Observing Floquet topological order by symmetry resolution

Azses, Daniel; Torre, Emanuele G. Dalla; Sela, Eran

doi:10.1103/physrevb.104.l220301

Cited by 18 publications

(3 citation statements)

References 51 publications

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“…These states include the cluster states as special cases and were shown to share common properties, for instance as universal resources of measurement-based quantum computations [67,68]. To address the error correction capabilities of SPT states it may be useful to extend the concept of symmetry-resolved entanglement [42,[69][70][71][72][73][74][75][76] to the multi-partite regime.…”

Section: Discussionmentioning

confidence: 99%

Multipartite entanglement and quantum error identification in $D$-dimensional cluster states

Sowrabh¹,

Azses²,

Torre³

et al. 2023

Preprint

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An entangled state is said to be m-uniform if the reduced density matrix of any m qubits is maximally mixed. This formal definition is known to be intimately linked to pure quantum error correction codes (QECCs), which allow not only to correct errors, but also to identify their precise nature and location. Here, we show how to create m-uniform states using local gates or interactions and elucidate several QECC applications. We first point out that D-dimensional cluster states, i.e. the ground states of frustration-free local cluster Hamiltonians, are m-uniform with m = 2D. We discuss finite size limitations of m-uniformity and how to achieve larger m values using quasi-D dimensional cluster states. We demonstrate experimentally on a superconducting quantum computer that the 1D cluster state allows to detect and identify 1-qubit errors, distinguishing, X, Y and Z errors. Finally, we show that m-uniformity allows to formulate pure QECCs with a finite logical space.

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Section: Discussionmentioning

confidence: 99%

Multipartite entanglement and quantum error identification in $D$-dimensional cluster states

Sowrabh¹,

Azses²,

Torre³

et al. 2023

Preprint

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“…Finally, we consider the way in which the entanglement splits into different charge sectors of a theory with a global symmetry, quantitatively determined by the symmetry-resolved entanglement measures. This phenomenon has attracted significant attention, sparked by some recent theoretical [57][58][59] and experimental [60,61] results, and has been studied in several contexts as lattice systems [62][63][64][65][66][67][68][69], quantum field theories [60,61,[70][71][72] and holography [73].…”

Section: 2)mentioning

confidence: 99%

Probing RG flows, symmetry resolution and quench dynamics through the capacity of entanglement

Arias¹,

Giulio²,

Keski-Vakkuri³

et al. 2023

Preprint

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We compare the capacity of entanglement with the entanglement entropy by considering various aspects of these quantities for free bosonic and fermionic models in one spatial dimension, both in the continuum and on the lattice. Substantial differences are observed in the subleading terms of these entanglement quantifiers when the subsystem is made by two disjoint intervals, in the massive scalar field and in the fermionic chain. We define c-functions based on the capacity of entanglement similar to the one based on the entanglement entropy, showing through a numerical analysis that they display a monotonic behaviour under the renormalisation group flow generated by the mass. The capacity of entanglement and its related quantities are employed to explore the symmetry resolution. The temporal evolutions of the capacity of entanglement and of the corresponding contour function after a global quench are also discussed.

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“…Specifically, it is given by the sum of entropies for each choice of these quantum numbers in one subsystem. The Rényi moments of the symmetry-resolved entanglement are experimentally measurable [10][11][12][13] as also demonstrated for onedimensional SPT states [14,15] on IBM quantum computers. For such states, each symmetry sector contributes equally to the total entropy [16].…”

Section: Introductionmentioning

confidence: 99%

Symmetry-resolved entanglement in symmetry-protected topological phases

Azses

Sela

2020

Phys. Rev. B

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Symmetry-resolved entanglement is a useful tool for characterizing symmetry-protected topological states. In two dimensions, their entanglement spectra are described by conformal field theories but the symmetry resolution is largely unexplored. However, addressing this problem numerically requires system sizes beyond the reach of exact diagonalization. Here, we develop tensor network methods that can access much larger systems and determine universal and nonuniversal features in their entanglement. Specifically, we construct one-dimensional matrix product operators that encapsulate all the entanglement data of two-dimensional symmetry-protected topological states. We first demonstrate our approach for the Levin-Gu model. Next, we use the cohomology formalism to deform the phase away from the fine-tuned point and track the evolution of its entanglement features and their symmetry resolution. The entanglement spectra are always described by the same conformal field theory. However, the levels undergo a spectral flow in accordance with an insertion of a many-body Aharonov-Bohm flux.

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Observing Floquet topological order by symmetry resolution

Cited by 18 publications

References 51 publications

Multipartite entanglement and quantum error identification in $D$-dimensional cluster states

Multipartite entanglement and quantum error identification in $D$-dimensional cluster states

Probing RG flows, symmetry resolution and quench dynamics through the capacity of entanglement

Symmetry-resolved entanglement in symmetry-protected topological phases

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