Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2312.02979

Floquet Chiral Quantum Walk in Quantum Computer

Chan Bin Bark, Young‐Seok Kim, Moon Jip Park

Published Dec 5, 2023• 0 citations
arXivHTMLPDF

Abstract

Chiral edge states in quantum Hall effect are the paradigmatic example of the quasi-particle with chirality. In even space-time dimensions, the Nielsen-Ninomiya theorem strictly forbids the chiral states in physical isolation. The exceptions to this theorem only occur in the presence of non-locality, non-Hermiticity, or by embedding the system at the boundary of the higher-dimensional bulk. In this work, using the IBM quantum computer platform, we realize the floquet chiral quantum walk enabled by non-locality. The unitary time evolution operator is described by the effective floquet Hamiltonian with infinitely long-ranged coupling. We find that the chiral wave packets lack the common features of the conventional wave phenomena such as Anderson localization. The absence of localization is witnessed by the robustness against the external perturbations. However, the intrinsic quantum errors of the current quantum device give rise to the finite lifetime where the chiral wave packet eventually disperses in the long-time limit. Nevertheless, we observe the stability of the chiral wave by comparing it with the conventional non-chiral model.

DOI
10.48550/arxiv.2312.02979

Related papers

Floquet chiral quantum walk in a quantum computer

Chan Bin Bark, Young‐Seok Kim, Moon Jip Park

Chiral edge states in a quantum Hall effect are the paradigmatic example of a quasiparticle with chirality. In even space-time dimensions, the Nielsen-Ninomiya theorem strictly forbids chiral states in physical isolation. The exceptions to this theorem only occur in the presence of nonlocality, non-Hermiticity, or by embedding the system at the boundary of the higher-dimensional bulk. In this Letter, using the IBM quantum computer platform, we realize a Floquet chiral quantum walk enabled by nonlocality. The unitary time-evolution operator is described by an effective Floquet Hamiltonian with long-ranged coupling. We find that the chiral wave packets lack the common features of conventional wave phenomena such as localization. The absence of localization is witnessed by the robustness against external perturbations. However, the intrinsic quantum errors of the current quantum device give rise to a finite lifetime where the chiral wave packet eventually disperses in the long-time limit. Nevertheless, we observe the stability of the chiral wave by comparing it with a conventional nonchiral model.

Physical review. B./Physical review. B•May 15, 2024•0 citations

The chiral random walk: A quantum-inspired framework for odd diffusion

Jan Wójcik, Erik Kalz

Chirality in active and passive fluids gives rise to odd transport properties, most notably the emergence of robust edge currents that defy standard dissipative dynamics. While these phenomena are well-described by continuum hydrodynamics, a microscopic framework connecting them to their topological origins has remained elusive. Here, we present a lattice model for an isotropic chiral random walk that bridges the gap between classical stochastic diffusion and unitary quantum evolution. By equipping the walker with an internal degree of freedom and a tunable chirality parameter, $p$, we interpolate between a standard diffusive random walk and a deterministic, topologically non-trivial quantum walk. We show that the topological protection characteristic of the unitary limit ($p=1$) remarkably persists into the dissipative regime ($p<1$). This correspondence allows us to theoretically ground the robustness of edge flows in classical chiral systems using the bulk-boundary correspondence of Floquet topological insulators. Our results provide a discrete microscopic description for odd diffusion, offering a powerful toolkit to predict transport in confined geometries and disordered chiral media.

cond-mat.stat-mechCross-listedarXiv:2602.09920•Feb 11, 2026

Chiral Parafermions in Floquet $\mathbb{Z}_N$ Topological Order

Melissa Will, Harald Schmid, Jan Egger +3 more

Floquet topological order (FTO) extends topology beyond equilibrium, giving rise to phenomena, such as the dynamical transmutation of anyons. Here, we realize $\mathbb{Z}_N$ FTO in a generalized Kitaev honeycomb model with clock degrees of freedom using a three-step periodic drive. The driven system admits an emergent description in terms of constrained parafermions coupled to conserved $\mathbb{Z}_N$ gauge fields. At the boundary, the drive generates chiral parafermionic Floquet edge modes. We resolve their propagation through correlation functions, characterize their fractional quantum-information transport through the radical chiral unitary index, and use their dynamics to probe exchange statistics. In the bulk, we explore the dynamical anyon transmutation with a non-equilibrium loop order parameter. At a Floquet sweet spot, where the drive becomes Clifford, these phenomena can be accessed using stabilizer simulations. Short-time matrix-product-state simulations away from this point show that the chiral edge response persists at accessible times. Our results establish $\mathbb{Z}_N$ Kitaev models as a setting for exploring intrinsically non-equilibrium topological phenomena on qudit-based quantum processors.

cond-mat.str-elCross-listedarXiv:2610.07156•Oct 7, 2026•0 citations

Topological quantum walk with discrete time-glide symmetry

Ken Mochizuki, Takumi Bessho, Masatoshi Sato +1 more

Discrete quantum walks are periodically driven systems with discrete time evolution. In contrast to ordinary Floquet systems, no microscopic Hamiltonian exists, and the one-period time evolution is given directly by a series of unitary operators. Regarding each constituent unitary operator as a discrete time step, we formulate discrete space-time symmetry in quantum walks and evaluate the corresponding symmetry protected topological phases. In particular, we study chiral and/or time-glide symmetric topological quantum walks in this formalism. Due to the discrete nature of time evolution, the topological classification is found to be different from that in conventional Floquet systems. As a concrete example, we study a two-dimensional quantum walk having both chiral and time-glide symmetries and identify the anomalous edge states protected by these symmetries.

arXiv:2004.09332•Physical review. B./Physical review. B•Jul 13, 2020•16 citations

Observation of Topologically Protected Edge States in a Photonic Two-Dimensional Quantum Walk

Chao Chen, Xing Ding, Jian Qin +13 more

Periodically driven systems have displayed a variety of fascinating phenomena without analogies in static systems, which enrich the classification of quantum phases of matter and stimulate a wide range of research interests. Here, we employ discrete-time quantum walks to investigate a nontrivial topological effect unique to a two-dimensional periodically driven system: chiral edge states can exist at the interface of Floquet insulators whose Chern numbers vanish. Thanks to a resource-saving and flexible fiber-loop architecture, we realize inhomogeneous two-dimensional quantum walks up to 25 steps, over an effective 51×51 lattice with tunable local parameters. Spin-polarized chiral edge states are observed at the boundary of two distinct quantum walk domains. Our results contribute to establishing a well-controlled platform for exploring nontrivial topological phases.

Physical Review Letters•Sep 6, 2018•128 citations

Quantized pumping of boundary Hilbert space in chiral Floquet phases

Ryota Nakai, Taozhi Guo, Shinsei Ryu

Chiral Floquet phases support quantized chiral flow along their boundaries even when the bulk is fully localized. In this Letter, we establish a complementary phenomenon, which we call Hilbert-space pumping: under a boundary condition twisted by time translation, a part of the boundary Hilbert space, of quantized dimension, is transferred between the opposite boundaries. The twist is the temporal analogue of Laughlin's flux insertion in the quantum Hall effect. For noninteracting fermions, the number of transferred boundary modes is determined by the winding number, as we show analytically for the boundary dynamics and numerically for the anomalous Floquet Anderson insulator. For interacting systems whose boundary dynamics is a quantum cellular automaton, the transferred dimension is set by the Gross-Nesme-Vogts-Werner (GNVW) index: the twisted boundary Floquet operator is the Floquet operator on a tilted time slice, whose Hilbert-space dimension is multiplied by the index for each period of twist. We derive this relation for matrix product unitaries and test it numerically in random unitary circuits. Applied to the matrix product operators of non-invertible symmetries, the same twisted rank returns the quantum dimension of the symmetry operator in addition to its flow index.

cond-mat.str-elCross-listedarXiv:2611.02785•Nov 3, 2026
Chiral edge states in quantum Hall effect are the paradigmatic example of the quasi-particle with chirality. In even space-time dimensions, the Nielsen-Ninomiya theorem strictly forbids the chiral states in physical isolation. The exceptions to this theorem only occur in the presence of non-locality, non-Hermiticity, or by embedding the system at the boundary of the higher-dimensional bulk. In this work, using the IBM quantum computer platform, we realize the floquet chiral quantum walk enabled by non-locality. The unitary time evolution operator is described by the effective floquet Hamiltonian with infinitely long-ranged coupling. We find that the chiral wave packets lack the common features of the conventional wave phenomena such as Anderson localization. The absence of localization is witnessed by the robustness against the external perturbations. However, the intrinsic quantum errors of the current quantum device give rise to the finite lifetime where the chiral wave packet eventually disperses in the long-time limit. Nevertheless, we observe the stability of the chiral wave by comparing it with the conventional non-chiral model.
Chiral edge states in a quantum Hall effect are the paradigmatic example of a quasiparticle with chirality. In even space-time dimensions, the Nielsen-Ninomiya theorem strictly forbids chiral states in physical isolation. The exceptions to this theorem only occur in the presence of nonlocality, non-Hermiticity, or by embedding the system at the boundary of the higher-dimensional bulk. In this Letter, using the IBM quantum computer platform, we realize a Floquet chiral quantum walk enabled by nonlocality. The unitary time-evolution operator is described by an effective Floquet Hamiltonian with long-ranged coupling. We find that the chiral wave packets lack the common features of conventional wave phenomena such as localization. The absence of localization is witnessed by the robustness against external perturbations. However, the intrinsic quantum errors of the current quantum device give rise to a finite lifetime where the chiral wave packet eventually disperses in the long-time limit. Nevertheless, we observe the stability of the chiral wave by comparing it with a conventional nonchiral model.
Chirality in active and passive fluids gives rise to odd transport properties, most notably the emergence of robust edge currents that defy standard dissipative dynamics. While these phenomena are well-described by continuum hydrodynamics, a microscopic framework connecting them to their topological origins has remained elusive. Here, we present a lattice model for an isotropic chiral random walk that bridges the gap between classical stochastic diffusion and unitary quantum evolution. By equipping the walker with an internal degree of freedom and a tunable chirality parameter, ppp, we interpolate between a standard diffusive random walk and a deterministic, topologically non-trivial quantum walk. We show that the topological protection characteristic of the unitary limit (p=1p=1p=1) remarkably persists into the dissipative regime (p<1p<1p<1). This correspondence allows us to theoretically ground the robustness of edge flows in classical chiral systems using the bulk-boundary correspondence of Floquet topological insulators. Our results provide a discrete microscopic description for odd diffusion, offering a powerful toolkit to predict transport in confined geometries and disordered chiral media.
Chiral Parafermions in Floquet ZN\mathbb{Z}_NZN​ Topological Order
Floquet topological order (FTO) extends topology beyond equilibrium, giving rise to phenomena, such as the dynamical transmutation of anyons. Here, we realize ZN\mathbb{Z}_NZN​ FTO in a generalized Kitaev honeycomb model with clock degrees of freedom using a three-step periodic drive. The driven system admits an emergent description in terms of constrained parafermions coupled to conserved ZN\mathbb{Z}_NZN​ gauge fields. At the boundary, the drive generates chiral parafermionic Floquet edge modes. We resolve their propagation through correlation functions, characterize their fractional quantum-information transport through the radical chiral unitary index, and use their dynamics to probe exchange statistics. In the bulk, we explore the dynamical anyon transmutation with a non-equilibrium loop order parameter. At a Floquet sweet spot, where the drive becomes Clifford, these phenomena can be accessed using stabilizer simulations. Short-time matrix-product-state simulations away from this point show that the chiral edge response persists at accessible times. Our results establish ZN\mathbb{Z}_NZN​ Kitaev models as a setting for exploring intrinsically non-equilibrium topological phenomena on qudit-based quantum processors.
Discrete quantum walks are periodically driven systems with discrete time evolution. In contrast to ordinary Floquet systems, no microscopic Hamiltonian exists, and the one-period time evolution is given directly by a series of unitary operators. Regarding each constituent unitary operator as a discrete time step, we formulate discrete space-time symmetry in quantum walks and evaluate the corresponding symmetry protected topological phases. In particular, we study chiral and/or time-glide symmetric topological quantum walks in this formalism. Due to the discrete nature of time evolution, the topological classification is found to be different from that in conventional Floquet systems. As a concrete example, we study a two-dimensional quantum walk having both chiral and time-glide symmetries and identify the anomalous edge states protected by these symmetries.
Periodically driven systems have displayed a variety of fascinating phenomena without analogies in static systems, which enrich the classification of quantum phases of matter and stimulate a wide range of research interests. Here, we employ discrete-time quantum walks to investigate a nontrivial topological effect unique to a two-dimensional periodically driven system: chiral edge states can exist at the interface of Floquet insulators whose Chern numbers vanish. Thanks to a resource-saving and flexible fiber-loop architecture, we realize inhomogeneous two-dimensional quantum walks up to 25 steps, over an effective 51×51 lattice with tunable local parameters. Spin-polarized chiral edge states are observed at the boundary of two distinct quantum walk domains. Our results contribute to establishing a well-controlled platform for exploring nontrivial topological phases.
Chiral Floquet phases support quantized chiral flow along their boundaries even when the bulk is fully localized. In this Letter, we establish a complementary phenomenon, which we call Hilbert-space pumping: under a boundary condition twisted by time translation, a part of the boundary Hilbert space, of quantized dimension, is transferred between the opposite boundaries. The twist is the temporal analogue of Laughlin's flux insertion in the quantum Hall effect. For noninteracting fermions, the number of transferred boundary modes is determined by the winding number, as we show analytically for the boundary dynamics and numerically for the anomalous Floquet Anderson insulator. For interacting systems whose boundary dynamics is a quantum cellular automaton, the transferred dimension is set by the Gross-Nesme-Vogts-Werner (GNVW) index: the twisted boundary Floquet operator is the Floquet operator on a tilted time slice, whose Hilbert-space dimension is multiplied by the index for each period of twist. We derive this relation for matrix product unitaries and test it numerically in random unitary circuits. Applied to the matrix product operators of non-invertible symmetries, the same twisted rank returns the quantum dimension of the symmetry operator in addition to its flow index.