Layer-by-layer disentangling two-dimensional topological quantum codes

• URL: http://arxiv.org/abs/2305.13827v1
• Date: Tue, 23 May 2023 08:49:55 GMT
• Title: Layer-by-layer disentangling two-dimensional topological quantum codes
• Authors: Mohammad Hossein Zarei and Mohsen Rahmani Haghighi
• Abstract summary: We introduce partially local unitary transformations which reduce the dimension of the initial topological model by a layer-by-layer disentangling mechanism. We show that the GHZ disentangler causes a transition from an intrinsic topological phase to a symmetry-protected topological phase. It shows that different topological features of these topological codes are reflected in different patterns of entangling ladders.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: While local unitary transformations are used for identifying quantum states which are in the same topological class, non-local unitary transformations are also important for studying the transition between different topological classes. In particular, it is an important task to find suitable non-local transformations that systematically sweep different topological classes. Here, regarding the role of dimension in the topological classes, we introduce partially local unitary transformations namely Greenberger-Horne-Zeilinger (GHZ) disentanglers which reduce the dimension of the initial topological model by a layer-by-layer disentangling mechanism. We apply such disentanglers to two-dimensional (2D) topological quantum codes and show that they are converted to many copies of Kitaev's ladders. It implies that the GHZ disentangler causes a transition from an intrinsic topological phase to a symmetry-protected topological phase. Then, we show that while Kitaev's ladders are building blocks of both color code and toric code, there are different patterns of entangling ladders in 2D color code and toric code. It shows that different topological features of these topological codes are reflected in different patterns of entangling ladders. In this regard, we propose that the layer-by-layer disentangling mechanism can be used as a systematic method for classification of topological orders based on finding different patterns of the long-range entanglement in topological lattice models.

Related papers

• Topological Tenfold Classification and the Entanglement of Two Qubits [0.0]
  We use the Cartan decomposition to characterize topological properties and their connection to quantum entanglement. Topological features are obtained systematically by a mapping to a quantum graph. An additional perspective is provided regarding the extension of this new approach to condensed matter systems.
  arXiv  Detail & Related papers  (2025-02-04T15:47:19Z)
• Hermitian and Non-Hermitian Topological Transitions Characterized by Manifold Distance [15.87545402988833]
  We propose a general definition based on fidelity and trace distance from quantum information theory: manifold distance (MD) It can measure different topological systems and exhibit some universal laws during the transformation between two topological phases. Compared to the strange correlator, MD is more universal and could be applied to non-Hermitian systems and long-range entangled states.
  arXiv  Detail & Related papers  (2025-01-07T03:05:45Z)
• Relative Representations: Topological and Geometric Perspectives [53.88896255693922]
  Relative representations are an established approach to zero-shot model stitching. We introduce a normalization procedure in the relative transformation, resulting in invariance to non-isotropic rescalings and permutations. Second, we propose to deploy topological densification when fine-tuning relative representations, a topological regularization loss encouraging clustering within classes.
  arXiv  Detail & Related papers  (2024-09-17T08:09:22Z)
• Topological phases of many-body non-Hermitian systems [0.0]
  Many-body fermionic non-Hermitian systems require two sets of topological invariants to describe the topology of energy bands and quantum states respectively. We identify 10 symmetry classes -- determined by particle-hole, linearized time-reversal, and linearized chiral symmetries.
  arXiv  Detail & Related papers  (2023-11-06T11:39:20Z)
• On Topology of the Moduli Space of Gapped Hamiltonians for Topological Phases [0.0]
  We study the moduli space of gapped Hamiltonians in the same topological phase. We show that nontrivial family of gapped systems with the same topological order can protect isolated phase transitions. We argue that family of gapped systems obey a version of bulk-boundary correspondence.
  arXiv  Detail & Related papers  (2022-11-29T19:01:18Z)
• Topological transitions of the generalized Pancharatnam-Berry phase [55.41644538483948]
  We show that geometric phases can be induced by a sequence of generalized measurements implemented on a single qubit. We demonstrate and study this transition experimentally employing an optical platform. Our protocol can be interpreted in terms of environment-induced geometric phases.
  arXiv  Detail & Related papers  (2022-11-15T21:31:29Z)
• Relative homotopy approach to topological phases in quantum walks [0.08896991256227595]
  We show that for translation symmetric systems they can be characterized by a homotopy relative to special points. We propose a new topological invariant corresponding to this concept. This invariant indicates the number of edge states at the interface between two distinct phases.
  arXiv  Detail & Related papers  (2022-09-26T16:27:56Z)
• Topological transitions with continuously monitored free fermions [68.8204255655161]
  We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy.
  arXiv  Detail & Related papers  (2021-12-17T22:01:54Z)
• Bridging the gap between topological non-Hermitian physics and open quantum systems [62.997667081978825]
  We show how to detect a transition between different topological phases by measuring the response to local perturbations. Our formalism is exemplified in a 1D Hatano-Nelson model, highlighting the difference between the bosonic and fermionic cases.
  arXiv  Detail & Related papers  (2021-09-22T18:00:17Z)
• Dynamical solitons and boson fractionalization in cold-atom topological insulators [110.83289076967895]
  We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities. We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors. Using a pumping argument, we show that it survives also for finite interactions.
  arXiv  Detail & Related papers  (2020-03-24T17:31:34Z)
• Bulk detection of time-dependent topological transitions in quenched chiral models [48.7576911714538]
  We show that the winding number of the Hamiltonian eigenstates can be read-out by measuring the mean chiral displacement of a single-particle wavefunction. This implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases.
  arXiv  Detail & Related papers  (2020-01-16T17:44:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.