Convergence Guarantees for Discrete Mode Approximations to Non-Markovian Quantum Baths

Rahul Trivedi; Daniel Malz; J. Ignacio Cirac

doi:10.1103/PhysRevLett.127.250404

Convergence Guarantees for Discrete Mode Approximations to Non-Markovian Quantum Baths

Rahul Trivedi^*
, Daniel Malz
, J. Ignacio Cirac

^*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

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.

Originalsprog	Engelsk
Artikelnummer	A36
Tidsskrift	Physical Review Letters
Vol/bind	127
Udgave nummer	25
ISSN	0031-9007
DOI	https://doi.org/10.1103/PhysRevLett.127.250404
Status	Udgivet - 17 dec. 2021
Udgivet eksternt	Ja

Bibliografisk note

Publisher Copyright:
© 2021 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Finansiering

We thank Martin Plenio, Mischa Woods, Christiane Koch, and Archak Purkayastha for pointing us to relevant literature on this topic. R. T. acknowledges Max Planck Harvard research center for support from the quantum optics (MPHQ) postdoctoral fellowship. We acknowledge support from the ERC Advanced Grant QUENOCOBA under the EU Horizon 2020 program (Grant No. 742102) and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Project No. 414325145 in the framework of the Austrian Science Fund (FWF): SFB F7104.

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10.1103/PhysRevLett.127.250404

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Citationsformater

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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. ",

author = "Rahul Trivedi and Daniel Malz and Cirac, \{J. Ignacio\}",

note = "Funding Information: We thank Martin Plenio, Mischa Woods, Christiane Koch, and Archak Purkayastha for pointing us to relevant literature on this topic. R. T. acknowledges Max Planck Harvard research center for support from the quantum optics (MPHQ) postdoctoral fellowship. We acknowledge support from the ERC Advanced Grant QUENOCOBA under the EU Horizon 2020 program (Grant No. 742102) and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Project No. 414325145 in the framework of the Austrian Science Fund (FWF): SFB F7104. Publisher Copyright: {\textcopyright} 2021 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the {"}https://creativecommons.org/licenses/by/4.0/{"}Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.",

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N1 - Funding Information: We thank Martin Plenio, Mischa Woods, Christiane Koch, and Archak Purkayastha for pointing us to relevant literature on this topic. R. T. acknowledges Max Planck Harvard research center for support from the quantum optics (MPHQ) postdoctoral fellowship. We acknowledge support from the ERC Advanced Grant QUENOCOBA under the EU Horizon 2020 program (Grant No. 742102) and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Project No. 414325145 in the framework of the Austrian Science Fund (FWF): SFB F7104. Publisher Copyright: © 2021 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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N2 - 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.

AB - 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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