• Corpus ID: 247594050

Adiabatic paths of Hamiltonians, symmetries of topological order, and automorphism codes

@inproceedings{Aasen2022AdiabaticPO,
  title={Adiabatic paths of Hamiltonians, symmetries of topological order, and automorphism codes},
  author={David Aasen and Zhenghan Wang and Matthew B. Hastings},
  year={2022}
}
The recent “honeycomb code” is a fault-tolerant quantum memory defined by a sequence of checks which implements a nontrivial automorphism of the toric code. We argue that a general framework to understand this code is to consider continuous adiabatic paths of gapped Hamiltonians and we give a conjectured description of the fundamental group and second and third homotopy groups of this space in two spatial dimensions. A single cycle of such a path can implement some automorphism of the… 
Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model
We consider a paradigmatic solvable model of topological order in two dimensions, Kitaev’s honeycomb Hamiltonian, and turn it into a measurement-only dynamics consisting of stochastic measurements of
Random Quantum Circuits
Quantum circuits — built from local unitary gates and local measurements — are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena
Gauging Lie group symmetry in (2+1)d topological phases
We present a general algebraic framework for gauging a 0-form compact, connected Lie group symmetry in (2+1)d topological phases. Starting from a symmetry fractionalization pattern of the Lie group
Fermionic approach to variational quantum simulation of Kitaev spin models
We use the variational quantum eigensolver (VQE) to simulate Kitaev spin models with and without integrability breaking perturbations, focusing in particular on the honeycomb and square-octagon
Generalized Thouless Pumps in 1+1-dimensional Interacting Fermionic Systems
The Thouless pump is a phenomenon in which U(1) charges are pumped from an edge of a fermionic system to another edge. The Thouless pump has been generalized in various dimensions and for various

References

SHOWING 1-10 OF 27 REFERENCES
On adiabatic cycles of quantum spin systems
Motivated by the Ω-spectrum proposal of unique gapped ground states by Kitaev [1], we study adiabatic cycles in gapped quantum spin systems from various perspectives. We give a few exactly solvable
String-net condensation: A physical mechanism for topological phases
We show that quantum systems of extended objects naturally give rise to a large class of exotic phases---namely topological phases. These phases occur when extended objects, called ``string-nets,''
Interacting invariants for Floquet phases of fermions in two dimensions
We construct a many-body quantized invariant that sharply distinguishes among two dimensional non-equilibrium driven phases of interacting fermions. This is an interacting generalization of a
Periodic table for topological insulators and superconductors
Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a
The Group Structure of Quantum Cellular Automata
We consider the group structure of quantum cellular automata (QCA) modulo circuits and show that it is abelian even without assuming the presence of ancillas, at least for most reasonable choices of
Anyons in an exactly solved model and beyond
Flow of (higher) Berry curvature and bulk-boundary correspondence in parametrized quantum systems
This paper is concerned with the physics of parametrized gapped quantum many-body systems, which can be viewed as a generalization of conventional topological phases of matter. In such systems,
Higher-dimensional generalizations of Berry curvature
A family of finite-dimensional quantum systems with a non-degenerate ground state gives rise to a closed 2-form on the parameter space: the curvature of the Berry connection. Its cohomology class is
Long-range entanglement from measuring symmetry-protected topological phases
A fundamental distinction between many-body quantum states are those with shortand longrange entanglement (SRE and LRE). The latter cannot be created by finite-depth circuits, underscoring the
Topological order with a twist: Ising anyons from an Abelian model.
  • H. Bombin
  • Mathematics
    Physical review letters
  • 2010
TLDR
The realization of topological defects that, under monodromy, transform anyons according to a symmetry are studied in the toric code model, showing that a process where defects are braided and fused has the same outcome as if they were Ising anyons.
...
...