Conversion of projected entangled pair states into a canonical form

Haghshenas, Reza; O’Rourke, Matthew J.; Chan, Garnet Kin‐Lic

doi:10.1103/physrevb.100.054404

Cited by 44 publications

(45 citation statements)

References 48 publications

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“…From the associated leading eigenvectors, as we have shown here, we can in turn to construct a reference dynamics which is nearly optimal for sampling rare trajectories. While PEPS algorithms do not currently allow for bond dimensions comparable to vMPS, they remain a fruitful area of research which is constantly being improved on [71][72][73][74][75][76][77][78][79]. Recent works [80] have shown the effectiveness of using recurrent neural networks (RNN) to approximate the leading eigenstates of tilted generators in two dimensions.…”

Section: Discussionmentioning

confidence: 99%

Optimal sampling of dynamical large deviations via matrix product states

2021

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The large deviation (LD) statistics of dynamical observables is encoded in the spectral properties of deformed Markov generators. Recent works have shown that tensor network methods are well suited to compute the relevant leading eigenvalues and eigenvectors accurately. However, the efficient generation of the corresponding rare trajectories is a harder task. Here we show how to exploit the MPS approximation of the dominant eigenvector to implement an efficient sampling scheme which closely resembles the optimal (so-called "Doob") dynamics that realises the rare events. We demonstrate our approach on three well-studied lattice models, the Fredrickson-Andersen and East kinetically constrained models (KCMs), and the symmetric simple exclusion process (SSEP). We discuss how to generalise our approach to higher dimensions.

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Section: Discussionmentioning

confidence: 99%

Optimal sampling of dynamical large deviations via matrix product states

2021

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“…The developed QDB-based VQE can be readily used in other currently available experimental platforms, such as quantum dots [71] or atoms coupled by (chiral) waveguides [72]. Moreover, we expect that the scaling and parametric efficiency of our results, found for the MPS circuit ansatz, extend to other efficiently-contractible tensor network states [58,61], such as MPS 2 [73,74], thus allowing us to accomodate the entanglement content required to explore higher dimensions. Also, by including simultaneous operations on multiple qubits, it is possible to build manybody wavefunction ansätze beyond tensor networks, ultimately enabling the efficient preparation of quantum states that can not be numerically simulated.…”

Section: Discussionmentioning

confidence: 73%

Variational quantum state preparation via quantum data buses

Kuzmin

Silvi

2020

Quantum

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We propose a variational quantum algorithm to prepare ground states of 1D lattice quantum Hamiltonians specifically tailored for programmable quantum devices where interactions among qubits are mediated by Quantum Data Buses (QDB). For trapped ions with the axial Center-Of-Mass (COM) vibrational mode as single QDB, our scheme uses resonant sideband optical pulses as resource operations, which are potentially faster than off-resonant couplings and thus less prone to decoherence. The disentangling of the QDB from the qubits by the end of the state preparation comes as a byproduct of the variational optimization. We numerically simulate the ground state preparation for the Su-Schrieffer-Heeger model in ions and show that our strategy is scalable while being tolerant to finite temperatures of the COM mode.

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“…Nevertheless, PEPS has recently proven its competitiveness and, for instance, provided new insights for underdoped Hubbard model [9,34,35] and t-J models [5,6,36], for spin- 1 2 [7,8] and spin-1 Kagome-Heisenberg models [37], as well as for the Shastry-Sutherland model [38,39]. At the same time, PEPS is still in its infancy and there is much room for technical progress boosting the performance of the method [40][41][42].…”

Section: Introductionmentioning

confidence: 99%

A beginner's guide to non-abelian iPEPS for correlated fermions

Bruognolo

Delft

et al. 2021

SciPost Phys. Lect. Notes

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Infinite projected entangled pair states (iPEPS) have emerged as a powerful tool for studying interacting two-dimensional fermionic systems. In this review, we discuss the iPEPS construction and some basic properties of this tensor network (TN) ansatz. Special focus is put on (i) a gentle introduction of the diagrammatic TN representations forming the basis for deriving the complex numerical algorithm, and (ii) the technical advance of fully exploiting non-abelian symmetries for fermionic iPEPS treatments of multi-band lattice models. The exploitation of non-abelian symmetries substantially increases the performance of the algorithm, enabling the treatment of fermionic systems up to a bond dimension D=24D=24 on a square lattice. A variety of complex two-dimensional (2D) models thus become numerically accessible. Here, we present first promising results for two types of multi-band Hubbard models, one with 22 bands of spinful fermions of \mathrm{SU}(2)_\mathrm{spin} \otimes \mathrm{SU}(2)_\mathrm{orb}SU(2)spin⊗SU(2)orb symmetry, the other with 33 flavors of spinless fermions of \mathrm{SU}(3)_\mathrm{flavor}SU(3)flavor symmetry.

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Conversion of projected entangled pair states into a canonical form

Cited by 44 publications

References 48 publications

Optimal sampling of dynamical large deviations via matrix product states

Optimal sampling of dynamical large deviations via matrix product states

Variational quantum state preparation via quantum data buses

A beginner's guide to non-abelian iPEPS for correlated fermions

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