Efficient non-Markovian quantum dynamics using time-evolving matrix product operators

Abstract

In order to model realistic quantum devices it is necessary to simulate quantum systems strongly coupled to their environment. To date, most understanding of open quantum systems is restricted either to weak system–bath couplings or to special cases where specific numerical techniques become effective. Here we present a general and yet exact numerical approach that efficiently describes the time evolution of a quantum system coupled to a non-Markovian harmonic environment. Our method relies on expressing the system state and its propagator as a matrix product state and operator, respectively, and using a singular value decomposition to compress the description of the state as time evolves. We demonstrate the power and flexibility of our approach by numerically identifying the localisation transition of the Ohmic spin-boson model, and considering a model with widely separated environmental timescales arising for a pair of spins embedded in a common environment.

Full text

Its licence does not allow us to show the full text. Read it at PubMed Central:

References 61

1. 1.

   Breuer, H. -P. & Petruccione, F. The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002).

   Not in our library

2. 2.

   Walls, D. F. & Milburn, G. J. Quantum Optics 2nd edn (Springer, Berlin, 2007).

   Not in our library

3. 3.

   de Vega I, Alonso D. Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 2017;89:015001.

   Not in our library10.1103/revmodphys.89.015001

4. 4.

   Gröblacher S, et al. Observation of non-Markovian micromechanical brownian motion. Nat. Commun. 2015;6:7606.

   Not in our library10.1038/ncomms8606

5. 5.

   Madsen KH, et al. Observation of non-Markovian dynamics of a single quantum dot in a micropillar cavity. Phys. Rev. Lett. 2011;106:233601.

   Not in our library10.1103/physrevlett.106.233601

6. 6.

   Mi X, Cady JV, Zajac DM, Deelman PW, Petta JR. Strong coupling of a single electron in silicon to a microwave photon. Science. 2017;355:156-158.

   Not in our library10.1126/science.aal2469

7. 7.

   Potočnik A, et al. Studying light-harvesting models with superconducting circuits. Nat. Commun. 2018;9:904.

   Not in our library10.1038/s41467-018-03312-x

8. 8.

   Aharonovich I, Englund D, Toth M. Solid-state single-photon emitters. Nat. Photon. 2016;10:631-641.

   Not in our library10.1038/nphoton.2016.186

9. 9.

   Chin AW, et al. The role of non-equilibrium vibrational structures in electronic coherence and recoherence in pigment–protein complexes. Nat. Phys. 2013;9:113-118.

   Not in our library10.1038/nphys2515

10. 10.

    Lee MK, Huo P, Coker DF. Semiclassical path integral dynamics: photosynthetic energy transfer with realistic environment interactions. Annu. Rev. Phys. Chem. 2016;67:639-668.

    Not in our library10.1146/annurev-physchem-040215-112252

11. 11.

    Barford W. Electronic and Optical Properties of Conjugated Polymers. 2013.

    Not in our library

12. 12.

    McCutcheon DPS, Dattani NS, Gauger EM, Lovett BW, Nazir A. A general approach to quantum dynamics using a variational master equation: application to phonon-damped rabi rotations in quantum dots. Phys. Rev. B. 2011;84:081305.

    Not in our library10.1103/physrevb.84.081305

13. 13.

    McCutcheon DPS, Nazir A. Coherent and incoherent dynamics in excitonic energy transfer: correlated fluctuations and off-resonance effects. Phys. Rev. B. 2011;83:165101.

    Not in our library10.1103/physrevb.83.165101

14. 14.

    Kaer P, Nielsen TR, Lodahl P, Jauho AP, Mørk J. Non-Markovian model of photon-assisted dephasing by electron–phonon interactions in a coupled quantum-dot–cavity system. Phys. Rev. Lett. 2010;104:157401.

    Not in our library10.1103/physrevlett.104.157401

15. 15.

    Roy C, Hughes S. Influence of electron–acoustic-phonon scattering on intensity power broadening in a coherently driven quantum-dot–cavity system. Phys. Rev. X. 2011;1:021009.

    Not in our library

16. 16.

    Segal D, Agarwalla BK. Vibrational heat transport in molecular junctions. Annu. Rev. Phys. Chem. 2016;67:185-209.

    Not in our library10.1146/annurev-physchem-040215-112103

17. 17.

    Subotnik JE, et al. Understanding the surface hopping view of electronic transitions and decoherence. Annu. Rev. Phys. Chem. 2016;67:387-417.

    Not in our library10.1146/annurev-physchem-040215-112245

18. 18.

    Bylicka B, Chruściński D, Maniscalco S. Non-Markovianity and reservoir memory of quantum channels: a quantum information theory perspective. Sci. Rep. 2014;4:5720.

    Not in our library10.1038/srep05720

19. 19.

    Xiang GY, et al. Entanglement distribution in optical fibers assisted by nonlocal memory effects. Phys. Lett. 2014;107:54006.

    Not in our library

20. 20.

    Mahan, G. D. Many Particle Physics 3rd edn (Springer, Berlin, 2000).

    Not in our library

21. 21.

    Jang S. Theory of coherent resonance energy transfer for coherent initial condition. J. Chem. Phys. 2009;131:164101.

    Not in our library10.1063/1.3247899

22. 22.

    Cohen G, Gull E, Reichman DR, Millis AJ. Taming the dynamical sign problem in real-time evolution of quantum many-body problems. Phys. Rev. Lett. 2015;115:266802.

    Not in our library10.1103/physrevlett.115.266802

23. 23.

    Chen HT, Cohen G, Reichman DR. Inchworm Monte Carlo for exact non-adiabatic dynamics. ii. Benchmarks and comparison with established methods. J. Chem. Phys. 2017;146:054106.

    Not in our library10.1063/1.4974329

24. 24.

    Yoshitaka T, Kubo R. Time evolution of a quantum system in contact with a nearly Gaussian-Markoffian noise bath. J. Phys. Soc. Jpn. 1989;58:101-114.

    Not in our library10.1143/jpsj.58.101

25. 25.

    Garraway BM. Non-perturbative decay of an atomic system in a cavity. Phys. Rev. A. 1997;55:2290-2303.

    Not in our library10.1103/physreva.55.2290

26. 26.

    Iles-Smith J, Lambert N, Nazir A. Environmental dynamics, correlations, and the emergence of noncanonical equilibrium states in open quantum systems. Phys. Rev. A. 2014;90:032114.

    Not in our library10.1103/physreva.90.032114

27. 27.

    Schröder, F. A. Y. N. et al. Multi-dimensional tensor network simulation of open quantum dynamics in singlet fission. Preprint at https://arxiv.org/abs/1710.01362 (2017).

    Not in our library

28. 28.

    Makri N, Makarov DE. Tensor propagator for iterative quantum time evolution of reduced density matrices. I. Theory. J. Chem. Phys. 1995;102:4600.

    Not in our library10.1063/1.469508

29. 29.

    Makri N, Makarov DE. Tensor propagator for iterative quantum time evolution of reduced density matrices. II. Numerical methodology. J. Chem. Phys. 1995;102:4611.

    Not in our library10.1063/1.469509

30. 30.

    Leggett AJ, et al. Dynamics of the dissipative two-state system. Rev. Mod. Phys. 1987;59:1-85.

    Not in our library10.1103/revmodphys.59.1

31. 31.

    Nalbach P, Ishizaki A, Fleming GR, Thorwart M. Iterative path-integral algorithm versus cumulant time-nonlocal master equation approach for dissipative biomolecular exciton transport. N. J. Phys. 2011;13:063040.

    Not in our library10.1088/1367-2630/13/6/063040

32. 32.

    Thorwart M, Eckel J, Mucciolo ER. Non-Markovian dynamics of double quantum dot charge qubits due to acoustic phonons. Phys. Rev. B. 2005;72:235320.

    Not in our library10.1103/physrevb.72.235320

33. 33.

    Sim E. Quantum dynamics for a system coupled to slow baths: on-the-fly filtered propagator method. J. Chem. Phys. 2001;115:4450-4456.

    Not in our library10.1063/1.1394208

34. 34.

    Lambert R, Makri N. Memory propagator matrix for long-time dissipative charge transfer dynamics. Mol. Phys. 2012;110:1967-1975.

    Not in our library10.1080/00268976.2012.700408

35. 35.

    Schollwöck U. The density-matrix renormalization group in the age of matrix product states. Ann. Phys. (N.Y.). 2011;326:96-192.

    Not in our library10.1016/j.aop.2010.09.012

36. 36.

    Orús R. A practical introduction to tensor networks: matrix product states and projected entangled pair states. Ann. Phys. (N.Y.). 2014;349:117-158.

    Not in our library10.1016/j.aop.2014.06.013

37. 37.

    White SR. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett. 1992;69:2863-2866.

    Not in our library10.1103/physrevlett.69.2863

38. 38.

    Derrida B, Evans MR, Hakim V, Pasquier V. Exact solution of a 1d asymmetric exclusion model using a matrix formulation. J. Phys. A. 1993;26:1493.

    Not in our library10.1088/0305-4470/26/7/011

39. 39.

    Vidal G. Efficient classical simulation of slightly entangled quantum computations. Phys. Rev. Lett. 2003;91:147902.

    Not in our library10.1103/physrevlett.91.147902

40. 40.

    Florens, S., Venturelli, D. & Narayanan, R. in Quantum Quenching, Annealing and Computation (eds Chandra, A. K., et al.) 145–162 (Springer, Berlin, Heidelberg, 2010).

    Not in our library

Reads

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.