DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Linear-algebraic bath transformation for simulating complex open quantum systems

Abstract

In studying open quantum systems, the environment is often approximated as a collection of non-interacting harmonic oscillators, a configuration also known as the star-bath model. It is also well known that the star-bath can be transformed into a nearest-neighbor interacting chain of oscillators. The chain-bath model has been widely used in renormalization group approaches. The transformation can be obtained by recursion relations or orthogonal polynomials. Based on a simple linear algebraic approach, we propose a bath partition strategy to reduce the system-bath coupling strength. As a result, the non-interacting star-bath is transformed into a set of weakly coupled multiple parallel chains. Furthermore, the transformed bath model allows complex problems to be practically implemented on quantum simulators, and it can also be employed in various numerical simulations of open quantum dynamics.

Authors:
 [1];  [1];  [1];  [2];  [1]
  1. Harvard Univ., Cambridge, MA (United States)
  2. Tsinghua Univ., Beijing (China)
Publication Date:
Research Org.:
Energy Frontier Research Centers (EFRC), Washington, D.C. (United States). Center for Excitonics (CE)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1210677
Grant/Contract Number:  
SC0001088
Resource Type:
Accepted Manuscript
Journal Name:
New Journal of Physics
Additional Journal Information:
Journal Volume: 16; Journal Issue: 12; Related Information: CE partners with Massachusetts Institute of Technology (lead); Brookhaven National Laboratory; Harvard University; Journal ID: ISSN 1367-2630
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; solar (photovoltaic); solid state lighting; photosynthesis (natural and artificial); charge transport; optics; synthesis (novel materials); synthesis (self-assembly); synthesis (scalable processing)

Citation Formats

Huh, Joonsuk, Mostame, Sarah, Fujita, Takatoshi, Yung, Man -Hong, and Aspuru-Guzik, Alan. Linear-algebraic bath transformation for simulating complex open quantum systems. United States: N. p., 2014. Web. doi:10.1088/1367-2630/16/12/123008.
Huh, Joonsuk, Mostame, Sarah, Fujita, Takatoshi, Yung, Man -Hong, & Aspuru-Guzik, Alan. Linear-algebraic bath transformation for simulating complex open quantum systems. United States. https://doi.org/10.1088/1367-2630/16/12/123008
Huh, Joonsuk, Mostame, Sarah, Fujita, Takatoshi, Yung, Man -Hong, and Aspuru-Guzik, Alan. Tue . "Linear-algebraic bath transformation for simulating complex open quantum systems". United States. https://doi.org/10.1088/1367-2630/16/12/123008. https://www.osti.gov/servlets/purl/1210677.
@article{osti_1210677,
title = {Linear-algebraic bath transformation for simulating complex open quantum systems},
author = {Huh, Joonsuk and Mostame, Sarah and Fujita, Takatoshi and Yung, Man -Hong and Aspuru-Guzik, Alan},
abstractNote = {In studying open quantum systems, the environment is often approximated as a collection of non-interacting harmonic oscillators, a configuration also known as the star-bath model. It is also well known that the star-bath can be transformed into a nearest-neighbor interacting chain of oscillators. The chain-bath model has been widely used in renormalization group approaches. The transformation can be obtained by recursion relations or orthogonal polynomials. Based on a simple linear algebraic approach, we propose a bath partition strategy to reduce the system-bath coupling strength. As a result, the non-interacting star-bath is transformed into a set of weakly coupled multiple parallel chains. Furthermore, the transformed bath model allows complex problems to be practically implemented on quantum simulators, and it can also be employed in various numerical simulations of open quantum dynamics.},
doi = {10.1088/1367-2630/16/12/123008},
journal = {New Journal of Physics},
number = 12,
volume = 16,
place = {United States},
year = {Tue Dec 02 00:00:00 EST 2014},
month = {Tue Dec 02 00:00:00 EST 2014}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 15 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Charge and Energy Transfer Dynamics in Molecular Systems
book, February 2011


Numerical Renormalization Group for Bosonic Systems and Application to the Sub-Ohmic Spin-Boson Model
journal, October 2003


Numerical renormalization group for quantum impurities in a bosonic bath
journal, January 2005


Atomistic Study of Energy Funneling in the Light-Harvesting Complex of Green Sulfur Bacteria
journal, January 2014

  • Huh, Joonsuk; Saikin, Semion K.; Brookes, Jennifer C.
  • Journal of the American Chemical Society, Vol. 136, Issue 5
  • DOI: 10.1021/ja412035q

Quantum Dynamics of System Strongly Coupled to Low-Temperature Colored Noise Bath: Reduced Hierarchy Equations Approach
journal, December 2005

  • Ishizaki, Akihito; Tanimura, Yoshitaka
  • Journal of the Physical Society of Japan, Vol. 74, Issue 12
  • DOI: 10.1143/JPSJ.74.3131

Theoretical examination of quantum coherence in a photosynthetic system at physiological temperature
journal, October 2009

  • Ishizaki, A.; Fleming, G. R.
  • Proceedings of the National Academy of Sciences, Vol. 106, Issue 41
  • DOI: 10.1073/pnas.0908989106

High-Performance Solution of Hierarchical Equations of Motion for Studying Energy Transfer in Light-Harvesting Complexes
journal, June 2011

  • Kreisbeck, Christoph; Kramer, Tobias; Rodríguez, Mirta
  • Journal of Chemical Theory and Computation, Vol. 7, Issue 7
  • DOI: 10.1021/ct200126d

Open System Dynamics with Non-Markovian Quantum Trajectories
journal, March 1999


Stochastic simulation of dissipation and non-Markovian effects in open quantum systems
journal, April 2008


Derivation of exact master equation with stochastic description: Dissipative harmonic oscillator
journal, November 2011


Nonperturbative stochastic method for driven spin-boson model
journal, January 2013


Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials
journal, September 2010

  • Chin, Alex W.; Rivas, Ángel; Huelga, Susana F.
  • Journal of Mathematical Physics, Vol. 51, Issue 9
  • DOI: 10.1063/1.3490188

Efficient Simulation of Strong System-Environment Interactions
journal, July 2010


Generalized Polaron Ansatz for the Ground State of the Sub-Ohmic Spin-Boson Model: An Analytic Theory of the Localization Transition
journal, October 2011


Exciton transfer dynamics and quantumness of energy transfer in the Fenna-Matthews-Olson complex
journal, October 2011


The renormalization group: Critical phenomena and the Kondo problem
journal, October 1975


Effect of friction on electron transfer in biomolecules
journal, November 1985

  • Garg, Anupam; Onuchic, José Nelson; Ambegaokar, Vinay
  • The Journal of Chemical Physics, Vol. 83, Issue 9
  • DOI: 10.1063/1.449017

Collective electronic oscillators for nonlinear optical response of conjugated molecules
journal, August 1996


A Continued-Fraction Representation of the Time-Correlation Functions
journal, September 1965


Moment and Continued Fraction Expansions of Time Autocorrelation Functions
journal, March 1967


Phonon thermal baths: A treatment in terms of reduced models
journal, April 1982


Non-Markovian reduced dynamics based upon a hierarchical effective-mode representation
journal, October 2012

  • Burghardt, Irene; Martinazzo, Rocco; Hughes, Keith H.
  • The Journal of Chemical Physics, Vol. 137, Issue 14
  • DOI: 10.1063/1.4752078

Exciton dissociation at donor-acceptor heterojunctions: Dynamics using the collective effective mode representation of the spin-boson model
journal, January 2014

  • Chenel, Aurélie; Mangaud, Etienne; Burghardt, Irene
  • The Journal of Chemical Physics, Vol. 140, Issue 4
  • DOI: 10.1063/1.4861853

Chain-boson model for the decoherence and relaxation of a few coupled SQUIDs in a phonon bath
journal, July 2008


Application of the coherent state formalism to multiply excited states
journal, June 2005


Simulating physics with computers
journal, June 1982

  • Feynman, Richard P.
  • International Journal of Theoretical Physics, Vol. 21, Issue 6-7
  • DOI: 10.1007/BF02650179

Universal Quantum Simulators
journal, August 1996


Quantum Simulators
journal, October 2009


On-chip quantum simulation with superconducting circuits
journal, April 2012

  • Houck, Andrew A.; Türeci, Hakan E.; Koch, Jens
  • Nature Physics, Vol. 8, Issue 4
  • DOI: 10.1038/nphys2251

Quantum simulator of an open quantum system using superconducting qubits: exciton transport in photosynthetic complexes
journal, October 2012


A scalable quantum computer with ions in an array of microtraps
journal, April 2000


Analog superconducting quantum simulator for Holstein polarons
journal, December 2013


Digital Quantum Simulation of Spin Systems in Superconducting Circuits
journal, May 2014


Transmon-based simulator of nonlocal electron-phonon coupling: A platform for observing sharp small-polaron transitions
journal, April 2014

  • Stojanović, Vladimir M.; Vanević, Mihajlo; Demler, Eugene
  • Physical Review B, Vol. 89, Issue 14
  • DOI: 10.1103/PhysRevB.89.144508

Analogue of Cosmological Particle Creation in an Ion Trap
journal, November 2007


Quantum Simulation of the Klein Paradox with Trapped Ions
journal, February 2011


Quantum Simulation of Quantum Field Theories in Trapped Ions
journal, December 2011


Quantum Simulation of the Majorana Equation and Unphysical Operations
journal, December 2011


Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions
journal, May 2012


Quantum simulations with trapped ions
journal, April 2012


Quantum Simulation of Small-Polaron Formation with Trapped Ions
journal, December 2012


Quantum simulation of dynamical maps with trapped ions
journal, May 2013

  • Schindler, P.; Müller, M.; Nigg, D.
  • Nature Physics, Vol. 9, Issue 6
  • DOI: 10.1038/nphys2630

Towards quantum chemistry on a quantum computer
journal, January 2010

  • Lanyon, B. P.; Whitfield, J. D.; Gillett, G. G.
  • Nature Chemistry, Vol. 2, Issue 2
  • DOI: 10.1038/nchem.483

Quantum simulator for the Schwinger effect with atoms in bichromatic optical lattices
journal, November 2011


Tunable Holstein model with cold polar molecules
journal, November 2011


Photonic quantum simulators
journal, April 2012

  • Aspuru-Guzik, Alán; Walther, Philip
  • Nature Physics, Vol. 8, Issue 4
  • DOI: 10.1038/nphys2253

Quantum simulations with ultracold quantum gases
journal, April 2012

  • Bloch, Immanuel; Dalibard, Jean; Nascimbène, Sylvain
  • Nature Physics, Vol. 8, Issue 4
  • DOI: 10.1038/nphys2259

NMR Implementation of a Molecular Hydrogen Quantum Simulation with Adiabatic State Preparation
journal, January 2010


Simulation of Chemical Isomerization Reaction Dynamics on a NMR Quantum Simulator
journal, July 2011


Accounting for intra-molecular vibrational modes in open quantum system description of molecular systems
journal, November 2012

  • Roden, Jan; Strunz, Walter T.; Whaley, K. Birgitta
  • The Journal of Chemical Physics, Vol. 137, Issue 20
  • DOI: 10.1063/1.4765329

Experimental simulation of quantum tunneling in small systems
journal, August 2013

  • Feng, Guan-Ru; Lu, Yao; Hao, Liang
  • Scientific Reports, Vol. 3, Issue 1
  • DOI: 10.1038/srep02232

Quantum simulator for the O(3) nonlinear sigma model
journal, September 2005

  • Schützhold, R.; Mostame, S.
  • Journal of Experimental and Theoretical Physics Letters, Vol. 82, Issue 5
  • DOI: 10.1134/1.2130906

Quantum Simulator for the Ising Model with Electrons Floating on a Helium Film
journal, November 2008


Collective coordinates for nuclear spectral densities in energy transfer and femtosecond spectroscopy of molecular aggregates
journal, September 1996

  • Chernyak, Vladimir; Mukamel, Shaul
  • The Journal of Chemical Physics, Vol. 105, Issue 11
  • DOI: 10.1063/1.472302

Exact master equation and quantum decoherence of two coupled harmonic oscillators in a general environment
journal, January 2008


Quantum Phase Transitions in the Sub-Ohmic Spin-Boson Model: Failure of the Quantum-Classical Mapping
journal, February 2005


Memory-Assisted Exciton Diffusion in the Chlorosome Light-Harvesting Antenna of Green Sulfur Bacteria
journal, August 2012

  • Fujita, Takatoshi; Brookes, Jennifer C.; Saikin, Semion K.
  • The Journal of Physical Chemistry Letters, Vol. 3, Issue 17
  • DOI: 10.1021/jz3008326

Theoretical characterization of excitation energy transfer in chlorosome light-harvesting antennae from green sulfur bacteria
journal, February 2014

  • Fujita, Takatoshi; Huh, Joonsuk; Saikin, Semion K.
  • Photosynthesis Research, Vol. 120, Issue 3
  • DOI: 10.1007/s11120-014-9978-7

On the alternatives for bath correlators and spectral densities from mixed quantum-classical simulations
journal, December 2012

  • Valleau, Stéphanie; Eisfeld, Alexander; Aspuru-Guzik, Alán
  • The Journal of Chemical Physics, Vol. 137, Issue 22
  • DOI: 10.1063/1.4769079

Effective-mode representation of non-Markovian dynamics: A hierarchical approximation of the spectral density. I. Application to single surface dynamics
journal, July 2009

  • Hughes, Keith H.; Christ, Clara D.; Burghardt, Irene
  • The Journal of Chemical Physics, Vol. 131, Issue 2
  • DOI: 10.1063/1.3159671

Molecular Mechanisms of Photosynthesis
book, December 2002


Reducing a matrix to Hessenberg form
journal, January 1969


Scaling and localization lengths of a topologically disordered system
text, January 2011


On the alternatives for bath correlators and spectral densities from mixed quantum-classical simulations
text, January 2012


Works referencing / citing this record:

Hierarchical Equations for Open System Dynamics in Fermionic and Bosonic Environments
journal, March 2015


Phonon-mediated repulsion, sharp transitions and (quasi)self-trapping in the extended Peierls-Hubbard model
journal, April 2017


Universal bound on sampling bosons in linear optics and its computational implications
journal, April 2019

  • Yung, Man-Hong; Gao, Xun; Huh, Joonsuk
  • National Science Review, Vol. 6, Issue 4
  • DOI: 10.1093/nsr/nwz048

Pseudomodes and the corresponding transformation of the temperature-dependent bath correlation function
journal, May 2015


Electron pumping in the strong coupling and non-Markovian regime: A reaction coordinate mapping approach
journal, July 2019


Hierarchical equations for open system dynamics in fermionic and bosonic environments
text, January 2014


Pseudomodes and the corresponding transformation of the temperature-dependent bath correlation function
text, January 2015