Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

This is an updated version of supplementary information to accompany "Quantum supremacy using a programmable superconducting processor", an article published in the October 24, 2019 issue of Nature. The main article is freely available at this https URL. Summary of changes since arXiv:1910.11333v1 (submitted 23 Oct 2019): added URL for qFlex source code; added Erratum section; added Figure S41 comparing statistical and total uncertainty for log and linear XEB; new References [1,65]; miscellaneous updates for clarity and style consistency; miscellaneous typographical and formatting corrections.

/pdf/supplementary-information-for-quantum-supremacy-using-a-3tkhfafpzk.pdf

Supplementary information for "Quantum supremacy using a programmable superconducting processor"

Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations that are necessary for quantum computation are carried out by braiding quasiparticles and then measuring the multiquasiparticle states. The fault tolerance of a topological quantum computer arises from the nonlocal encoding of the quasiparticle states, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the $\ensuremath{\nu}=5∕2$ state, although several other prospective candidates have been proposed in systems as disparate as ultracold atoms in optical lattices and thin-film superconductors. In this review article, current research in this field is described, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. Both the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the $\ensuremath{\nu}=5∕2$ fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.

Non-Abelian Anyons and Topological Quantum Computation

Anyons in an exactly solved model and beyond

Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.

Weyl and Dirac semimetals in three-dimensional solids

Phases of matter are traditionally seen as families of static systems exhibiting the same long-distance and low-energy correlations. In this work, the authors propose and classify a new family of phases of matter. They are novel insofar as they are intrinsically driven and out of equilibrium --- they can only be realized in systems with time-dependent Hamiltonians. The phases we consider arise in 1D periodically driven systems, in the presence of strong disorder and interactions, and are similar to but qualitatively distinct from the symmetry-protected topological phases now well known in the equilibrium setting. In a companion paper, the authors examine similar intrinsically driven families of states with long-range order, and an order parameter that oscillates at a frequency that is robustly an integer multiple of the underlying drive frequency.

Phase structure of one-dimensional interacting Floquet systems. I. Abelian symmetry-protected topological phases

We study classical hard-core dimer models on three-dimensional lattices using analytical approaches and Monte Carlo simulations. On the bipartite cubic lattice, a local gauge field generalization of the height representation used on the square lattice predicts that the dimers are in a critical Coulomb phase with algebraic, dipolar correlations, in excellent agreement with our large-scale Monte Carlo simulations. The nonbipartite fcc and Fisher lattices lack such a representation, and we find that these models have both confined and exponentially deconfined but no critical phases. We conjecture that extended critical phases are realized only on bipartite lattices, even in higher dimensions.

https://arxiv.org/pdf/cond-mat/0305318.pdf

Coulomb and Liquid Dimer Models in Three Dimensions

Near a critical point, the equilibrium relaxation time of a system diverges and any change of control/thermodynamic parameters leads to nonequilibrium behavior. The Kibble-Zurek problem is to determine the dynamical evolution of the system parametrically close to its critical point when the change is parametrically slow. The nonequilibrium behavior in this limit is controlled entirely by the critical point and the details of the trajectory of the system in parameter space (the protocol) close to the critical point. Together, they define a universality class consisting of critical exponents, discussed in the seminal work by Kibble and Zurek, and scaling functions for physical quantities, which have not been discussed hitherto. In this article, we give an extended and pedagogical discussion of the universal content in the Kibble-Zurek problem. We formally define a scaling limit for physical quantities near classical and quantum transitions for different sets of protocols. We report computations of a few scaling functions in model Gaussian and large-$N$ problems and prove their universality with respect to protocol choice. We also introduce a protocol in which the critical point is approached asymptotically at late times with the system marginally out of equilibrium, wherein logarithmic violations to scaling and anomalous dimensions occur even in the simple Gaussian problem.

Kibble-Zurek problem: Universality and the scaling limit

Recent work shows that highly excited many-body localized eigenstates can exhibit broken symmetries and topological order, including in dimensions where such order would be forbidden in equilibrium. In this paper we extend this analysis to discrete symmetry-protected order via the explicit examples of the Haldane phase of one-dimensional spin chains and the topological Ising paramagnet in two dimensions. We comment on the challenge of extending these results to cases where the protecting symmetry is continuous.

Many-body localization and symmetry-protected topological order

Floquet systems are governed by periodic, time-dependent Hamiltonians. Prima facie they should absorb energy from the external drives involved in modulating their couplings and heat up to infinite ...

Shivaji Lal Sondhi

Papers

Phase structure of one-dimensional interacting Floquet systems. I. Abelian symmetry-protected topological phases

Coulomb and Liquid Dimer Models in Three Dimensions

Kibble-Zurek problem: Universality and the scaling limit

Many-body localization and symmetry-protected topological order

Topology and Broken Symmetry in Floquet Systems