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Matrix-product-state methods for non-Markovian models

ORAL · Invited

Abstract

When an open quantum system is strongly coupled to a structured environment, describing the dynamics of that system becomes a challenging problem.   Moreover, traditional approaches, based on time evolution of the reduced density matrix are generally not able to correctly calculate higher-order or multi-time correlations.  I will review recent progress that addresses both these issues, by showing how the time evolution of the system can be efficiently simulated using tensor network methods [1].  Such a tensor network naturally leads one to consider the process tensor (PT), an object which encodes all multi-time correlations of the reservoir [2].  A key insight is that one can construct efficient MPO representations of the PT.  This idea makes possible many otherwise challenging tasks, including optimisation of non-Markovian systems [3] (requiring repeated simulation of the dynamics),  and modelling the non-Markovian dynamics of many-body open quantum systems [4,5]. It also prompts identification of alternate algorithms to constrcut an MPO form of the PT [6].   

The code underpinning this work is publicly available [7], and we are keen to help support other researchers in using this approach.

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Publication: [1] Efficient non-Markovian quantum dynamics using time-evolving matrix product operators. A. Strathearn, P. Kirton, D. Kilda, J. Keeling, B. W. Lovett. Nature Commun. 9, 3322 (2018) <br><br>[2] Exploiting the causal tensor network structure of quantum processes to ef-<br>ficiently simulate non-markovian path integrals, M. R. Jørgensen and F. A. Pollock, Phys. Rev. Lett. 123, 240602 (2019).<br><br>[3] Efficient exploration of hamiltonian parameter space for optimal control of non-markovian open quantum systems. G. E. Fux, E. P. Butler, P. R. Eastham, B. W. Lovett, J. Keeling, Phys. Rev. Lett. 126, 200401 (2021).<br><br>[4] Efficient many-body non-Markovian dynamics of organic polaritons. P. Fowler-Wright, B. W. Lovett, J. Keeling, in preparation<br><br>[5] Thermalization of a spin chain with strong environment coupling. G. E. Fux, D. Kilda, B. W. Lovett, J. Keeling, in preparation<br><br>[6] Numerically-exact simulations of arbitrary open quantum systems using automated compression of environments. M. Cygorek, M. Cosacchi, A. Vagov, V. M. Axt, B. W. Lovett, J. Keeling, E. M. Gauger<br><br>[7] The TEMPO collaboration, TimeEvolvingMPO: A Python 3 package to efficiently compute non-Markovian open quantum systems. (2020).<br>

Presenters

  • Jonathan Keeling

    Univ of St Andrews

Authors

  • Jonathan Keeling

    Univ of St Andrews