Studies of the dynamics of open quantum systems are limited by the large Hilbert space of typical environments, which is too large to be treated exactly. In some cases, approximate descriptions of the system are possible, for example, when the environment has a short memory time or only interacts weakly with the system. Accurate numerical methods exist, but these are typically restricted to baths with Gaussian correlations, such as non-interacting bosons. Here we present a method for simulating open quantum systems with arbitrary environments that consist of a set of independent degrees of freedom. Our approach automatically reduces the large number of environmental degrees of freedom to those which are most relevant. Specifically, we show how the process tensor describing the effect of the environment can be iteratively constructed and compressed using matrix product state techniques. We demonstrate the power of this method by applying it to a range of open quantum systems, including bosonic, fermionic and spin environments. The versatility and efficiency of our automated compression of environments method provides a practical general-purpose tool for open quantum systems.
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The data presented in the figures including the parameter files to generate them are available online in the ‘examples’ subdirectory of the Zenodo repository at https://doi.org/10.5281/zenodo.5214128.
The C++ computer code including documentation is available online at https://doi.org/10.5281/zenodo.5214128.
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M. Cosacchi and V.M.A. are grateful for funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under project no. 419036043. A.V. acknowledges support from the Russian Science Foundation under Project 18-12-00429 and from the Basic Research Program at the HSE University. M. Cygorek and E.M.G. acknowledge funding from EPSRC grant no. EP/T01377X/1. B.W.L. and J.K. were supported by EPSRC grant no. EP/T014032/1.
The authors declare no competing interests.
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Cygorek, M., Cosacchi, M., Vagov, A. et al. Simulation of open quantum systems by automated compression of arbitrary environments. Nat. Phys. 18, 662–668 (2022). https://doi.org/10.1038/s41567-022-01544-9