Adiabatic Preparation of Topological Order

Abstract

Topological order characterizes those phases of matter that defy a description in terms of symmetry and cannot be distinguished in terms local order parameters. This type of order plays a key role in the theory of the fractional quantum Hall effect, as well as in topological quantum information processing. Here we show that a system of n spins forming a lattice on a Riemann surface can undergo a second order quantum phase transition between a spin-polarized phase and a string-net condensed phase. This is an example of a phase transition between magnetic and topological order. We furthermore show how to prepare the topologically ordered phase through adiabatic evolution in a time that is upper bounded by O(\sqrt{n}). This provides a physically plausible method for constructing a topological quantum memory. We discuss applications to topological and adiabatic quantum computing.

4 pages, one figure. v4: includes new error estimates for the adiabatic evolution

References in corpus (15)

• Fault-tolerant quantum computation by anyons
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Topological quantum memory
• String-net condensation: A physical mechanism for topological phases
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Bounds for the adiabatic approximation with applications to quantum computation
• Topological Order and Conformal Quantum Critical Points
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Adiabatic Quantum Computation in Open Systems
• Topologically protected quantum bits from Josephson junction arrays
• General entanglement scaling laws from time evolution
• Error correcting codes for adiabatic quantum computation
• General error estimate for adiabatic quantum computing
• Finite-Size Scaling in the transverse Ising Model on a Square Lattice

Cited by in corpus (92)

• Area laws in a many-body localized state and its implications for topological order
• Solving strongly correlated electron models on a quantum computer
• Low-energy effective theory of the toric code model in a parallel field
• Robustness of a perturbed topological phase
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
• Topology induced anomalous defect production by crossing a quantum critical point
• Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems
• Self-duality and bound states of the toric code model in a transverse field
• Entanglement, fidelity and topological entropy in a quantum phase transition to topological order
• Entanglement renormalization and gauge symmetry
• Quantum correlations in topological quantum phase transitions
• Condensation of achiral simple currents in topological lattice models: a Hamiltonian study of topological symmetry breaking
• Topological Phase Transitions in the Golden String-Net Model
• Breakdown of a perturbed Z_N topological phase
• Universal Signatures of Quantum Critical Points from Finite-Size Torus Spectra: A Window into the Operator Content of Higher-Dimensional Conformal Field Theories
• Toric-boson model: Toward a topological quantum memory at finite temperature
• Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes
• Topological models in rotationally symmetric quasicrystals
• Bound states in two-dimensional spin systems near the Ising limit: A quantum finite-lattice study
• Superconducting Quantum Simulator for Topological Order and the Toric Code
• Localization of Toric Code Defects
• Topological quantum phase transition in bond-alternating spin-1/2 Heisenberg chains
• Bridging Perturbative Expansions with Tensor Networks
• ${\mathbb{Z}}_2$ lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation
• Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization
• Experimentally Probing Topological Order and Its Breakdown via Modular Matrices
• Entanglement patterns and generalized correlation functions in quantum many body systems
• Experimental implementation of adiabatic passage between different topological orders
• Robustness of a topological phase: Topological color code in parallel magnetic field
• Probing topological order with Rényi entropy
• Robust topological order in fermionic ${\mathbb{Z}}_2$ gauge theories: from Aharonov-Bohm instability to soliton-induced deconfinement
• Relaxation vs. adiabatic quantum steady state preparation: which wins?
• Eigenstate Tracking in Open Quantum Systems
• Generating topological order: no speedup by dissipation
• The Capabilities of a Perturbed Toric Code as a Quantum Memory
• Bilayer Kitaev models: Phase diagrams and novel phases
• Exact results on the quench dynamics of the entanglement entropy in the toric code
• Tensor-network approach to phase transitions in string-net models
• Frustrated topological symmetry breaking: geometrical frustration and anyon condensation
• Quantum critical phase transition between two topologically-ordered phases in the Ising toric code bilayer
• Persisting topological order via geometric frustration
• Mean-field ansatz for topological phases with string tension
• Quantum robustness and phase transitions of the 3D Toric Code in a field
• Quantum phase transitions out of a Z2 x Z2 topological phase
• Robustness of Topological Order in the Toric Code with Open Boundaries
• Adiabatic topological quantum computing
• Phase transitions in three-dimensional topological lattice models with surface anyons
• Optimal local unitary encoding circuits for the surface code
• On the robustness of topological quantum codes: Ising perturbation
• The Kitaev-Ising model, Transition between topological and ferromagnetic order
• Baxter-Wu model in a transverse magnetic field
• Global entanglement in a topological quantum phase transition
• Local convertibility of the ground state of the perturbed Toric code
• Circuit-based digital adiabatic quantum simulation and pseudoquantum simulation as new approaches to lattice gauge theory
• Spectroscopy of a topological phase
• An Interferometry-Free Protocol for Demonstrating Topological Order
• Non universality of entanglement convertibility
• Counterdiabatic route for preparation of state with long-range topological order
• Compass and Kitaev models -- Theory and Physical Motivations
• Thermalization of Topological Entropy after a Quantum Quench
• Emergent XY* transition driven by symmetry fractionalization and anyon condensation
• Quantum phase transition in the $Z_3$ Kitaev-Potts model
• Dynamical Equilibration of Topological Properties
• Predicting topological quantum phase transition from dynamics via multisite entanglement
• Topological Minimally Entangled States via Geometric Measure
• Full characterization of a spin liquid phase: from topological entropy to robustness and braid statistics
• Graph state representation of the toric code
• Non-perturbative Floquet engineering of the toric-code Hamiltonian and its ground state
• Quench dynamics of topological quantum phase transition in Wen-plaquette model
• Steady-state topological order
• Discrete Abelian lattice gauge theories on a ladder and their dualities with quantum clock models
• Quantum phase transitions in the $K$-layer Ising toric code
• Experimental Preparation of Topologically Ordered States via Adiabatic Evolution
• Creating fractional quantum Hall states with atomic clusters using light-assisted insertion of angular momentum
• Variational Tensor Network Operator
• Fracton and topological order in the XY checkerboard toric code
• Quantum robustness of the toric code in a parallel field on the honeycomb and triangular lattice
• Quantum metrology enhanced by the $XY$ spin interaction in a generalized Tavis-Cummings model
• Entanglement and area law with a fractal boundary in a topologically ordered phase
• Robust preparation and manipulation of protected qubits using time--varying Hamiltonians
• Partially topological phase in a quantum loop gas model with tension and pressure
• Entanglement and fidelity across quantum phase transitions in locally perturbed topological codes with open boundaries
• Quantum phase transitions to topological Haldane phases in spin-one chains studied by linked-cluster expansions
• Preparing topologically ordered states by Hamiltonian interpolation
• Layer-by-layer disentangling two-dimensional topological quantum codes
• Optimizing the dynamical preparation of quantum spin lakes on the ruby lattice
• Duality in spin systems via the $SU(4)$ algebra
• Unveiling topological order through multipartite entanglement
• Topological order on the Bloch sphere
• Quantum adiabaticity in many-body systems and almost-orthogonality in complementary subspace
• Nonadiabatic Self-Healing of Trotter Errors in Digitized Counterdiabatic Dynamics