https://doi.org/10.1140/epjp/s13360-023-04205-9
Regular Article
Correspondence between open bosonic systems and stochastic differential equations
1
Department of Physics, University of Colorado, 80309, Boulder, CO, USA
2
Renewable and Sustainable Energy Institute, University of Colorado, 80309, Boulder, CO, USA
Received:
3
February
2023
Accepted:
17
June
2023
Published online:
30
June
2023
Bosonic mean-field theories can approximate the dynamics of systems of n bosons provided that 
. We show that there can also be an exact correspondence at finite n when the bosonic system is generalized to include interactions with the environment and the mean-field theory is replaced by a stochastic differential equation. When the 
limit is taken, the stochastic terms in this differential equation vanish, and a mean-field theory is recovered. Besides providing insight into the differences between the behavior of finite quantum systems and their classical limits given by , the developed mathematics can provide a basis for quantum algorithms that solve some stochastic nonlinear differential equations. We discuss conditions on the efficiency of these quantum algorithms, with a focus on the possibility for the complexity to be polynomial in the log of the stochastic system size. A particular system with the form of a stochastic discrete nonlinear Schrödinger equation is analyzed in more detail.
Contribution to the Focus Point on “Mathematics and Physics at the Quantum-Classical Interface” edited by D.I. Bondar, I. Joseph, G. Marmo, C. Tronci.
Copyright comment corrected publication 2023
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. corrected publication 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
