A general quantum algorithm for open quantum dynamics demonstrated with the Fenna-Matthews-Olson complex

Zixuan Hu; Kade Head-Marsden; David A. Mazziotti; Prineha Narang; Sabre Kais

doi:10.22331/q-2022-05-30-726

A general quantum algorithm for open quantum dynamics demonstrated with the Fenna-Matthews-Olson complex

Zixuan Hu¹, Kade Head-Marsden², David A. Mazziotti³, Prineha Narang², and Sabre Kais¹

¹Department of Chemistry, Department of Physics, and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN 47907, USA
²John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
³Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, IL 60637 USA

Published:	2022-05-30, volume 6, page 726
Eprint:	arXiv:2101.05287v3
Doi:	https://doi.org/10.22331/q-2022-05-30-726
Citation:	Quantum 6, 726 (2022).

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Abstract

Using quantum algorithms to simulate complex physical processes and correlations in quantum matter has been a major direction of quantum computing research, towards the promise of a quantum advantage over classical approaches. In this work we develop a generalized quantum algorithm to simulate any dynamical process represented by either the operator sum representation or the Lindblad master equation. We then demonstrate the quantum algorithm by simulating the dynamics of the Fenna-Matthews-Olson (FMO) complex on the IBM QASM quantum simulator. This work represents a first demonstration of a quantum algorithm for open quantum dynamics with a moderately sophisticated dynamical process involving a realistic biological structure. We discuss the complexity of the quantum algorithm relative to the classical method for the same purpose, presenting a decisive query complexity advantage of the quantum approach based on the unique property of quantum measurement.

Featured image: One monomer of the Fenna-Matthews-Olson (FMO) complex is shown on the left, with the three-chromophore functional subsystem shown in dark green. The dynamical evolution of the populations of the FMO complex model is shown on the right, with the dots representing results simulated by our quantum algorithm on the IBM quantum simulator. The dots agree well with the curves that are generated by classical numerical methods.

Popular summary

Open quantum dynamics is an important subfield of quantum physics that studies the time evolution of a system interacting with an environment. Although numerous quantum algorithms have been developed to simulate quantum systems, so far few studies have been done to simulate open quantum dynamics despite its importance. In this work we develop a generalized quantum algorithm for open quantum dynamics and simulate the Fenna-Matthews-Olson complex on the IBM quantum simulator. This is so far as we know the first quantum simulator demonstration of using a quantum algorithm to simulate such a complex dynamical model.

► BibTeX data

@article{Hu2022generalquantum,
  doi = {10.22331/q-2022-05-30-726},
  url = {https://doi.org/10.22331/q-2022-05-30-726},
  title = {A general quantum algorithm for open quantum dynamics demonstrated with the {F}enna-{M}atthews-{O}lson complex},
  author = {Hu, Zixuan and Head-Marsden, Kade and Mazziotti, David A. and Narang, Prineha and Kais, Sabre},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {726},
  month = may,
  year = {2022}
}

► References

[1] S. Kais. Quantum Information and Computation for Chemistry. John Wiley & Sons, 2014.

[2] Y. Cao, J. Romero, J. P. Olson, M. Degroote, P. D. Johnson, M. Kieferová, I. D. Kivlichan, T. Menke, B. Peropadre, N. P. D. Sawaya, S. Sim, L. Veis, and A. Aspuru-Guzik. Quantum chemistry in the age of quantum computing. Chem. Rev., 119 (19): 10856–10915, 2019. 10.1021/acs.chemrev.8b00803.
https://doi.org/10.1021/acs.chemrev.8b00803

[3] B. Bauer, S. Bravyi, M. Motta, and G. Kin-Lic Chan. Quantum algorithms for quantum chemistry and quantum materials science. Chem. Rev., 120 (22): 12685–12717, 2020. 10.1021/acs.chemrev.9b00829.
https://doi.org/10.1021/acs.chemrev.9b00829

[4] K. Head-Marsden, J. Flick, C. J. Ciccarino, and P. Narang. Quantum information and algorithms for correlated quantum matter. Chem. Rev., 121 (5): 3061–3120, 2021a. 10.1021/acs.chemrev.0c00620.
https://doi.org/10.1021/acs.chemrev.0c00620

[5] H.-Y. Huang, R. Kueng, and J. Preskill. Predicting many properties of a quantum system from very few measurements. Nature Physics, 16 (10): 1050–1057, 2020. 10.1038/s41567-020-0932-7.
https://doi.org/10.1038/s41567-020-0932-7

[6] A. M. Childs, D. Maslov, Y. Nam, N. J. Ross, and Y. Su. Toward the first quantum simulation with quantum speedup. Proceedings of the National Academy of Sciences, 115 (38): 9456–9461, 2018. 10.1073/pnas.1801723115.
https://doi.org/10.1073/pnas.1801723115

[7] H.-P. Breuer and F. Petruccione. The Theory of Open Quantum Systems. Oxford University Press, 2002.

[8] H. Wang, S. Ashhab, and F. Nori. Quantum algorithm for simulating the dynamics of an open quantum system. Phys. Rev. A, 83: 062317, 2011. 10.1103/PhysRevA.83.062317.
https://doi.org/10.1103/PhysRevA.83.062317

[9] D.-S. Wang, D. W. Berry, M. C. de Oliveira, and B. C. Sanders. Solovay-kitaev decomposition strategy for single-qubit channels. Phys. Rev. Lett., 111: 130504, 2013. 10.1103/PhysRevLett.111.130504.
https://doi.org/10.1103/PhysRevLett.111.130504

[10] S.-J. Wei, D. Ruan, and G.-L. Long. Duality quantum algorithm efficiently simulates open quantum systems. Sci. Rep., 6 (1): 30727, 2016. 10.1038/srep30727.
https://doi.org/10.1038/srep30727

[11] R. Di Candia, J. S. Pedernales, A. del Campo, E. Solano, and J. Casanova. Quantum simulation of dissipative processes without reservoir engineering. Sci. Rep., 5 (1): 9981, 2015. 10.1038/srep09981.
https://doi.org/10.1038/srep09981

[12] R. Sweke, I. Sinayskiy, D. Bernard, and F. Petruccione. Universal simulation of Markovian open quantum systems. Phys. Rev. A, 91: 062308, 2015. 10.1103/PhysRevA.91.062308.
https://doi.org/10.1103/PhysRevA.91.062308

[13] G. García-Pérez, M. A. C. Rossi, and S. Maniscalco. Ibm q experience as a versatile experimental testbed for simulating open quantum systems. NPJ Quant. Inf., 6 (1): 1, 2020. 10.1038/s41534-019-0235-y.
https://doi.org/10.1038/s41534-019-0235-y

[14] A. M. Childs and T. Li. Efficient simulation of sparse markovian quantum dynamics. arXiv preprint arXiv:1611.05543, 2016. 10.26421/QIC17.11-12.
https://doi.org/10.26421/QIC17.11-12
arXiv:1611.05543

[15] M. Kliesch, T. Barthel, C. Gogolin, M. Kastoryano, and J. Eisert. Dissipative quantum church-turing theorem. Phys. Rev. Lett., 107: 120501, 2011. 10.1103/PhysRevLett.107.120501.
https://doi.org/10.1103/PhysRevLett.107.120501

[16] Z. Hu, R. Xia, and S. Kais. A quantum algorithm for evolving open quantum dynamics on quantum computing devices. Sci. Rep., 10 (1): 3301, 2020. 10.1038/s41598-020-60321-x.
https://doi.org/10.1038/s41598-020-60321-x

[17] K. Head-Marsden and D. A. Mazziotti. Ensemble of lindblad's trajectories for non-Markovian dynamics. Phys. Rev. A, 99: 022109, 2019a. 10.1103/PhysRevA.99.022109.
https://doi.org/10.1103/PhysRevA.99.022109

[18] K. Head-Marsden and D. A. Mazziotti. Satisfying fermionic statistics in the modeling of non-Markovian dynamics with one-electron reduced density matrices. J. Chem. Phys., 151 (3): 034111, 2019b. 10.1063/1.5100143.
https://doi.org/10.1063/1.5100143

[19] K. Head-Marsden, S. Krastanov, D. A. Mazziotti, and P. Narang. Capturing non-Markovian dynamics on near-term quantum computers. Phys. Rev. Research, 3: 013182, 2021b. 10.1103/PhysRevResearch.3.013182.
https://doi.org/10.1103/PhysRevResearch.3.013182

[20] H. Nakazato, Y. Hida, K. Yuasa, B. Militello, A. Napoli, and A. Messina. Solution of the lindblad equation in the kraus representation. Phys. Rev. A, 74: 062113, 2006. 10.1103/PhysRevA.74.062113.
https://doi.org/10.1103/PhysRevA.74.062113

[21] E. Andersson, J. D. Cresser, and M. J. W. Hall. Finding the Kraus decomposition from a master equation and vice versa. J. Mod. Opt., 54 (12): 1695–1716, 2007. 10.1080/09500340701352581.
https://doi.org/10.1080/09500340701352581

[22] R.E. Blankenship. Molecular mechanisms of photosynthesis. 2nd Ed. Chichester, West Sussex, UK: Wiley/Blackwell, 2014.

[23] D.L. Andrews and A.A. Demidov. Resonance Energy Transfer. Wiley, 1999.

[24] R. J. Sension. Quantum path to photosynthesis. Nature, 446 (7137): 740–741, 2007. 10.1038/446740a.
https://doi.org/10.1038/446740a

[25] J. Barroso-Flores. Evolution of the Fenna–Matthews–Olson complex and its quantum coherence features. which led the way? ACS Cent. Sci., 3 (10): 1061–1062, 2017. 10.1021/acscentsci.7b00386.
https://doi.org/10.1021/acscentsci.7b00386

[26] A. Ishizaki and G. R. Fleming. Theoretical examination of quantum coherence in a photosynthetic system at physiological temperature. Proc. Natl. Acad. Sci., 106 (41): 17255–17260, 2009a. 10.1073/pnas.0908989106.
https://doi.org/10.1073/pnas.0908989106

[27] 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, 2009b. 10.1063/1.3155372.
https://doi.org/10.1063/1.3155372

[28] J. Zhu, S. Kais, A. Aspuru-Guzik, S. Rodriques, B. Brock, and P. J. Love. Multipartite quantum entanglement evolution in photosynthetic complexes. J. Chem. Phys., 137 (7): 074112, 2012. 10.1063/1.4742333.
https://doi.org/10.1063/1.4742333

[29] E. Thyrhaug, R. Tempelaar, M. J. P. Alcocer, K. Žídek, D. Bína, J. Knoester, T. L. C. Jansen, and D. Zigmantas. Identification and characterization of diverse coherences in the Fenna–Matthews–Olson complex. Nat. Chem., 10 (7): 780–786, 2018. 10.1038/s41557-018-0060-5.
https://doi.org/10.1038/s41557-018-0060-5

[30] S. Irgen-Gioro, K. Gururangan, R. G. Saer, R. E. Blankenship, and E. Harel. Electronic coherence lifetimes of the fenna–matthews–olson complex and light harvesting complex ii. Chem. Sci., 10: 10503–10509, 2019. 10.1039/C9SC03501J.
https://doi.org/10.1039/C9SC03501J

[31] S. A. Oh, D. F. Coker, and D. A. W. Hutchinson. Optimization of energy transport in the fenna-matthews-olson complex via site-varying pigment-protein interactions. J. Chem. Phys., 150 (8): 085102, 2019. 10.1063/1.5048058.
https://doi.org/10.1063/1.5048058

[32] Y. Suzuki, H. Watanabe, Y. Okiyama, K. Ebina, and S. Tanaka. Comparative study on model parameter evaluations for the energy transfer dynamics in Fenna–Matthews–Olson complex. Chem. Phys., 539: 110903, 2020. https://doi.org/10.1016/j.chemphys.2020.110903.
https://doi.org/10.1016/j.chemphys.2020.110903

[33] Y. Kim, D. Morozov, V. Stadnytskyi, S. Savikhin, and L. V. Slipchenko. Predictive first-principles modeling of a photosynthetic antenna protein: The fenna–matthews–olson complex. J. Phys. Chem. Lett., 11 (5): 1636–1643, 2020. 10.1021/acs.jpclett.9b03486.
https://doi.org/10.1021/acs.jpclett.9b03486

[34] S.-H. Yeh, J. Zhu, and S. Kais. Population and coherence dynamics in light harvesting complex ii (lh2). J. Chem. Phys., 137 (8): 084110, 2012. 10.1063/1.4747622.
https://doi.org/10.1063/1.4747622

[35] Z. Hu, G. S. Engel, and S. Kais. Double-excitation manifold's effect on exciton transfer dynamics and the efficiency of coherent light harvesting. Phys. Chem. Chem. Phys., 20: 30032–30040, 2018. 10.1039/C8CP05535A.
https://doi.org/10.1039/C8CP05535A

[36] P. Gupta and C. M. Chandrashekar. Digital quantum simulation framework for energy transport in an open quantum system. New J. Phys., 22 (12): 123027, 2020. 10.1088/1367-2630/abcdc9.
https://doi.org/10.1088/1367-2630/abcdc9

[37] M. Mahdian and H. D. Yeganeh. Quantum simulation of fmo complex using one-parameter semigroup of generators. Braz. J. Phys., 50 (6): 807–813, 2020. 10.1007/s13538-020-00804-4.
https://doi.org/10.1007/s13538-020-00804-4

[38] M. Mahdian, H. D. Yeganeh, and A. Dehghani. Quantum simulation dynamics and circuit synthesis of fmo complex on an nmr quantum computer. Int. J. Quantum Inf., 18 (06): 2050034, 2020. 10.1142/S0219749920500343.
https://doi.org/10.1142/S0219749920500343

[39] H. Abraham et al. Qiskit: An open-source framework for quantum computing, 2019.

[40] E. Levy and O. M. Shalit. Dilation theory in finite dimensions: The possible, the impossible and the unknown. Rocky Mountain J. Math., 44 (1): 203–221, 2014. 10.1216/RMJ-2014-44-1-203.
https://doi.org/10.1216/RMJ-2014-44-1-203

[41] A. Krishnamoorthy and D. Menon. Matrix inversion using cholesky decomposition. In 2013 Signal Processing: Algorithms, Architectures, Arrangements, and Applications (SPA), pages 70–72, 2013.

[42] M. A. Nielson and I. L. Chuang. Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, 2011.

[43] 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): 782–786, 2007. 10.1038/nature05678.
https://doi.org/10.1038/nature05678

[44] G. D. Scholes, G. R. Fleming, L. X. Chen, A. Aspuru-Guzik, A. Buchleitner, D. F. Coker, G. S. Engel, R. van Grondelle, A. Ishizaki, D. M. Jonas, J. S. Lundeen, J. K. McCusker, S. Mukamel, J. P. Ogilvie, A. Olaya-Castro, M. A. Ratner, F. C. Spano, K. B. Whaley, and X. Zhu. Using coherence to enhance function in chemical and biophysical systems. Nature, 543 (7647): 647–656, 2017. 10.1038/nature21425.
https://doi.org/10.1038/nature21425

[45] J. Adolphs and T. Renger. How proteins trigger excitation energy transfer in the fmo complex of green sulfur bacteria. Biophys. J., 91 (8): 2778 – 2797, 2006. https://doi.org/10.1529/biophysj.105.079483.
https://doi.org/10.1529/biophysj.105.079483

[46] N. Skochdopole and D. A. Mazziotti. Functional subsystems and quantum redundancy in photosynthetic light harvesting. J. Phys. Chem. Lett., 2 (23): 2989–2993, 2011. 10.1021/jz201154t.
https://doi.org/10.1021/jz201154t

[47] R. A. Valleau, S.and Studer, F. Häse, C. Kreisbeck, R. G. Saer, R. E. Blankenship, E. I. Shakhnovich, and A. Aspuru-Guzik. Absence of selection for quantum coherence in the fenna–matthews–olson complex: A combined evolutionary and excitonic study. ACS Cent. Sci., 3 (10): 1086–1095, 2017. 10.1021/acscentsci.7b00269.
https://doi.org/10.1021/acscentsci.7b00269

[48] J. Preskill. Quantum Computing in the NISQ era and beyond. Quantum, 2: 79, 2018. 10.22331/q-2018-08-06-79.
https://doi.org/10.22331/q-2018-08-06-79

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