Strong zero modes in integrable quantum circuits

Abstract

It is a classic result that certain interacting integrable spin chains host robust edge modes known as strong zero modes (SZMs). In this work, we extend this result to the Floquet setting of local quantum circuits, focusing on a prototypical model providing an integrable Trotterization for the evolution of the XXZ Heisenberg spin chain. By exploiting the algebraic structures of integrability, we show that an exact SZM operator can be constructed for these integrable quantum circuits in certain regions of parameter space. Our construction, which recovers a well-known result by Paul Fendley in the continuous-time limit, relies on a set of commuting transfer matrices known from integrability, and allows us to easily prove important properties of the SZM, including normalizabilty. Our approach is different from previous methods and could be of independent interest even in the Hamiltonian setting. Our predictions, which are corroborated by numerical simulations of infinite-temperature autocorrelation functions, are potentially interesting for implementations of the XXZ quantum circuit on available quantum platforms.

arXiv comment7 pages + 11 pages of Supplementary Material

References in corpus (57)

• Unpaired Majorana fermions in quantum wires
• Majorana Zero Modes and Topological Quantum Computation
• On the phase structure of driven quantum systems
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Time crystals: a review
• Parafermionic edge zero modes in Z_n-invariant spin chains
• Absolute Stability and Spatiotemporal Long-Range Order in Floquet systems
• Typicality for Generalized Microcanonical Ensembles
• Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
• Floquet generation of Majorana end modes and topological invariants
• Many-body Localization and Symmetry Protected Topological Order
• Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs
• 1D Many-body localized Floquet systems II: Symmetry-Broken phases
• Exact ground states and topological order in interacting Kitaev/Majorana chains
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Strong zero modes and eigenstate phase transitions in the XYZ/interacting Majorana chain
• Floquet symmetry-protected topological phases in cold atomic systems
• Integrable Trotterization: Local Conservation Laws and Boundary Driving
• Ballistic spin transport in a periodically driven integrable quantum system
• Abelian Floquet symmetry-protected topological phases in one dimension
• Correlation functions of the open XXZ chain I
• Stability of zero modes in parafermion chains
• Long coherence times for edge spins
• Surface excitations and surface energy of the antiferromagnetic XXZ chain by the Bethe ansatz approach
• Exactly conserved quasilocal operators for the XXZ spin chain
• Formation of robust bound states of interacting microwave photons
• Boundary bound states and boundary bootstrap in the sine-Gordon model with Dirichlet boundary conditions.
• Prethermal Strong Zero Modes and Topological Qubits
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Exact Solution to Interacting Kitaev Chain at Symmetric Point
• Correlation functions of the open XXZ chain II
• Temporal entanglement, quasiparticles and the role of interactions
• Nonequilibrium Quantum Phase Transitions in the Ising Model
• Spin and energy currents in integrable and nonintegrable spin-1/2 chains: A typicality approach to real-time autocorrelations
• Lifetime of almost strong edge-mode operators in one dimensional, interacting, symmetry protected topological phases
• Dynamics of almost strong edge modes in spin chains away from integrability
• Evidence of Kardar-Parisi-Zhang scaling on a digital quantum simulator
• Quasi-local conserved charges and spin transport in spin-$1$ integrable chains
• Correlations and commuting transfer matrices in integrable unitary circuits
• Long-lived period-doubled edge modes of interacting and disorder-free Floquet spin chains
• Almost strong 0, π edge modes in clean, interacting 1D Floquet systems
• Parafermion chain with $2\pi /k$ Floquet edge modes
• Stroboscopic Symmetry-Protected Topological Phases
• Topologically-Protected Long Edge Coherence Times in Symmetry-Broken Phases
• Enhancing correlation times for edge spins through dissipation
• Rigorous bounds on dynamical response functions and time-translation symmetry breaking
• Symmetry enhanced boundary qubits at infinite temperature
• Strong zero modes in a class of generalised Ising spin ladders with plaquette interactions
• Topological order in random interacting Ising-Majorana chains stabilized by many-body localization
• Conserved charges in the quantum simulation of integrable spin chains
• Open XXZ chain and boundary modes at zero temperature
• String order parameters for 1d Floquet Symmetry Protected Topological Phases
• Topological and quantum critical properties of the interacting Majorana chain model
• Decay rates of almost strong modes in Floquet spin chains beyond Fermi's Golden Rule
• Integrable Quantum Circuits from the Star-Triangle Relation
• Slowly decaying zero mode in a weakly non-integrable boundary impurity model

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• Inhomogeneous SU(2) symmetries in homogeneous integrable U(1) circuits and transport
• Integrability of Goldilocks quantum cellular automata
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• Integrability and charge transport in asymmetric quantum-circuit geometries
• Floquet Product Mode
• Signatures of Integrability and Exactly Solvable Dynamics in an Infinite-Range Many-Body Floquet Spin System
• Design and benchmarks for emulating Kondo dynamics on a quantum chip
• Anomalous parametric resonance in a spin-1/2 chain: dynamical effects of nontrivial topology
• Strong zero modes in integrable spin-S chains
• Noninvertible Kramers-Wannier duality symmetries for the discrete-time quantum Ising chain