Related papers: Symmetry protected topological order at nonzero te…
Resource states that contain nontrivial symmetry-protected topological order are identified for universal single-qudit measurement-based quantum computation. Our resource states fall into two classes: one as the qudit generalizations of the…
We present simple lattice realizations of symmetry-protected topological (SPT) phases with $q$-form global symmetries where charged excitations have $q$ spatial dimensions. Specifically, we construct $d$ space-dimensional models supported…
We explore the stability of certain many-body quantum states which may exist at zero or finite temperatures, may lack long-range order and even topological order, and still are thermodynamically distinct from uncorrelated disordered phases.…
We study the non-equilibrium phase structure of the three-state random quantum Potts model in one dimension. This spin chain is characterized by a non-Abelian $D_3$ symmetry recently argued to be incompatible with the existence of a…
Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G. They can all be smoothly connected to the same trivial product state if we break the symmetry. The Haldane phase of spin-1 chain…
We study ensembles described by density matrices with potentially nontrivial topological features. In particular, we study a class of symmetry protected topological (SPT) phases under various types of decoherence, which can drive a pure SPT…
It is widely expected that at sufficiently high temperatures order is always lost, e.g. magnets loose their ferromagnetic properties. We pose the question of whether this is always the case in the context of quantum field theory in $d$…
We discuss the characterization and stability of the Haldane phase in integer spin chains on the basis of simple, physical arguments. We find that an odd-$S$ Haldane phase is a topologically non-trivial phase which is protected by any one…
Symmetry protected topological (SPT) phases are fundamental quantum many-body states of matter beyond Landau's paradigm. Here, we introduce the concept of quantum restored SPTs (QRSPTs), where the protecting symmetry is spontaneously broken…
As a prototype model of topological quantum memory, two-dimensional toric code is genuinely immune to generic local static perturbations, but fragile at finite temperature and also after non-equilibrium time evolution at zero temperature.…
High temperature is usually expected to destroy order: as the Gibbs state approaches the infinite-temperature limit, it becomes an equal-weight ensemble over all states and the system is generically disordered. Recent works showed that…
We describe a fault-tolerant version of the one-way quantum computer using a cluster state in three spatial dimensions. Topologically protected quantum gates are realized by choosing appropriate boundary conditions on the cluster. We…
While topological quantum computation is intrinsically fault-tolerant at zero temperature, it loses its topological protection at any finite temperature. We present a scheme to protect the information stored in a system supporting…
It is an ongoing quest to realize topologically ordered quantum states on different platforms including condensed matter systems, quantum simulators and digital quantum processors. Unlike conventional states characterized by their local…
Symmetry protected topological (SPT) phases are gapped quantum phases with a certain symmetry, which can all be smoothly connected to the same trivial product state if we break the symmetry. For non-interacting fermion systems with time…
Gapless surface states on topological insulators are protected from elastic scattering on non-magnetic impurities which makes them promising candidates for low-power electronic applications. However, for wide-spread applications, these…
We propose a bulk order parameter for extracting symmetry-protected topological (SPT) invariants of quantum many-body mixed states on a two dimensional lattice using partial symmetries. The procedure builds on the partial symmetry order…
We explore 1+1 dimensional (1+1D) gapped phases in systems with non-invertible symmetries, focusing on symmetry-protected topological (SPT) phases (defined as gapped phases with non-degenerate ground states), as well as SPT orders (defined…
Recent progress in characterization for gapped quantum phases has also triggered the search of universal resource for quantum computation in symmetric gapped phases. Prior works in one dimension suggest that it is a feature more common than…
Symmetry protected topological (SPT) states have boundary 't Hooft anomalies that obstruct an effective boundary theory realized in its own dimension with UV completion and an on-site $G$-symmetry. In this work, yet we show that a certain…