Efficient quantum simulation of open quantum dynamics at various Hamiltonians and spectral densities
Na-Na Zhang (张娜娜)1, Ming-Jie Tao (陶明杰)2, Wan-Ting He (何宛亭)1, Xin-Yu Chen (陈鑫宇)3, Xiang-Yu Kong (孔祥宇)3, Fu-Guo Deng (邓富国)1, Neill Lambert4, Qing Ai (艾清)1()
1. Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China 2. Space Engineering University, Beijing 101416, China 3. Department of Physics, Tsinghua University, Beijing 100084, China 4. Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
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.
. [J]. Frontiers of Physics, 2021, 16(5): 51501.
Na-Na Zhang (张娜娜), Ming-Jie Tao (陶明杰), Wan-Ting He (何宛亭), Xin-Yu Chen (陈鑫宇), Xiang-Yu Kong (孔祥宇), Fu-Guo Deng (邓富国), Neill Lambert, Qing Ai (艾清). Efficient quantum simulation of open quantum dynamics at various Hamiltonians and spectral densities. Front. Phys. , 2021, 16(5): 51501.
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) https://doi.org/10.1016/j.scib.2019.12.009
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) https://doi.org/10.1002/que2.53
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) https://doi.org/10.1038/nphys2474
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) https://doi.org/10.1126/sciadv.aaz4888
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) https://doi.org/10.1038/nature05678
8
H. Lee, Y. C. Cheng, and G. R. Fleming, Coherence dynamics in photosynthesis: Protein protection of excitonic coherence, Science 316(5830), 1462 (2007) https://doi.org/10.1126/science.1142188
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) https://doi.org/10.1038/nature08811
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) https://doi.org/10.1126/science.1235820
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) https://doi.org/10.1038/srep27535
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) https://doi.org/10.1103/PhysRevE.92.052720
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) https://doi.org/10.1103/RevModPhys.88.021002
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) https://doi.org/10.1063/1.3155214
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) https://doi.org/10.1007/s11433-019-1470-6
21
Y. Tanimura, Stochastic Liouville, Langevin, Fokker-Planck, and master equation approaches to quantum dissipative systems, J. Phys. Soc. Jpn. 75(8), 082001 (2006) https://doi.org/10.1143/JPSJ.75.082001
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) https://doi.org/10.1063/1.3155372
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) https://doi.org/10.1016/j.cplett.2004.07.036
J. Shao, Decoupling quantum dissipation interaction via stochastic fields, J. Chem. Phys. 120(11), 5053 (2004) https://doi.org/10.1063/1.1647528
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) https://doi.org/10.1063/1.4936924
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) https://doi.org/10.1063/1.4870035
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) https://doi.org/10.1063/1.2538754
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) https://doi.org/10.1103/PhysRevB.78.085115
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) https://doi.org/10.1088/1367-2630/16/5/053033
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) https://doi.org/10.1063/1.2977974
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) https://doi.org/10.1016/S0301-0104(02)00604-3
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) https://doi.org/10.1016/j.chemphys.2014.11.026
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) https://doi.org/10.1038/lsa.2012.2
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) https://doi.org/10.1038/ncomms3296
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) https://doi.org/10.1021/acs.jpclett.7b00829
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) https://doi.org/10.1088/1367-2630/16/5/055002
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) https://doi.org/10.1103/PhysRevE.97.042124
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) https://doi.org/10.1007/s11467-019-0903-6
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) https://doi.org/10.1007/s11467-020-1002-4
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) https://doi.org/10.1038/s41534-018-0102-2
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) https://doi.org/10.1021/jz4011477
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) https://doi.org/10.1063/1.3077918
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) https://doi.org/10.1007/s11467-020-0976-2
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) https://doi.org/10.1007/s11467-020-1025-x
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) https://doi.org/10.1007/s11467-020-1005-1
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) https://doi.org/10.1021/jz400058a
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) https://doi.org/10.1103/PhysRevX.8.011038
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) https://doi.org/10.1063/1.4905721
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) https://doi.org/10.1063/1.479669
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) https://doi.org/10.1038/nphys3115
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) https://doi.org/10.1103/PhysRevA.89.042329
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) https://doi.org/10.1016/j.jmr.2004.11.004
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) https://doi.org/10.1103/PhysRevLett.118.150503
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 https://doi.org/10.1002/9783527653652
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) https://doi.org/10.1073/pnas.0908989106
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) https://doi.org/10.1103/PhysRevA.98.052134
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) https://doi.org/10.1103/PhysRevA.93.022304
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) https://doi.org/10.1016/j.fmre.2020.11.003
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) https://doi.org/10.1103/RevModPhys.59.1
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) https://doi.org/10.1038/s41598-017-12564-4
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) https://doi.org/10.1021/jp3081707
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) https://doi.org/10.1038/ncomms5170
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) https://doi.org/10.1021/jp0496001
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) https://doi.org/10.1103/PhysRevLett.107.020501
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) https://doi.org/10.1038/30181
E. Knill, I. Chuang, and R. Laflamme, Effective pure states for bulk quantum computation, Phys. Rev. A 57(5), 3348 (1998) https://doi.org/10.1103/PhysRevA.57.3348
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) https://doi.org/10.1016/S0167-2789(98)00046-3
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) https://doi.org/10.1103/PhysRevLett.116.230501
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) https://doi.org/10.1103/PhysRevLett.118.020401