Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session S32: Invited Session: Topological Quantum Information and Phases of Matter |
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Sponsoring Units: GQI DCMP Chair: Parsa Bonderson, Microsoft Corporation Room: 708-712 |
Thursday, March 6, 2014 8:00AM - 8:36AM |
S32.00001: The search for Majorana zero-energy modes in solid-state systems Invited Speaker: Roman Lutchyn The search for topological phases of matter has become an active and exciting pursuit in condensed matter physics. Among the notable recent developments in this direction are the discoveries of topological insulators and superconductors. In this talk, I will focus on topological superconductors and discuss how one can engineer non-trivial superconductivity in the laboratory at the interface of a conventional s-wave superconductor and a semiconductor with a spin-orbit interaction. I will show that the topological superconducting state emerging at the interface supports Majorana zero-energy modes. The defects carrying these modes are Ising anyons and obey unconventional (non-Abelian) exchange statistics. The unique properties of Majoranas can be exploited for implementing fault-tolerant quantum computation schemes that are inherently decoherence-free. I will conclude this talk by reviewing recent experimental efforts in realizing and detecting Majorana zero-energy modes in one-dimensional nanowires. [Preview Abstract] |
Thursday, March 6, 2014 8:36AM - 9:12AM |
S32.00002: Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure Invited Speaker: Roger Mong Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Green's observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional $p+ip$ superconductor both support so-called Ising non-Abelian anyons. Here we establish a similar correspondence between the $Z_3$ Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge-$2e$ Cooper pairs are built from fractionalized quasiparticles. In particular, both phases harbor Fibonacci anyons that---unlike Ising anyons---allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kane's construction of non-Abelian phases from weakly coupled chains, we provide a blueprint for such a superconductor using Abelian quantum Hall states interlaced with an array of superconducting islands. These results imply that one can, in principle, combine well-understood and widely available phases of matter to realize non-Abelian anyons with universal braid statistics. [Preview Abstract] |
Thursday, March 6, 2014 9:12AM - 9:48AM |
S32.00003: Lattice quantum codes and exotic topological phases of matter Invited Speaker: Jeongwan Haah Is it possible to build a ``hard disk drive'' for quantum information? The quantum coherence time in a usual thermal system is fundamentally limited by the inverse Boltzmann factor $\exp[\Delta/kT]$, where $\Delta$ is the energy scale of the system. This limitation is not enhanced even with a conventional topologically ordered system in three or lower dimensions. Here, a new three-dimensional spin model is presented that shows a qualitatively different behavior. It can be viewed as a quantum error correcting code, and is thus exactly solvable. The ground states are locally indistinguishable, for which it may be called topologically ordered. However, the model only admits immobile pointlike excitations, and the immobility is not affected by small perturbations of the Hamiltonian. The degeneracy of the ground state, though also insensitive to perturbations, is a complicated number-theoretic function of the system size. Under real-space renormalization group transformations, the system bifurcates into multiple noninteracting copies of itself. Similarities and differences of the model in comparison to Wegner's Ising gauge theory will be explained. When quantum information is encoded into a ground state of this model and subjected to thermal errors, the errors remain easily correctable for a long time without any active intervention, because a macroscopic energy barrier due to the immobility of excitations keeps the errors well localized. As a result, stored quantum information can be retrieved faithfully for a memory time $\exp[(\Delta/kT)^2]$. [Preview Abstract] |
Thursday, March 6, 2014 9:48AM - 10:24AM |
S32.00004: Genons and twist defects Invited Speaker: Xiao-Liang Qi |
Thursday, March 6, 2014 10:24AM - 11:00AM |
S32.00005: Topological Phases and Surface States with Strong Interactions Invited Speaker: Ashvin Vishwanath Previous work on topological insulators and superconductors has been largely based on free fermions with topological ``band'' structures. We will discuss qualitatively new phenomena that arise with strong interactions, where one cannot invoke a band structure. First, we point out examples of new topological phases with protected edge modes that only appear in the presence of interactions. Next, in contrast to conventional wisdom which held that 3D Topological Insulators and superconductors must be associated with gapless, metallic surface states if the symmetries are preserved, we argue that the 2D surface \textit{can} in fact acquire a gap while remaining fully symmetric if it develops topological order. That is, if the surface state contains excitations with fractional statistics, like in a fractional Quantum Hall state. Interestingly, in some cases the surface states must contain particles with non-Abelian statistics. Finally, we discuss how interactions can modify the classification of free fermion topological phases in 3D. In particular, using surface topological order as a tool, we show that the integer classification of topological superconductors in 3D (class DIII, with time reversal symmetry) is actually reduced to a Z$_{16}$ classification. [Preview Abstract] |
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