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Cited by 160Quantum many-body systemsQuantum Computing Algorithms and ArchitectureQuantum Mechanics and Applications

Quantum simulation of generic many-body open system dynamics using classical noise

Open access
Chenu, A., Beau, M., Cao, J., del Campo, A.·2017·Physical Review Letters
DOI 10.1103/physrevlett.118.140403
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Abstract

We introduce a scheme for the quantum simulation of many-body decoherence based on the unitary evolution of a stochastic Hamiltonian. Modulating the strength of the interactions with stochastic processes, we show that the noise-averaged density matrix simulates an effectively open dynamics governed by k-body Lindblad operators. Markovian dynamics can be accessed with white-noise fluctuations; non-Markovian dynamics requires colored noise. The time scale governing the fidelity decay under many-body decoherence is shown to scale as N^{-2k} with the system size N. Our proposal can be readily implemented in a variety of quantum platforms including optical lattices, superconducting circuits, and trapped ions.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper proposes simulating many-body open-system dynamics by adding classical stochastic noise to the coupling constants of a unitary quantum simulator. Averaging over noise realizations produces an effective master equation with many-body Lindblad operators, with white noise giving Markovian dynamics and colored noise enabling non-Markovian dynamics.

Key findings

  • The noise-averaged density matrix evolves under a master equation whose dissipator contains many-body Lindblad operators inherited from the stochastic terms in the simulator Hamiltonian.
  • For white noise, the dissipator takes diagonal Lindblad form; for real white noise it becomes unital and purity decays monotonically.
  • The decoherence time scales as \(N^{-2k}\) for \(N\) particles and \(k\)-body interactions, with the bound \(1/\tau_D \le \binom{N}{k}^2 \sum_\alpha \gamma_\alpha \|L^{(\alpha,k)}\|^2/4 \sim N^{2k}/k!^2 \sum_\alpha \gamma_\alpha \|L^{(\alpha,k)}\|^2/4\).
  • In the long-range Ising example, \(\tau_D \sim 1/N^2\) for a product state and \(\tau_D \sim 1/N^4\) for maximally entangled states, where the bound is saturated.

Methods

  • Theoretical quantum-simulation proposal: a target many-body Hamiltonian is supplemented by stochastic terms \(\sum_\alpha \lambda_\alpha(t) L_\alpha\), with Gaussian noise fields and coupling strengths \(\lambda_\alpha(t)=\hbar\sqrt{\gamma_\alpha}\,\eta_\alpha(t)\).
  • The noise-averaged dynamics is derived using Novikov’s theorem; the Markovian limit is obtained with white noise, while non-Markovian dynamics is treated perturbatively to second order in noise strength using colored noise.
  • Two illustrative platforms are discussed: a Bose-Hubbard model in an optical lattice with stochastic on-site interaction, and a long-range transverse-field Ising chain with stochastic spin-spin couplings.

Limitations

  • The paper states that solving the non-Markovian master equation requires stochastic unraveling or perturbative schemes, and the explicit non-Markovian treatment is second order in noise strength.
  • The scheme assumes Hermitian simulator and target Hamiltonians; implementing non-Hermitian stochastic terms is stated to be outside its scope.
  • Evident from the text: the work is a theoretical proposal without experimental demonstration or numerical simulations, and it relies on Gaussian, independent noise processes and permutation-symmetric \(k\)-body Lindblad operators.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1103/physrevlett.118.140403

Cites

45 of 45 references verified0 citation errors · 0 not checkable

Statistics

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Claims the paper makes

0 of 6 cited sources checked · 0 supported · 0 flagged

  • Findingreasoning

    For the Bose-Hubbard model with stochastic modulation of U via real white noise, the noise-averaged density matrix evolves with a dissipator given by a double sum over sites of commutators of n_i(n_i-1).

    “Our scheme shows that its stochastic modulation via a single real white noise, U → U þ 2ℏ ffiffi ffi γ p ηðtÞ, makes the dynamics of the noise-averaged density matrix effectively open.”
    • Also stated in: § P H Y S I C A L R E V I E W L E T T E R S · plain
      “The evolution is then dictated by the master equation ( 6) with the dissipator D½ρðtÞ ¼ -γ X i;j ½ ni ð ni -1Þ; ½ nj ð nj -1Þ; ρðtÞ:ð18Þ”
    Quote in the paperSubstantial claim
  • Findingreasoning

    The obtained master equation for the Bose-Hubbard case is exact to all orders in U.

    “The obtained master equation is exact to all orders in U.”
    Quote in the paperSubstantial claim
  • Findingreasoning

    For the long-range Ising chain, up to parity effects, the decoherence time scales as 1/N^2 for large N for an initial product state.

    “Up to parity effects, the decoherence time scales quadratically with the particle number, τ D ∼ 1=N 2 , for large N for an initial product state.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The initial state is deterministically prepared in a pure state at t = 0.
  • Findingreasoning

    Modulating interaction strengths with stochastic processes makes the noise-averaged density matrix simulate open dynamics governed by k-body Lindblad operators.

    “Modulating the strength of the interactions with stochastic processes, we show that the noise-averaged density matrix simulates an effectively open dynamics governed by k-body Lindblad operators.”
    • Also stated in: § Abstract · plain
      “we focus on the addition of noise (understood as a stochastic modulation in time) to the coupling constants of k-body operators in the Hamiltonian, and show that the ensemble-average over noise realizations is described by a density matrix that evolves according to a master equation with many-body Lindblad operators.”
    • Also stated in: § P H Y S I C A L R E V I E W L E T T E R S · plain
      “Averaging over the noise realizations yields an effectively open dynamics, which describes a wide variety of master equations characterized by many-body decoherence.”
    Quote in the paperSubstantial claim
  • Findingnone given

    The characteristic time scale of evolution, estimated from fidelity decay, exhibits a strong signature of many-body decoherence as a function of system size.

    “The characteristic time scale of evolution, as estimated from the fidelity decay, exhibits a strong signature of many-body decoherence as a function of the system size.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The initial state is deterministically prepared in a pure state at t = 0.
  • May combine two claims. 7
  • The quote only partly states this claim. 1
  • Classified as probably not a substantial claim. 1

  • May combine two claims.

    Findingcitation

    In the real white-noise case, the fidelity decay rate 1/τ_D equals the sum of γ_α ΔL_α^2 and is bounded by 1/4 Σ γ_α ||L_α||^2.

    “where 1 τ D ¼ X α γ α ΔL 2 α ≤ 1 4 X α γ α ∥ Lα ∥ 2 ;ð15Þ”
    • Also stated in: § P H Y S I C A L R E V I E W L E T T E R S · plain
      “The inequality follows from using the seminorm of the Hermitian operator Lα -the difference between its largest and lowest eigenvalue-as an upper bound for the variance [40].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [40] source

      Not checked in the free run.

    • The authors state this as an assumption: The initial state is deterministically prepared in a pure state at t = 0.

  • May combine two claims.

    Findingreasoning

    For maximally entangled states in the long-range Ising chain, the bound is saturated and the enhancement scales as 1/N^4.

    “By contrast, for maximally entangled states, the bound ( 16) is saturated and the enhancement scales as τ D ∼ 1=N 4 , a telltale sign of many-body decoherence.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The initial state is deterministically prepared in a pure state at t = 0.

  • May combine two claims.

    Findingreasoning

    The noise-averaged dynamics under stochastic Hamiltonians exhibits linear fidelity decay, with a decoherence time revealing many-body decoherence.

    “Here, we recover the linear dynamics for the noise-averaged dynamics under stochastic Hamiltonians such as (2), but with a decoherence time that now reveals a strong signature of many-body decoherence.”
    • Also stated in: § P H Y S I C A L R E V I E W L E T T E R S · plain
      “It is found that FðtÞ ¼ 1 -t=τ D þ Oðt 2 Þ”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The initial state is deterministically prepared in a pure state at t = 0.

  • May combine two claims. The quote only partly states this claim.

    Findingreasoning

    If the stochastic processes are real, the Lα operators are Hermitian and the resulting dissipator is unital, leading to monotonic decay of purity.

    “Notice that, if the stochastic processes are taken to be real from the beginning (η 00 α ðtÞ ¼ 0), the Lα operators in (2) then fulfill Hermiticity.”
    • Also stated in: § Abstract · plain
      “The noise-averaged dynamics thus leads to a monotonic decay of purity [35].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [35] source

      Not checked in the free run.

  • May combine two claims.

    Findingreasoning

    In the Markovian limit with independent white noises, the dissipator depends only on the average density operator and takes diagonal Lindblad form.

    “In particular, the dissipator now only depends on the average density operator hρ st ðtÞi, that we hereafter denote by ρðtÞ to simplify the notation.”
    • Also stated in: § Abstract · plain
      “This form corresponds to the diagonal Lindblad form [33,34] of a Markovian dynamics”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [33] source

      Not checked in the free run.

    • cites [34] source

      Not checked in the free run.

  • May combine two claims.

    Interpretationcitation

    The approach is not restricted to optical lattices and can be applied to ultracold atoms and polar molecules, including scenarios governed by three-body interactions.

    “Clearly, our approach is not restricted to optical lattices and can be applied to ultracold atoms and polar molecules, including scenarios governed by three-body interactions [43].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [43] source

      Not checked in the free run.

  • May combine two claims.

    Interpretationcitation

    A specific non-Markovian evolution can be simulated from a specific type of colored noise, which can be designed using a filter function or Cholesky decomposition.

    “A specific non-Markovian evolution can thereby be simulated from a specific type of colored noises, which can be designed using a filter function convoluted with a white noise signal, as in signal analysis, or via a Cholesky decomposition as described in [37].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [37] source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationnone given

    The proposal can be readily implemented in optical lattices, superconducting circuits, and trapped ions.

    “Our proposal can be readily implemented in a variety of quantum platforms including optical lattices, superconducting circuits, and trapped ions.”
    • Also stated in: § Abstract · plain
      “Our scheme exploits current technologies for digital and analog quantum simulation of unitary dynamics, and can be readily implemented in various experimental platforms such as trapped ions, superconducting circuits, and cold atoms.”
    • Also stated in: § P H Y S I C A L R E V I E W L E T T E R S · plain
      “Further, it can be readily implemented in a variety of platforms, including ultracold atoms in an optical lattice, trapped ions, and superconducting qubits.”
    Quote in the paperNot a substantial claim
8 of 8

  • The authors state this as an assumption.

    The initial state is deterministically prepared in a pure state at t = 0.

    “Assuming the initial state to be deterministically prepared in a pure state jψð0Þi at t ¼ 0, the fidelity simply reads FðtÞ ¼ hψð0ÞjρðtÞjψð0Þi ¼ cos 2 L½ρð0Þ; ρðtÞ.”
1 of 1

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Fidelity-decay rate differs by a factor of two

    Major

    For an initially pure state, the dissipator in Eq. (10) gives an initial fidelity-decay rate of 2∑αγαΔLα2. Equation (15) reports ∑αγαΔLα2 instead, so the stated decoherence time is twice the value implied by the paper's master equation.

1 of 1

Cites

Flagged first, then by citations

Research works printed but not linked: 1

  1. E. A. Novikov, 1965, JETP, 20, 1290

Cited by

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Related

Authors
Chenu, A., Beau, M., Cao, J., & del Campo, A.
Affiliations
  • Massachusetts Institute of Technology (US)
  • University of Massachusetts Boston (US)
ORCID
Venue
Physical Review Letters
Publisher
American Physical Society (APS)
Published
2017-04-05
Volume
118
Issue
14
Pages
140403-140403
ISSN
  • 0031-9007 (ISSN-L)
  • 1079-7114
DOI
10.1103/physrevlett.118.140403
OpenAlex
W2604247548
Semantic Scholar
5b1070ecbcf011be31876b5ab576271444ddadf5
Cited by
160
References
45
Citations by year
2026: 11 · 2025: 31 · 2024: 19 · 2023: 15 · 2022: 17 · 2021: 18 · 2020: 14 · 2019: 10 · 2018: 14 · 2017: 11
FWCI
6.57
Type
journal article
Language
en
Open access
Licence
Locations
  • Physical Review Letters (publishedVersion)
  • arXiv (Cornell University) (publishedVersion)
  • PubMed (publishedVersion)
  • DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc)
  • arXiv (Cornell University)
Funders
  • John Templeton Foundation
  • Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
  • National Science Foundation (CHE-1112825)
  • UMass Boston (P20150000029279)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
Keywords
quantum simulation, open quantum systems, stochastic Hamiltonian, Lindblad operators, non-Markovian dynamics, colored noise, white noise, fidelity decay, system size scaling, hybrid quantum-classical simulation

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