Quantum walks reveal topological flat bands, robust edge states and topological phase transitions in cyclic graphs

• URL: http://arxiv.org/abs/2507.17250v2
• Date: Thu, 24 Jul 2025 02:12:02 GMT
• Title: Quantum walks reveal topological flat bands, robust edge states and topological phase transitions in cyclic graphs
• Authors: Dinesh Kumar Panda, Colin Benjamin,
• Abstract summary: Topological phases, edge states, and flat bands are a key resource for topological quantum computing and noise-resilient information processing.<n>We introduce a scheme based on step-dependent quantum walks on cyclic graphs to simulate exotic topological phenomena.<n>We numerically demonstrate that the edge states are robust against moderate static and dynamic gate disorder and remain stable against phase-preserving perturbations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Topological phases, edge states, and flat bands in synthetic quantum systems are a key resource for topological quantum computing and noise-resilient information processing. We introduce a scheme based on step-dependent quantum walks on cyclic graphs, termed cyclic quantum walks (CQWs), to simulate exotic topological phenomena using discrete Fourier transforms and an effective Hamiltonian. Our approach enables the generation of both gapped and gapless topological phases, including Dirac cone-like energy dispersions, topologically nontrivial flat bands, and protected edge states, all without resorting to split-step or split-coin protocols. Odd and even-site cyclic graphs exhibit markedly different spectral characteristics, with rotationally symmetric flat bands emerging exclusively in $4n$-site graphs ($n\in \mathbf{N}$). We analytically establish the conditions for the emergence of topological, gapped flat bands and show that gap closings in rotation space imply the formation of Dirac cones in momentum space. Further, we engineer protected edge states at the interface between distinct topological phases in both odd and even cycle graphs. We numerically demonstrate that the edge states are robust against moderate static and dynamic gate disorder and remain stable against phase-preserving perturbations. This scheme serves as a resource-efficient and versatile platform for engineering topological phases, transitions, edge states, and flat bands in quantum systems, opening new avenues for fault-tolerant quantum technologies.

Related papers

• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation [41.94295877935867]
  We explore the finite-density phase diagram of the single-flavour Gross-Neveu-Wilson (GNW) model.<n>We find a sequence of inhomogeneous ground states that arise through a real-space version of the mechanism of Hilbert-space fragmentation.
  arXiv  Detail & Related papers  (2025-06-23T14:19:35Z)
• Nonlinearity-driven Topology via Spontaneous Symmetry Breaking [79.16635054977068]
  We consider a chain of parametrically-driven quantum resonators coupled only via weak nearest-neighbour cross-Kerr interaction.<n>Topology is dictated by the structure of the Kerr nonlinearity, yielding a non-trivial bulk-boundary correspondence.
  arXiv  Detail & Related papers  (2025-03-15T00:20:45Z)
• Robust Simulations of Many-Body Symmetry-Protected Topological Phase Transitions on a Quantum Processor [7.515748475237134]
  Topology and symmetry play critical roles in characterizing quantum phases of matter.<n>Recent advancements have unveiled symmetry-protected topological (SPT) phases in many-body systems.<n>We demonstrate the robust simulation of many-body ground states of an Ising-cluster model on a quantum computer.
  arXiv  Detail & Related papers  (2025-03-11T18:00:02Z)
• Strain-Tunable Topological Phase Transitions in Line- and Split-Graph Flat-Band Lattices [7.0566221827695506]
  We show that a single mechanical knob drives universal transitions between trivial insulating, Dirac semimetal, and quantum spin-Hall phases across all lattices.<n>The framework yields several flat band lattices that were hitherto absent or largely unexplored in the literature.
  arXiv  Detail & Related papers  (2025-01-20T23:16:37Z)
• Observation of extrinsic topological phases in Floquet photonic lattices [0.0]
  We report the observation of topological phases unique to discrete-step walks.<n>Our work opens new perspectives for the engineering of topological modes for particles subject to quantum walks.
  arXiv  Detail & Related papers  (2024-12-18T20:37:53Z)
• Quantum Signatures of Topological Phase in Bosonic Quadratic System [0.38850145898707145]
  We show that an open bosonic quadratic chain exhibits topology-induced entanglement effect. When the system is in the topological phase, the edge modes can be entangled in the steady state, while no entanglement appears in the trivial phase. Our work reveals that the stationary entanglement can be a quantum signature of the topological phase in bosonic systems.
  arXiv  Detail & Related papers  (2023-09-13T15:18:33Z)
• Geometric phases along quantum trajectories [58.720142291102135]
  We study the distribution function of geometric phases in monitored quantum systems. For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle. For the same parameters, the density matrix does not show any interference.
  arXiv  Detail & Related papers  (2023-01-10T22:05:18Z)
• Topological squashed entanglement: nonlocal order parameter for one-dimensional topological superconductors [0.0]
  We show the end-to-end, long-distance, bipartite squashed entanglement between the edges of a many-body system. For the Kitaev chain in the entire topological phase, the edge squashed entanglement is quantized to log(2)/2, half the maximal Bell-state entanglement, and vanishes in the trivial phase. Such topological squashed entanglement exhibits the correct scaling at the quantum phase transition, is stable in the presence of interactions, and is robust against disorder and local perturbations.
  arXiv  Detail & Related papers  (2022-01-28T10:57:51Z)
• 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)
• Unconventional Floquet topological phases from quantum engineering of band inversion surfaces [2.722229723122409]
  Floquet engineering provides a toolbox for the realization of novel quantum phases without static counterparts. We propose a scheme to realize unconventional Floquet topological phases by engineering local band structures in particular momentum subspace called band surfaces (BISs) This scheme is based on a new bulk-boundary correspondence that for a class of generic $d$-dimensional periodically driven systems, the local topological structure formed in each BIS uniquely determines the features of gapless boundary modes.
  arXiv  Detail & Related papers  (2021-12-02T10:08:20Z)
• Quantum anomalous Hall phase in synthetic bilayers via twistless twistronics [58.720142291102135]
  We propose quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions. We show that our system exhibits topologicalband structures under appropriate conditions.
  arXiv  Detail & Related papers  (2020-08-06T19:58:05Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)

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.