPI) methodology to investigate the relaxation dynamics of an excess proton that has been inserted in a water dimer embedded in the gramicidin A channel at room temperature. We obtain one-dimensional potential slices for the quantum degree of freedom through a proper transformation to internal coordinates. Our results indicate that the proton transfer is driven by the oscillation of the oxygen pair, and that the transfer occurs primarily at single-well or nearby low-barrier configurations. Yet, we find that tunneling and zero-point energy lead to a significant acceleration of the proton transfer dynamics.
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Affiliation(s)
- Marco Nava
- Department of Chemistry, University of Illinois, 505 South Mathews Avenue, Urbana, Illinois 61801, United States
| | - Nancy Makri
- Department of Chemistry, University of Illinois, 505 South Mathews Avenue, Urbana, Illinois 61801, United States
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Bose A, Makri N. All-Mode Quantum–Classical Path Integral Simulation of Bacteriochlorophyll Dimer Exciton-Vibration Dynamics. J Phys Chem B 2020; 124:5028-5038. [DOI: 10.1021/acs.jpcb.0c03032] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Affiliation(s)
- Amartya Bose
- 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
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