Simulation of open quantum systems by automated compression of arbitrary environments

Cygorek, Moritz; Cosacchi, Michael; Vagov, Alexei; Axt, Vollrath M.; Lovett, Brendon W.; Keeling, Jonathan; Gauger, Erik M.

doi:10.1038/s41567-022-01544-9

Cited by 77 publications

(24 citation statements)

References 54 publications

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“…In this work, similar to some other recent contributions [22,26], we have used the representation of the influence functional within the tensor network language, motivated by the limitations of modeling spatial entanglement growth in quantum dynamics. We have discussed a transverse tensor network contraction algorithm that allows us to compute the influence functional in cases where the analytical form is not known.…”

Section: Discussionmentioning

confidence: 99%

“…Alternatively one can construct an ansatz for the IF; a natural choice is a matrix product state (MPS) in the time direction, which compactly encodes short-range time correlations. This approach has been used in a number of recent works, which, although they do not necessarily use the language of IFs, all proceed by constructing a compressed version of the IF [22] or a closely related object such as the auxiliary density operator as defined in QUAPI [23,24], the process tensor [25,26], or other variants [27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

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Constructing Tensor Network Influence Functionals for General Quantum Dynamics

Ye,

Chan

2021

Preprint

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We describe an iterative formalism to compute influence functionals that describe the general quantum dynamics of a subsystem beyond the assumption of linear coupling to a quadratic bath. We use a space-time tensor network representation of the influence functional and investigate its approximability in terms of the bond dimensions and time-like entanglement in the tensor network description. We study two numerical models, the spin-boson model and a model of interacting hard-core bosons in a 1D harmonic trap. We find that the influence functional and the intermediates involved in its construction can be efficiently approximated by low bond dimension tensor networks in certain dynamical regimes, which allows the quantum dynamics to be accurately computed for longer times than with direct time evolution methods. However, as one iteratively integrates out the bath, the correlations in the influence functional can first increase before decreasing, indicating that the final compressibility of the influence functional is achieved via non-trivial cancellation.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Constructing Tensor Network Influence Functionals for General Quantum Dynamics

Ye,

Chan

2021

Preprint

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“…More recently it has been understood as but one of a family of methods based on producing matrix product operator (MPO) representations of the process tensor [25,32]. This PT-MPO formalism also allows one to devise alternate numerical methods to find the MPO representation of the PT for more general forms of reservoir [34,35]. In the following we will however be focused on the original formalism of TEMPO as a time evolving algorithm.…”

Section: Imaginary-time Tempomentioning

confidence: 99%

Numerical evaluation and robustness of the quantum mean force Gibbs state

Chiu,

Strathearn,

Keeling

2021

Preprint

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We introduce a numerical method to determine the Hamiltonian of Mean Force (HMF) Gibbs state for a quantum system strongly coupled to a reservoir. The method adapts the Time Evolving Matrix Product Operator (TEMPO) algorithm to imaginary time propagation. By comparing the real-time and imaginary-time propagation for a generalized spin-boson model, we confirm that the HMF Gibbs state correctly predicts the steady state. We show that the numerical dynamics match the polaron master equation at strong coupling. We illustrate the potential of the imaginary-time TEMPO approach by exploring reservoir-induced entanglement between qubits.

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“…based on Redfield master equations [17], do not allow us to exactly study the correlations that build between the system and the baths, or even between the baths. Importantly, the effect of the baths may not be additive [11,[18][19][20][21]. One approach that goes beyond these limitations is to simulate both the system and the baths.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic performance of a periodically driven harmonic oscillator correlated with the baths

Chen,

Poletti

2021

Preprint

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We consider a harmonic oscillator under periodic driving and coupled to two harmonic oscillator heat baths at different temperatures. We use the thermofield transformation with chain mapping for this setup which allows us to study the unitary evolution of the system and the baths up to a time long enough to see the emergence of periodic steady state in the system. We characterize this periodic steady state and we show that, by tuning the system and the bath parameters, one can turn this system from an engine to an accelerator or even to a heater. The possibility to study the unitary evolution of system and baths also allow us to evaluate the steady correlations that build between the system and the baths, and correlations that grow between the baths.

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Simulation of open quantum systems by automated compression of arbitrary environments

Cited by 77 publications

References 54 publications

Constructing Tensor Network Influence Functionals for General Quantum Dynamics

Constructing Tensor Network Influence Functionals for General Quantum Dynamics

Numerical evaluation and robustness of the quantum mean force Gibbs state

Thermodynamic performance of a periodically driven harmonic oscillator correlated with the baths

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