Convergence guarantees for discrete mode approximations to non-Markovian quantum baths

• URL: http://arxiv.org/abs/2107.07196v2
• Date: Fri, 12 Nov 2021 17:33:55 GMT
• Title: Convergence guarantees for discrete mode approximations to non-Markovian quantum baths
• Authors: Rahul Trivedi, Daniel Malz, J. Ignacio Cirac
• Abstract summary: Non-Markovian effects are important in modeling the behavior of open quantum systems in solid-state physics, quantum optics, and in study of biological and chemical systems. We show that under some physically motivated assumptions on the system-environment interaction, the finite-time dynamics of the non-Markovian open quantum system computed with a sufficiently large number of modes guaranteed to converge is an approximation. Our results lend rigor to classical and quantum algorithms for approximating non-Markovian dynamics.
• Score: 0.7734726150561088
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Non-Markovian effects are important in modeling the behavior of open quantum systems arising in solid-state physics, quantum optics as well as in study of biological and chemical systems. The non-Markovian environment is often approximated by discrete bosonic modes, thus mapping it to a Lindbladian or Hamiltonian simulation problem. While systematic constructions of such modes have been previously proposed, the resulting approximation lacks rigorous and general convergence guarantees. In this letter, we show that under some physically motivated assumptions on the system-environment interaction, the finite-time dynamics of the non-Markovian open quantum system computed with a sufficiently large number of modes is guaranteed to converge to the true result. Furthermore, we show that this approximation error typically falls off polynomially with the number of modes. Our results lend rigor to classical and quantum algorithms for approximating non-Markovian dynamics.

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