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Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise
Open accessAbstract
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.
Overview
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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.
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11 No basis given · 10 Own interpretation · 5 Not checked yet
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In the paper
“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”
§ Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise > P H Y S I C A L R E V I E W L E T T E R S
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In the paper
“The obtained master equation is exact to all orders in U.”
§ Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise > P H Y S I C A L R E V I E W L E T T E R S
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In the paper
“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.”
§ Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise > P H Y S I C A L R E V I E W L E T T E R S
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- The authors state this as an assumption: The initial state is deterministically prepared in a pure state at t = 0.
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In the paper
“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.”
§ Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise > Abstract
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In the paper
“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.”
§ Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise > P H Y S I C A L R E V I E W L E T T E R S
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In the paper
“Markovian dynamics can be accessed with white-noise fluctuations; non-Markovian dynamics requires colored noise.”
- Also stated in: § Abstract · plain
“Markovian dynamics can be accessed modulating the coupling constants with a white noise; non-Markovian dynamics requires colored noise.”
§ Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise > Abstract
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In the paper
“Markovian dynamics can be accessed with white-noise fluctuations; non-Markovian dynamics requires colored noise.”
- Also stated in: § Abstract · plain
“Such a general evolution can be obtained using colored noise.”
- 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
“Non-Markovian effects can be accessed using colored noise.”
§ Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise > Abstract
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In the paper
“By adding a white-noise contribution to the interactions, J ij → J ij þ ℏ ffiffi ffi γ p ηðtÞ, our results predict that the noise-averaged density matrix then obeys a master equation ( 6), where the target Hamiltonian is that of the Ising chain (19) and the dissipator takes a many-body nonlocal form given by D½ρðtÞ ¼ -γ X i<j X i 0 <j 0 [σ z i σ z j ; ½σ z i 0 σ z j 0 ; ρðtÞ]:ð20Þ”
§ Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise > P H Y S I C A L R E V I E W L E T T E R S
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In the paper
“The time scale governing the fidelity decay under many-body decoherence is shown to scale as N -2k with the system size N.”
- 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
“i.e. the decoherence time τ D scales as N -2k where N ≫ k is the number of particles in the quantum simulator and k denotes the range of the interaction terms.”
- Also stated in: § P H Y S I C A L R E V I E W L E T T E R S · hedged
“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.”
§ Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise > Abstract
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- 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
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We introduce a scheme for the quantum simulation of many-body decoherence based on the unitary evolution of a stochastic Hamiltonian.”
- Also stated in: § Abstract · plain
“In this Letter, we introduce a versatile scheme for the quantum simulation of the open dynamics of a many-body system embedded in an environment to which it couples via many-body interactions.”
- 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
“To summarize, we have developed a scheme for the quantum simulation of many-body decoherence, where classical noise is a tool used to facilitate the experimental realization of such a simulation.”
§ Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise > Abstract
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- It may state two separate claims as one. 7
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In the paper
“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].”
§ Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise > P H Y S I C A L R E V I E W L E T T E R S
What the sources say
- Not checked yetcites [40] source
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- The authors state this as an assumption: The initial state is deterministically prepared in a pure state at t = 0.
- 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 paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“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.”
§ Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise > P H Y S I C A L R E V I E W L E T T E R S
plaincorrelational- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- The authors state this as an assumption: The initial state is deterministically prepared in a pure state at t = 0.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“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”
§ Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise > P H Y S I C A L R E V I E W L E T T E R S
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- 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
In the paper
“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].”
§ Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise > Abstract
What the sources say
- Not checked yetcites [35] source
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None of the sources cited for this claim have been checked yet.
In the paper
“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”
§ Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise > Abstract
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In the paper
“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].”
§ Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise > P H Y S I C A L R E V I E W L E T T E R S
What the sources say
- Not checked yetcites [43] source
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In the paper
“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].”
§ Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise > Abstract
What the sources say
- Not checked yetcites [37] source
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“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.”
§ Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise > Abstract
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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.”
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“Finally, it is worth noting that the quantum speed limit time also sets the time-scale over which decoherence is effective [30,156,157].”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [156]
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In the paper
§ Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise > P H Y S I C A L R E V I E W L E T T E R S
“1 τ D ¼ X α γ α ΔL 2 α ≤ 1 4 X α γ α ∥ Lα ∥ 2 ;ð15Þ”
§ Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise > Abstract
“D½ρðtÞ ¼ - X α γ α [ Lα ; ½ Lα ; ρðtÞ];ð10Þ”
Citations
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Metadata
- Authors
- Chenu, A., Beau, M., Cao, J., & del Campo, A.
- Affiliations
- Massachusetts Institute of Technology (US)
- University of Massachusetts Boston (US)
- 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
- 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
- bronze
- doi.org
- 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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