Defects: A new window into topological quantum matter
Maissam Barkeshli University of California, Santa Barbara
PIRSA:14100048
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Irreversibility and Entanglement Spectrum Statistics in Quantum Circuits
Eduardo Mucciolo University of Central Florida
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3d Gravity, Universality and Poincare Series
PIRSA:14090005 -
ADMX: The Axion Dark Matter Experiment
Gray Rybka University of Washington
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Fault-tolerant logical gates in quantum error-correcting codes
Beni Yoshida Perimeter Institute for Theoretical Physics
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Lifshitz Field Theories, Anomalies and Hydrodynamics
Shira Chapman University of Amsterdam
PIRSA:14090083 -
Algebraic characterization of entanglement classes
Markus Grassl Max Planck Institute for the Science of Light
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Observables and Change in Totally Constrained Systems
Karim Thebault Ludwig-Maximilians-Universitiät München (LMU)
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Evolution of quantum field, particle content, and classicality in the three stage universe
Suprit Singh IUCAA - The Inter-University Centre for Astronomy and Astrophysics
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Defects: A new window into topological quantum matter
Maissam Barkeshli University of California, Santa Barbara
PIRSA:14100048Topologically ordered states, such as the fractional quantum Hall (FQH) states, are quantum states of matter with various exotic properties, including quasiparticles with fractional quantum numbers and fractional statistics, and robust topology-dependent ground state degeneracies. In this talk, I will describe a new aspect of topological states: their extrinsic defects. These include extrinsically imposed point-like or line-like defects that couple to the topological properties of the state in non-trivial ways. The extrinsic point defects localize topologically protected "parafermion" zero modes, which generalize the notion of Majorana fermion zero modes, and provide a new direction for realizing non-Abelian quantum statistics and topological quantum computation. The line defects allow direct quantum mechanical coupling between electrons and fractionalized anyons, leading to new ways to probe fractionalization. After describing the conceptual framework, I will focus on a specific set of experimental proposals, using conventional bilayer FQH states, to detect parafermion zero modes and to directly observe the long-predicted topological ground state degeneracy of FQH states. In the end I will comment on other ways in which extrinsic defects provide a new window into fractionalization. -
The Topology of Information Flow
Jamie Vicary University of Oxford
PIRSA:14090076I will outline a new topological foundation for computation, and show how it gives rise to a unified treatment of classical encryption and quantum teleportation, and a strong classical model for many quantum phenomena. This work connects to some other interesting topics, including quantum field theory, classical combinatorics, thermodynamics, Morse theory and higher category theory, which I will introduce in an elementary way. -
Irreversibility and Entanglement Spectrum Statistics in Quantum Circuits
Eduardo Mucciolo University of Central Florida
We show that for a system evolving unitarily under a stochastic quantum circuit, the notions of irreversibility, universality of computation, and entanglement are closely related. As the state of the system evolves from an initial product state, it becomes increasingly entangled until entanglement reaches a maximum. We define irreversibility as the failure to find a circuit that disentangles a maximally entangled state. We show that irreversibility occurs when maximally entangled states are generated with a quantum circuit formed by gates from a universal quantum computation set. We find that irreversibility is also associated to a Wigner-Dyson statistics in the fluctuations of spacings between adjacent eigenvalues of the system’s reduced density matrix. In contrast, when the system is evolved with a non-universal set of gates, the statistics of the entanglement spacing deviates from Wigner-Dyson and the disentangling algorithm succeeds. We discuss how these findings open a new way to characterize non-integrability in quantum systems. -
3d Gravity, Universality and Poincare Series
PIRSA:14090005Modular invariance plays an important role in the AdS3/CFT2 correspondence. Using modular invariance, I discuss under what conditions a 2d CFT shows a Hawking-Page phase transition in the large c limit, and what this implies for the range of validity of the Cardy formula and the universality of its spectrum. I will also discuss partition functions obtained by summing over the modular group, how their properties are compatible with their gravity interpretation, and briefly touch on implications for the existence of pure gravity. -
ADMX: The Axion Dark Matter Experiment
Gray Rybka University of Washington
Axions are an exceptionally well-motivated dark matter candidate in addition to being a consequence of the Peccei-Quinn solution to the strong CP problem. ADMX (Axion Dark Matter eXperiment) has recently been selected as the axion search for the US DOE Second-Generation Dark Matter Program. I will discuss the imminent upgrade of ADMX to a definitive search for micro-eV mass dark matter axions as well as the ongoing research and development of new technologies to expand the reach of ADMX to the entire plausible dark matter axion mass range. -
From Black Holes to Big Bang, and Back
Niayesh Afshordi University of Waterloo
PIRSA:14090088By now, both black hole astrophysics and big bang cosmology are empirically well-established disciplines of physics and astronomy. They are also the only circumstances in nature where Einstein's general relativity can be seen in its full glory, and yet contain within them, its eventual and inevitable folly. Here, I will outline subtle lines evidence for why a phenomenologically successful description of big bang cosmology and black hole horizons may be intimately connected. These lines include a holographic description of big bang, thermal tachyacoustic cosmology, and the firewall controversy. Astrophysical observations, ranging from CMB and dark energy probes, to astrophysical neutrinos could shed further light on these potential connections. -
Fault-tolerant logical gates in quantum error-correcting codes
Beni Yoshida Perimeter Institute for Theoretical Physics
Recently, Bravyi and Koenig have shown that there is a tradeoff between fault-tolerantly implementable logical gates and geometric locality of stabilizer codes. They consider locality-preserving operations which are implemented by a constant depth geometrically local circuit and are thus fault-tolerant by construction. In particular, they shown that, for local stabilizer codes in D spatial dimensions, locality preserving gates are restricted to a set of unitary gates known as the D-th level of the Clifford hierarchy. In this paper, we elaborate this idea and provide several extensions and applications of their characterization in various directions. First, we present a new no-go theorem for self-correcting quantum memory. Namely, we prove that a three-dimensional stabilizer Hamiltonian with a locality-preserving implementation of a non-Clifford gate cannot have a macroscopic energy barrier. Second, we prove that the code distance of a D-dimensional local stabilizer code with non-trivial locality-preserving m-th level Clifford logical gate is upper bounded by L^{D+1-m}. For codes with non-Clifford gates (m>2), this improves the previous best bound by Bravyi and Terhal. Third we prove that a qubit loss threshold of codes with non-trivial transversal m-th level Clifford logical gate is upper bounded by 1/m. As such, no family of fault-tolerant codes with transversal gates in increasing level of the Clifford hierarchy may exist. This result applies to arbitrary stabilizer and subsystem codes, and is not restricted to geometrically-local codes. Fourth we extend the result of Bravyi and Koenig to subsystem codes. A technical difficulty is that, unlike stabilizer codes, the so-called union lemma does not apply to subsystem codes. This problem is avoided by assuming the presence of error threshold in a subsystem code, and the same conclusion as Bravyi-Koenig is recovered. This is a joint work with Fernando Pastawski. arXiv:1408.1720 -
Lifshitz Field Theories, Anomalies and Hydrodynamics
Shira Chapman University of Amsterdam
PIRSA:14090083I will review various aspects of field theories that posses a Lifshitz scaling symmetry. I will detail our study of the cohomological structure of anisotropic Weyl anomalies (the equivalent of trace anomalies in relativistic scale invariant field theories). I will also analyze the hydrodynamics of Lifshitz field theories and in particular of Lifshitz superfluids which may give insights into the physics of high temperature superconductors. -
Algebraic characterization of entanglement classes
Markus Grassl Max Planck Institute for the Science of Light
Entanglement is a key feature of composite quantum system which is directly related to the potential power of quantum computers. In most computational models, it is assumed that local operations are relatively easy to implement. Therefore, quantum states that are related by local operations form a single entanglement class. In the case of local unitary operations, a finite set of polynomial invariants provides a complete characterization of the entanglement classes. Unfortunately, one faces the problem of combinatorial explosion so that computing such a complete set of invariants becomes difficult already for quite small system. The two main problems in this context are to compute invariants and to decide completeness, i.e., whether a given set of invariants generates the full invariant ring. Important tools are both univariate and multivariate Hilbert series which are already difficult to compute. We will also address computational aspects of these problems and techniques for showing completeness of a set of invariants. -
Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography
We discuss properties of 2-point functions in CFTs in 2+1D at finite temperature. For concreteness, we focus on those involving conserved flavour currents, in particular on the associated conductivity. At frequencies much greater than the temperature, ω >> T, the ω dependence of the conductivity can be computed from the operator product expansion (OPE) between the currents and operators which acquire a non-zero expectation value at T > 0. Such results are found to be in excellent agreement with quantum Monte Carlo studies of the O(2) Wilson-Fisher CFT. Results for the conductivity and other observables are also obtained in vector 1/N expansions. We match these large ω results to the corresponding correlators of holographic representations of the CFT: the holographic approach then allows us to extrapolate to small ω/T. Other holographic studies implicitly only used the OPE between the currents and the energy-momentum tensor, and this yields the correct leading large ω behavior for a large class of CFTs. However, for the Wilson-Fisher CFT a relevant “thermal” operator must also be considered, and then consistency with the Monte Carlo results is obtained without a previously needed ad hoc rescaling of the T value [1]. We also use the OPE to prove sum rules obeyed by the conductivity. **In collaboration with A. Katz, S. Sachdev and E. Sørensen** [1] WWK, E. Sørensen, S. Sachdev, Nat. Phys. 10, 361 (2014) -
Observables and Change in Totally Constrained Systems
Karim Thebault Ludwig-Maximilians-Universitiät München (LMU)
We isolate an important physical distinction between gauge symmetries which exist at the level of histories and states, and those which exist at the level of histories and not states. This distinction is characterised explicitly using a generalized Hamilton-Jacobi formalism within which a non-standard prescription for the observables of classical totally constrained systems is developed. These ideas motivate a `relational quantization' procedure which is different from the standard `Dirac quanization'. In particular, relational quantization of totally constrained systems leads to a formalism with superpositions of energy eigenstates and an enlarged set of quantum observables. These `Kucha\v{r} observables' can change independently of each other, and thus are associated with measurable quantities in excess of the `perennials' of the standard Dirac approach. -
Evolution of quantum field, particle content, and classicality in the three stage universe
Suprit Singh IUCAA - The Inter-University Centre for Astronomy and Astrophysics
I will discuss the evolution of a quantum scalar field in a toy universe which has three stages of evolution, viz., (i) an early (inflationary) de Sitter phase (ii) radiation-dominated phase and (iii) late-time (cosmological constant dominated) de Sitter phase. Using the Schr\"odinger picture, the scalar field equations are solved separately for the three stages and matched at the transition points. The boundary conditions are chosen so that field modes in the early de Sitter phase evolve from the Bunch-Davies vacuum state. I shall look the (time-dependent) particle content of this quantum state for the entire evolution of the universe and describe the various features both numerically and analytically. I shall also describe the quantum to classical transition in terms of a classicality parameter which tracks the particle creation and its effect on phase space correlation of the quantum field.