Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states

Kohn, Lucas; Tschirsich, Ferdinand; Keck, Maximilian; Plenio, Martin B.; Tamascelli, Dario; Montangero, Simone

doi:10.1103/physreve.97.013301

Cited by 14 publications

(15 citation statements)

References 79 publications

(100 reference statements)

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“…where the angular frequency is defined in Eq. (25). In particular, P 1 (0, t|λ) is periodic with period T N := π/ω N (λ), it is symmetric with respect to λ * = −1/N, and P 1 (0, t|λ * ) = 0, which means that the walker occupies only the outer vertices of the star graph.…”

Section: Star Graphmentioning

confidence: 99%

“…with ω N (λ) defined in Eq. (25). Due to the symmetry of the graph, both the QFI and the FI do not depend on the starting vertex, i.e., the estimation is completely indifferent to the choice of the initially localized state.…”

Section: Complete Graphmentioning

confidence: 99%

“…with ω N (λ) defined in Eq. (25). Hence, a localized state |1 , i.e., an outer vertex, evolves in time according to…”

Section: Star Graphmentioning

confidence: 99%

“…A notable exception exists, though, given by the quantum spatial search, where the perturbation induced by the so-called oracle Hamiltonian has been largely investigated as a tool to induce localization on a desired site [13][14][15][16][17][18]. In fact, quantum walks have found several applications ranging from universal quantum computation [19] to quantum algorithms [20][21][22][23][24][25] and to the study of excitation transport on networks [26][27][28] and biological systems [29,30]. As such, due to the diversity of the physical platforms on which quantum walks have been implemented [31,32], a precise characterization of the quantum-walk Hamiltonian is desired.…”

Section: Introductionmentioning

confidence: 99%

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Continuous-time quantum walks in the presence of a quadratic perturbation

et al. 2020

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We address the properties of continuous-time quantum walks with Hamiltonians of the form H = L + λL 2 , with L the Laplacian matrix of the underlying graph and the perturbation λL 2 motivated by its potential use to introduce next-nearest-neighbor hopping. We consider cycle, complete, and star graphs as paradigmatic models with low and high connectivity and/or symmetry. First, we investigate the dynamics of an initially localized walker. Then we devote attention to estimating the perturbation parameter λ using only a snapshot of the walker dynamics. Our analysis shows that a walker on a cycle graph spreads ballistically independently of the perturbation, whereas on complete and star graphs one observes perturbation-dependent revivals and strong localization phenomena. Concerning the estimation of the perturbation, we determine the walker preparations and the simple graphs that maximize the quantum Fisher information. We also assess the performance of position measurement, which turns out to be optimal, or nearly optimal, in several situations of interest. Besides fundamental interest, our study may find applications in designing enhanced algorithms on graphs.

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Section: Star Graphmentioning

confidence: 99%

Section: Complete Graphmentioning

confidence: 99%

“…with ω N (λ) defined in Eq. (25). Hence, a localized state |1 , i.e., an outer vertex, evolves in time according to…”

Section: Star Graphmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Continuous-time quantum walks in the presence of a quadratic perturbation

et al. 2020

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“…For the examples provided in the main text, chains of n=15 sites are enough to avoid boundary effects. In order to further optimize our simulations, we augmented our TEDOPA code with a reduced-rank randomized singular value decomposition (RRSVD) routine [57,58]. Singular value decomposition (SVD) is at the heart of the dimensionality reduction TEBD relies on.…”

Section: Appendix B Tdmrg Simulations Using the Tedopa Algorithmmentioning

confidence: 99%

A trapped-ion simulator for spin-boson models with structured environments

et al. 2018

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We propose a method to simulate the dynamics of spin-boson models with small crystals of trapped ions where the electronic degree of freedom of one ion is used to encode the spin while the collective vibrational degrees of freedom are employed to form an effective harmonic environment. The key idea of our approach is that a single damped mode can be used to provide a harmonic environment with Lorentzian spectral density. More complex spectral functions can be tailored by combining several individually damped modes. The protocol is especially well-suited to simulate spin-boson models with structured environments. We propose to work with mixed-species crystals such that one species serves to encode the spin while the other species is used to cool the vibrational degrees of freedom to engineer the environment. The strength of the dissipation on the spin can be controlled by tuning the coupling between spin and vibrational degrees of freedom. In this way the dynamics of spin-boson models with macroscopic and non-Markovian environments can be simulated using only a few ions. We illustrate the approach by simulating an experiment with realistic parameters and show by computing quantitative measures that the dynamics is genuinely non-Markovian.

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Quantum probing beyond pure dephasing

et al. 2020

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Quantum probing is the art of exploiting simple quantum systems interacting with a complex environment to extract precise information about some environmental parameters, e.g. the temperature of the environment or its spectral density. Here we analyze the performance of a single-qubit probe in characterizing Ohmic bosonic environments at thermal equilibrium. In particular, we analyze the effects of tuning the interaction Hamiltonian between the probe and the environment, going beyond the traditional paradigm of pure dephasing. In the weak-coupling and short-time regime, we address the dynamics of the probe analytically, whereas numerical simulations are employed in the strong coupling and long-time regime. We then evaluate the quantum Fisher information for the estimation of the cutoff frequency and the temperature of the environment. Our results provide clear evidence that pure dephasing is not optimal, unless we focus attention to short times. In particular, we found several working regimes where the presence of a transverse interaction improves the maximum attainable precision, i.e. it increases the quantum Fisher information. We also explore the role of the initial state of the probe and of the probe characteristic frequency in determining the estimation precision, thus providing quantitative guidelines to design optimized detection to characterize bosonic environments at the quantum level.

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Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states

Cited by 14 publications

References 79 publications

Continuous-time quantum walks in the presence of a quadratic perturbation

Continuous-time quantum walks in the presence of a quadratic perturbation

A trapped-ion simulator for spin-boson models with structured environments

Quantum probing beyond pure dephasing

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