Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise

Chenu, Aurélia; Beau, Mathieu; Cao, Jianshu; Campo, Adolfo del

doi:10.1103/physrevlett.118.140403

Cited by 125 publications

(117 citation statements)

References 44 publications

(75 reference statements)

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“…Such democratic couplings are, however, difficult to create in nature. Recently, those results were extended to describe both open and noisy systems [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited

et al. 2018

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We address the question of whether the super-Heisenberg scaling for quantum estimation is indeed realizable. We unify the results of two approaches. In the first one, the original system is compared with its copy rotated by the parameter-dependent dynamics. If the parameter is coupled to the one-body part of the Hamiltonian, the precision of its estimation is known to scale at most as N −1 (Heisenberg scaling) in terms of the number of elementary subsystems used N. The second approach compares the overlap between the ground states of the parameter-dependent Hamiltonian in critical systems, often leading to an apparent super-Heisenberg scaling. However, we point out that if one takes into account the scaling of time needed to perform the necessary operations, i.e., ensuring adiabaticity of the evolution, the Heisenberg limit given by the rotation scenario is recovered. We illustrate the general theory on a ferromagnetic Heisenberg spin chain example and show that it exhibits such super-Heisenberg scaling of ground-state fidelity around the critical value of the parameter (magnetic field) governing the one-body part of the Hamiltonian. Even an elementary estimator represented by a single-site magnetization already outperforms the Heisenberg behavior providing the N −1.5 scaling. In this case, Fisher information sets the ultimate scaling as N −1.75 , which can be saturated by measuring magnetization on all sites simultaneously. We discuss universal scaling predictions of the estimation precision offered by such observables, both at zero and finite temperatures, and support them with numerical simulations in the model. We provide an experimental proposal of realization of the considered model via mapping the system to ultracold bosons in a periodically shaken optical lattice. We explicitly derive that the Heisenberg limit is recovered when the time needed for preparation of quantum states involved is taken into account.

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“…Such democratic couplings are, however, difficult to create in nature. Recently, those results were extended to describe both open and noisy systems [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited

et al. 2018

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“…By the method introduced in ref. [], we use

H_{normals} false(t false) = γ ξ false(t false) σ_{z}

to describe the effect of environment on the system, where

σ_{z}

is the Pauli matrix and

γ ξ (t)

denotes the system–bath coupling constant. γ will be chosen positive real constant, and

ξ (t)

can be treated as a real stochastic field to represent a real random Gaussian process.…”

Section: In a Dirac–weyl Magnetic Junctionmentioning

confidence: 99%

“…According to ref. [], the Schrödinger equation of Equation can equivalently describe the dynamics of a quantum open system governed by a master equation

\begin{matrix} true \\ right \frac{d}{d t} ρ (t) = - \frac{i}{ℏ} [H_{0}, ρ false(t false)] + \frac{γ^{2}}{2 ℏ^{2}} (() σ_{z} ρ false(t false) σ_{z} - ρ false(t false)) \end{matrix}

where

ρ (t)

denotes the reduced density matrix of the time‐independent target system (see Appendix for details). Then we use the order of generating the stochastic part of Equation to characterize the continuous time t of

ξ (t)

, which is the key technique of our scheme.…”

Section: In a Dirac–weyl Magnetic Junctionmentioning

confidence: 99%

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Effect of Environment on the Scattering of Electrons by a Junction of Different Topological Materials

Shao

2020

Annalen der Physik

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The studies of electron transport through a junction of topological materials in the literature so far ignore the coupling of a topological material to its surrounding environment. Here, the dynamics of an open system through a stochastic Hamiltonian are simulated to investigate the influence of the environment on the scattering of electrons by a junction of different topological materials, such as a Dirac–Weyl magnetic junction and a topological insulator. It is found that, although the detrimental effect of the environment is inevitable, the Landauer conductance can be enhanced via adjusting the system–environment coupling strength. This result supplies the possibilty of changing the transport feature of topological materials by modulating the surrounded environment. It is also demonstrated that a non‐Hermitian Hamiltonian can be used to replace the stochastic Hamiltonian for this study, when the system and the environment coupling are weak.

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“…[2,3,24,25]. The origin of the long-time deviations can be appreciated using the Ersak equation for the survival amplitude [4,26,27] A(t) = A(t − t )A(t ) + m(t, t ),…”

mentioning

confidence: 99%

Nonexponential Quantum Decay under Environmental Decoherence

et al. 2017

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A system prepared in an unstable quantum state generally decays following an exponential law, as environmental decoherence is expected to prevent the decay products from recombining to reconstruct the initial state. Here we show the existence of deviations from exponential decay in open quantum systems under very general conditions. Our results are illustrated with the exact dynamics under quantum Brownian motion and suggest an explanation of recent experimental observations.The exponential decay law of unstable systems is ubiquitous in Nature and has widespread applications [1][2][3]. Yet, in isolated quantum systems deviations occur at both short and long times of evolution [4][5][6]. Short time deviations underlie the quantum Zeno effect [7, 8], ubiquitously used to engineer decoherence free-subspaces and preserve quantum information. Long-time deviations are expected in any nonrelativistic systems with a ground state; they slow down the decay and generally manifest as a power-law in time [9]. Both short and long-time deviations are present as well in manyparticle systems [11][12][13][14][15][16]. Indeed, the latter signal the advent of thermalization in isolated many-body systems [17,18]. In quantum cosmology, power-law deviations constrain the likelihood of scenarios with eternal inflation [10]. They also rule the scrambling of information as measured by the decay of the form factor [19][20][21][22] in blackhole physics and strongly coupled quantum systems described by AdS/CFT, that are believed to be maximally chaotic [23].Given a unstable quantum state |Ψ 0 prepared at time t = 0, it is customary to describe the closed-system decay dynamics via the survival probability, which is the fidelity between the initial state and its time evolution S(t) := |A(t)| 2 = | Ψ 0 |Ψ(t) | 2 .Explicitly, the survival amplitude reads A(t)is the time evolution operator generated by the Hamiltonian of the systemĤ. Short time deviations are associated with the quadratic decayand are generally suppressed by the coupling to an environment that induces the appearance of a term linear in t, see, e.g. [2, 3,24,25]. The origin of the long-time deviations can be appreciated using the Ersak equation for the survival amplitude [4,26,27]that follows from the unitarity of time evolution in isolated quantum systems. The memory term readsHere, we denote the projector onto the space spanned by the initial state byP ≡ |Ψ 0 Ψ 0 | and its orthogonal complement byQ ≡ 1 −P. As a result, the memory term m(t, t ) represents the formation of decay products at an intermediate time t and their subsequent recombination to reconstruct the initial state |Ψ 0 . The suppression of this term leads to the exponential decay law for A(t) and S(t), as an ansatz of the form A(t) = e −γt is a solution of Eq. (3) with m(t, t ) = 0, i.e, A(t) = A(t − t )A(t ). [4,27]. In addition, using the definition of the survival probability and Eq. (3), it has been demonstrated that the long-time non-exponential behavior of S(t) is dominated by |m(t, t )| 2 . The onset of lon...

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Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise

Cited by 125 publications

References 44 publications

At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited

At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited

Effect of Environment on the Scattering of Electrons by a Junction of Different Topological Materials

Nonexponential Quantum Decay under Environmental Decoherence

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