Efficient quantum simulation of open quantum dynamics at various Hamiltonians and spectral densities

Abstract

Simulation of open quantum dynamics for various Hamiltonians and spectral densities are ubiquitous for studying various quantum systems. On a quantum computer, only log₂N qubits are required for the simulation of an N-dimensional quantum system, hence simulation in a quantum computer can greatly reduce the computational complexity compared with classical methods. Recently, a quantum simulation approach was proposed for studying photosynthetic light harvesting [npj Quantum Inf. 4, 52 (2018)]. In this paper, we apply the approach to simulate the open quantum dynamics of various photosynthetic systems. We show that for Drude–Lorentz spectral density, the dimerized geometries with strong couplings within the donor and acceptor clusters respectively exhibit significantly improved efficiency. We also demonstrate that the overall energy transfer can be optimized when the energy gap between the donor and acceptor clusters matches the optimum of the spectral density. The effects of different types of baths, e.g., Ohmic, sub-Ohmic, and super-Ohmic spectral densities are also studied. The present investigations demonstrate that the proposed approach is universal for simulating the exact quantum dynamics of photosynthetic systems.

Video abstract

Keywords

nuclear magnetic resonance / quantum simulation / open quantum system

References

[1] G. R. Fleming and R. Grondelle, The primary steps of photosynthesis, Phys. Today 47(2), 48 (1994)

[2] Y. C. Cheng and G. R. Fleming, Dynamics of light harvesting in photosynthesis, Annu. Rev. Phys. Chem. 60(1), 241 (2009)

[3] M. J. Tao, N. N. Zhang, P. Y. Wen, F. G. Deng, Q. Ai, and G. L. Long, Coherent and incoherent theories for photosynthetic energy transfer, Sci. Bull. (Beijing) 65(4), 318 (2020)

[4] M. J. Tao, M. Hua, N. N. Zhang, W. T. He, Q. Ai, and F. G. Deng, Quantum simulation of clustered photosynthetic light harvesting in a superconducting quantum circuit, Quantum Eng. 2(3), e53 (2020)

[5] N. Lambert, Y. N. Chen, Y. C. Cheng, C. M. Li, G. Y. Chen, and F. Nori, Quantum biology, Nat. Phys. 9(1), 10 (2013)

[6] J. S. Cao, R. J. Cogdell, D. F. Coker, H. G. Duan, J. Hauer, U. Kleinekathöfer, T. L. C. Jansen, T. Mančal, R. J. D. Miller, J. P. Ogilvie, V. I. Prokhorenko, T. Renger, H. S. Tan, R. Tempelaar, M. Thorwart, E. Thyrhaug, S. Westenhoff, and D. Zigmantas, Quantum biology revisited, Sci. Adv. 6(14), eaaz4888 (2020)

[7] G. S. Engel, T. R. Calhoun, E. L. Read, T. K. Ahn, T. Mančal, Y. C. Cheng, R. E. Blankenship, and G. R. Fleming, Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems, Nature 446(7137), 782 (2007)

[8] H. Lee, Y. C. Cheng, and G. R. Fleming, Coherence dynamics in photosynthesis: Protein protection of excitonic coherence, Science 316(5830), 1462 (2007)

[9] P. G. Wolynes, Some quantum weirdness in physiology, Proc. Natl. Acad. Sci. USA 106(41), 17247 (2009)

[10] E. Collini, C. Y. Wong, K. E. Wilk, P. M. G. Curmi, P. Brumer, and G. D. Scholes, Coherently wired lightharvesting in photosynthetic marine algae at ambient temperature, Nature 463(7281), 644 (2010)

[11] R. Hildner, D. Brinks, J. B. Nieder, R. J. Cogdell, and N. F. van Hulst, Quantum coherent energy transfer over varying pathways in single light-harvesting complexes, Science 340(6139), 1448 (2013)

[12] M. J. Tao, Q. Ai, F. G. Deng, and Y. C. Cheng, Proposal for probing energy transfer pathway by single-molecule pump-dump experiment, Sci. Rep. 6(1), 27535 (2016)

[13] L. G. Mourokh and F. Nori, Energy transfer efficiency in the chromophore network strongly coupled to a vibrational mode, Phys. Rev. E 92(5), 052720 (2015)

[14] H. P. Breuer, E. M. Laine, J. Piilo, and B. Vacchini, Non-Markovian dynamics in open quantum systems, Rev. Mod. Phys. 88(2), 021002 (2016)

[15] I. de Vega and D. Alonso, Dynamics of non-Markovian open quantum systems, Rev. Mod. Phys. 89(1), 015001 (2017)

[16] L. Li, M. J. W. Hall, and H. M. Wiseman, Concepts of quantum non-Markovianity: A hierarchy, Phys. Rep. 759, 1 (2018)

[17] H. P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, Oxford University Press, New York, 2007

[18] A. Ishizaki and G. R. Fleming, On the adequacy of the Redfield equation and related approaches to the study of quantum dynamics in electronic energy transfer, J. Chem. Phys. 130(23), 234110 (2009)

[19] G. Watanabe, Heat engines using small quantum systems, AAPPS Bull. 29, 30 (2019)

[20] J. X. Zhao, J. J. Cheng, Y. Q. Chu, Y. X. Wang, F. G. Deng, and Q. Ai, Hyperbolic metamaterial using chiral molecules, Sci. China Phys. Mech. Astron. 63(6), 260311 (2020)

[21] Y. Tanimura, Stochastic Liouville, Langevin, Fokker-Planck, and master equation approaches to quantum dissipative systems, J. Phys. Soc. Jpn. 75(8), 082001 (2006)

[22] A. Ishizaki and G. R. Fleming, Unified treatment of quantum coherent and incoherent hopping dynamics in electronic energy transfer: Reduced hierarchy equation approach, J. Chem. Phys. 130(23), 234111 (2009)

[23] Y. Yan, F. Yan, Y. Liu, and J. Shao, Hierarchical approach based on stochastic decoupling to dissipative systems, Chem. Phys. Lett. 395(4–6), 216 (2004)

[24] Y. Zhou, Y. Yan, and J. Shao, Stochastic simulation of quantum dissipative dynamics, Europhys. Lett. 72(3), 334 (2005)

[25] J. Shao, Decoupling quantum dissipation interaction via stochastic fields, J. Chem. Phys. 120(11), 5053 (2004)

[26] Z. F. Tang, X. L. Ouyang, Z. H. Gong, H. B. Wang, and J. L. Wu, Extended hierarchy equation of motion for the spin-boson model, J. Chem. Phys. 143(22), 224112 (2015)

[27] H. Liu, L. L. Zhu, S. M. Bai, and Q. Shi, Reduced quantum dynamics with arbitrary bath spectral densities: Hierarchical equations of motion based on several different bath decomposition schemes, J. Chem. Phys. 140(13), 134106 (2014)

[28] M. Schröder, M. Schreiber, and U. Kleinekathöfer, Reduced dynamics of coupled harmonic and anharmonic oscillators using higherorder perturbation theory, J. Chem. Phys. 126(11), 114102 (2007)

[29] A. Olaya-Castro, C. F. Lee, F. F. Olsen, and N. F. Johnson, Efficiency of energy transfer in a light-harvesting system under quantum coherence, Phys. Rev. B 78(8), 085115 (2008)

[30] Q. Ai, Y. J. Fan, B. Y. Jin, and Y. C. Cheng, An efficient quantum jump method for coherent energy transfer dynamics in photosynthetic systems under the influence of laser fields, New J. Phys. 16(5), 053033 (2014)

[31] S. Jang, Y. C. Cheng, D. R. Reichman, and J. D. Eaves, Theory of coherent resonance energy transfer, J. Chem. Phys. 129(10), 101104 (2008)

[32] M. Yang and G. R. Fleming, Influence of phonons on exciton transfer dynamics: Comparison of the Redfield, F rster, and modified Redfield equations, Chem. Phys. 282(1), 163 (2002)

[33] Y. H. Hwang-Fu, W. Chen, and Y. C. Cheng, A coherent modified Redfield theory for excitation energy transfer in molecular aggregates, Chem. Phys. 447, 46 (2015)

[34] H. Dong, D. Z. Xu, J. F. Huang, and C. P. Sun, Coherent excitation transfer via the dark-state channel in a bionic system, Light Sci. Appl. 1(3), e2 (2012)

[35] S. Mostarda, F. Levi, D. Prada-Gracia, F. Mintert, and F. Rao, Structure-dynamics relationship in coherent transport through disordered systems, Nat. Commun. 4(1), 2296 (2013)

[36] G. C. Knee, P. Rowe, L. D. Smith, A. Troisi, and A. Datta, Structure-dynamics relation in physically-plausible multichromophore systems, J. Phys. Chem. Lett. 8(10), 2328 (2017)

[37] T. Zech, R. Mulet, T. Wellens, and A. Buchleitner, Centrosymmetry enhances quantum transport in disordered molecular networks, New J. Phys. 16(5), 055002 (2014)

[38] L. Xu, Z. R. Gong, M. J. Tao, and Q. Ai, Artificial light harvesting by dimerized Möbius ring, Phys. Rev. E 97(4), 042124 (2018)

[39] Y. H. Lui, B. Zhang, and S. Hu, Rational design of photoelectrodes for photoelectrochemical water splitting and CO₂ reduction, Front. Phys. 14(5), 53402 (2019)

[40] L. Ju, M. Bie, X. Zhang, X. Chen, and L. Kou, Twodimensional Janus van der Waals heterojunctions: A review of recent research progresses, Front. Phys. 16(1), 13201 (2021)

[41] B. X. Wang, M. J. Tao, Q. Ai, T. Xin, N. Lambert, D. Ruan, Y. C. Cheng, F. Nori, F. G. Deng, and G. L. Long, Efficient quantum simulation of photosynthetic light harvesting, npj Quantum Inf. 4, 52 (2018)

[42] Q. Ai, T. C. Yen, B. Y. Jin, and Y. C. Cheng, Clustered geometries exploiting quantum coherence effects for efficient energy transfer in light harvesting, J. Phys. Chem. Lett. 4(15), 2577 (2013)

[43] Q. Shi, L. Chen, G. Nan, R. X. Xu, and Y. J. Yan, Efficient hierarchical liouville space propagetor to quantum dissipative dynamics, J. Chem. Phys. 130(8), 084105 (2009)

[44] I. Buluta and F. Nori, Quantum simulators, Science 326(5949), 108 (2009)

[45] I. M. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys. 86(1), 153 (2014)

[46] J. Xu, S. Li, T. Chen, and Z.Y. Xue, Nonadiabatic geometric quantum computation with optimal control on superconducting circuits, Front. Phys. 15(4), 41503 (2020)

[47] Z. D. Ye, D. Pan, Z. Sun, C. G. Du, L. G. Yin, and G. L. Long, Generic security analysis framework for quantum secure direct communication, Front. Phys. 16(2), 21503 (2021)

[48] Y. F. Yan, L. Zhou, W. Zhong, and Y. B. Sheng, Measurementdevice-independent quantum key distribution of multiple degrees of freedom of a single photon, Front. Phys. 16(1), 11501 (2021)

[49] M. Rey, A. W. Chin, S. F. Huelga, and M. B. Plenio, Exploiting structured environments for efficient energy transfer: The phonon antenna mechanism, J. Phys. Chem. Lett. 4(6), 903 (2013)

[50] D. J. Gorman, B. Hemmerling, E. Megidish, S. A. Moeller, P. Schindler, M. Sarovar, and H. Haeffner, Engineering vibrationally assisted energy transfer in a trapped-ion quantum simulator, Phys. Rev. X 8(1), 011038 (2018)

[51] Y. Chang and Y. C. Cheng, On the accuracy of coherent modified Redfield theory in simulating excitation energy transfer dynamics, J. Chem. Phys. 142(3), 034109 (2015)

[52] C. Meier and D. J. Tannor, Non-Markovian evolution of the density operator in the presence of strong laser fields, J. Chem. Phys. 111(8), 3365 (1999)

[53] A. Soare, H. Ball, D. Hayes, J. Sastrawan, M. C. Jarratt, J. J. McLoughlin, X. Zhen, T. J. Green, and M. J. Biercuk, Experimental noise filtering by quantum control, Nat. Phys. 10(11), 825 (2014)

[54] A. Soare, H. Ball, D. Hayes, X. Zhen, M. C. Jarratt, J. Sastrawan, H. Uys, and M. J. Biercuk, Experimental bath engineering for quantitative studies of quantum control, Phys. Rev. A 89(4), 042329 (2014)

[55] N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrüggen, and S. J. Glaser, Optimal control of coupled spin dynamics: Design of NMR pulse sequences by gradient ascent algorithms, J. Magn. Reson. 172(2), 296 (2005)

[56] J. Li, X. D. Yang, X. H. Peng, and C. P. Sun, Hybrid quantum-classical approach to quantum optimal control, Phys. Rev. Lett. 118(15), 150503 (2017)

[57] P. Fulde, Wavefunctions for extended electron systems, AAPPS Bull. 29, 50 (2019)

[58] L. Valkunas, D. Abramavicius, and T. Mančal, Molecular Excitation Dynamics and Relaxation: Quantum Theory and Spectroscopy, Wiley-VCH, Weinheim, Germany, 2013

[59] A. Ishizaki, and G. R. Fleming, Theoretical examination of quantum coherence in a photosythetic system at physiological temperature, Proc. Natl. Acad. Sci. USA 106(41), 17255 (2009)

[60] W. Jiang, F. Z. Wu, and G. J. Yang, Non-Markovian entanglement dynamics of open quantum systems with continuous measurement feedback, Phys. Rev. A 98(5), 052134 (2018)

[61] X. L. Zhen, F. H. Zhang, G. Y. Feng, L. Hang, and G. L. Long, Optimal experimental dynamical decoupling of both longitudinal and transverse relaxations, Phys. Rev. A 93(2), 022304 (2016)

[62] Y. H. Ma, H. Dong, H. T. Quan, and C. P. Sun, The uniqueness of the integration factor associated with the exchanged heat in thermodynamics, Fundamental Research 1(1), 6 (2021)

[63] A. J. Leggett, S. Chakravarty, A. Dorsey, M. Fisher, A. Garg, and W. Zwerger, Dynamics of the dissipative twostate system, Rev. Mod. Phys. 59(1), 1 (1987)

[64] U. Weiss, Quantum Dissipative Systems, World Scientific, Singapore, 2008

[65] A. W. Chin, S. F. Huelga, and M. B. Plenio, Quantum metrology in non-Markovian environments, Phys. Rev. Lett. 109(23), 233601 (2012)

[66] H. G. Duan, V. I. Prokhorenko, E. Wientjes, R. Croce, M. Thorwart, and R. J. D. Miller, Primary charge separation in the photosystem II reaction center revealed by a global analysis of the two-dimensional electronic spectra, Sci. Rep. 7(1), 12347 (2017)

[67] K. L. M. Lewis, F. D. Fuller, J. A. Myers, C. F. Yocum, D. Abramavicius, and J. P. Ogilvie, Simulations of the twodimensional electronic spectroscopy of the photosystem II reaction center, J. Phys. Chem. A 117(1), 34 (2013)

[68] L. Zhang, D. A. Silva, H. D. Zhang, A. Yue, Y. J. Yan, and X. H. Huang, Dynamic protein conformations preferentially drive energy transfer along the active chain of the photosystem II reaction centre, Nat. Commun. 5(1), 4170 (2014)

[69] H. Robbins, A remark on Stirling’s formula, Am. Math. Mon. 62, 26 (1955)

[70] V. I. Novoderezhkin, M. A. Palacios, H. van Amerongen, and R. van Grondelle, Energy-transfer dynamics in the LHCII complex of higher plants: Modified Redfield approach, J. Phys. Chem. B 108(29), 10363 (2004)

[71] J. W. Goodman, Statistical Optics, 2nd Ed., Wiley, Hoboken, NJ, 2015

[72] D. W. Lu, N. Y. Xu, R. X. Xu, H. W. Chen, J. B. Gong, X. H. Peng, and J. F. Du, Simulation of chemical isomerization reaction dynamics on a NMR quantum simulator, Phys. Rev. Lett. 107(2), 020501 (2011)

[73] I. L. Chuang, L. M. K. Vandersypen, X. L. Zhou, D. W. Leung, and S. Lloyd, Experimental realization of a quantum algorithm, Nature 393(6681), 143 (1998)

[74] L. M. K. Vandersypen and I. Chuang, NMR techniques for quantum control and computation, Rev. Mod. Phys. 76(4), 1037 (2005)

[75] E. Knill, I. Chuang, and R. Laflamme, Effective pure states for bulk quantum computation, Phys. Rev. A 57(5), 3348 (1998)

[76] D. G. Cory, M. D. Price, and T. F. Havel, Nuclear magnetic resonance spectroscopy: An experimentally accessible paradigm for quantum computing, Physica D 120(1–2), 82 (1998)

[77] J. S. Lee, The quantum state tomography on an NMR system, Phys. Lett. A 305(6), 349 (2002)

[78] D. W. Lu, T. Xin, N. K. Yu, Z. F. Ji, J. X. Chen, G. L. Long, J. Baugh, X. H. Peng, B. Zeng, and R. Laflamme, Tomography is necessary for universal entanglement detection with single-copy observables, Phys. Rev. Lett. 116(23), 230501 (2016)

[79] T. Xin, D. W. Lu, J. Klassen, N. K. Yu, Z. F. Ji, J. X. Chen, X. Ma, G. L. Long, B. Zeng, and R. Laflamme, Quantum state tomography via reduced density matrices, Phys. Rev. Lett. 118(2), 020401 (2017)

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