Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session N1: Topological Phases and Quantum Computing |
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Sponsoring Units: DCMP Chair: Eduardo Fradkin, University of Illinois Room: Baltimore Convention Center Ballroom IV |
Wednesday, March 15, 2006 8:00AM - 8:36AM |
N1.00001: Protected qubits and quantum computation using Josephson junctions Invited Speaker: Several schemes of topological protection have been proposed, in which qubits are realized as degenerate ground states of quantum many-body systems so that all likely perturbations are exponentially suppressed. In the realm of Josephson junction physics, this approach was pioneered by Doucot, Vidal, Ioffe, and Feigelman in 2002. I will report a variation of their scheme that offers greater robustness and flexibility. Its key element is a ``quantum transformer'', a superconducting current mirror operated in the quantum regime. This is a four-terminal device whose energy depends only on $\phi_1-\phi_2+\phi_3-\phi_4$, with exponentially small ``error terms'' like $\cos(\phi_1-\phi_4)$. The qubit is implemented by connecting terminal $1$ with $3$ and $2$ with $4$. I will describe a realization of the basic element, qubit measurements and unitary gates, and also discuss some parameter tradeoffs. [Preview Abstract] |
Wednesday, March 15, 2006 8:36AM - 9:12AM |
N1.00002: Quantum critical phases in two dimensions: U(1) spin liquids Invited Speaker: Usually, we expect that stable phases of matter can be described in terms of quasiparticle excitations that interact only weakly at low energies. However, it is now clear that certain quantum spin liquids dramatically violate this expectation, but can nonetheless exist as stable zero-temperature phases in two-dimensional systems. These are the critical or algebraic spin liquids, which have no broken- symmetry ordering, but support gapless spin-carrying excitations. These states are promising candidates for the longstanding goal of the unambiguous experimental detection of a quantum spin liquid state; they have been suggested to play a role in certain strongly correlated materials, and they possess a variety of striking, and measurable, properties. I will discuss recent work on the simplest algebraic spin liquids. These are a type of two-dimensional U(1) spin liquid, and can be described at low energies by gapless Dirac fermions (spinons) coupled to a compact U(1) gauge field (photon). I will outline an argument that establishes the stability of these states in a large-N limit, and thus resolved a longstanding controversy. Next, I will discuss some of the remarkable properties of these states, and conclude with a discussion of open issues. [Preview Abstract] |
Wednesday, March 15, 2006 9:12AM - 9:48AM |
N1.00003: Non-Abelian topological phases Invited Speaker: I will discuss the role of topology in the storage and processing quantum information. Chern-Simons theories in their chiral and doubled versions will be discussed. The Fractional quantum hall effect is the leading example of topological phases and may be home to striking nonabelian examples such as the $\nu=5/2$ state. These examples will be considered within a larger mathematical framework. [Preview Abstract] |
Wednesday, March 15, 2006 9:48AM - 10:24AM |
N1.00004: Proposed experiments to probe the non-abelian $\nu=5/2$ quantum Hall state Invited Speaker: We propose several experiments to test the non-abelian nature of quasi-particles in the fractional quantum Hall state of $\nu=5/2$. One set of experiments studies interference contribution to back-scattering of current, and is a simplified version of an experiment suggested recently by Das Sarma et al. A second set looks at thermodynamic properties of a closed system. A third set looks at electronic transport in an array of immobile quesi-particles. The first two sets are only weakly sensitive to disorder-induced distribution of localized quasi-particles. [Preview Abstract] |
Wednesday, March 15, 2006 10:24AM - 11:00AM |
N1.00005: Realizing non-Abelian statistics in time-reversal invariant systems Invited Speaker: Motivated by the search for a quantum computer robust against errors, much theoretical effort has been devoted to finding systems with quasiparticles obeying non-abelian statistics. I discuss a general method of constucting quantum loop gases with such behavior, focusing in particular on the simplest time-reversal-invariant model (P. Fendley and E. Fradkin, Phys. Rev. B 72 (2005) 024412 [cond-mat/0502071]). The quasiparticles of this model are called ``Fibonacci anyons'', and their braiding is related to SO(3) Chern-Simons theory. I also discuss the quantum critical point governing the transition from a topological phase to a conventionally-ordered phase. [Preview Abstract] |
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