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.

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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

On the nature of the Hall insulator

We have conducted an experimental study of the linear transport properties of the magnetic-field induced insulating phase which terminates the quantum Hall (QH) series in two dimensional electron systems. We found that a direct and simple relation exists between measurements of the longitudinal resistivity, $\rho_{xx}$, in this insulating phase and in the neighboring QH phase. In addition, we find that the Hall resistivity, $\rho_{xy}$, can be quantized in the insulating phase. Our results indicate that a close relation exists between the conduction mechanism in the insulator and in the QH liquid.

The Nature of the Hall Insulator

We introduce a new field theory for studying quantum Hall systems. The quantum field is a modified version of the bosonic operator introduced by Read. In contrast to Read's original work we do not work in the lowest Landau level alone, and this leads to a much simpler formalism. We identify an appropriate canonical conjugate field, and write a Hamiltonian that governs the exact dynamics of our bosonic field operators. We describe a Lagrangian formalism, derive the equations of motion for the fields and present a family of mean-field solutions. Finally, we show that these mean field solutions are precisely the Laughlin states. We do not, in this work, address the treatment of fluctuations.

A Field theory for the read operator

Following on from our previous work [M. J. Bhaseen , Phys. Rev. Lett. 98, 166801 (2007)] we examine the finite temperature magnetothermoelectric response in the vicinity of a quantum critical point (QCP). We begin with general scaling considerations relevant to an arbitrary QCP, either with or without Lorentz invariance, and in arbitrary dimension. In view of the broad connections to high-temperature superconductivity and cold atomic gases, we focus on the quantum critical fluctuations of the relativistic Landau-Ginzburg theory. This paradigmatic model arises in many contexts and describes the (particle-hole symmetric) superfluid-Mott insulator quantum phase transition in the Bose-Hubbard model. The application of a magnetic field opens up a wide range of physical observables, and we present a detailed overview of the charge and thermal transport and thermodynamic response. We combine several different approaches including the epsilon expansion and associated quantum Boltzmann equation, entropy drift, and arguments based on Lorentz invariance. The results differ markedly from the zero-field case, and we include an extended discussion of the finite thermal conductivity which emerges in the presence of a magnetic field. We derive an integral equation that governs its response and explore the crossover upon changing the magnetic field. This equation may be interpreted as a projection equation in the low-field limit, and clearly highlights the important role of collision invariants (or zero modes) in the hydrodynamic regime. Using an epsilon expansion around three dimensions, our analytic and numerical results interpolate between our previously published value and the exact limit of two-dimensional relativistic magnetohydrodynamics.

Magnetothermoelectric response near quantum critical points

We have studied the consequences of long-range interactions for the properties of the quasiparticles in the quantum Hall effect. We find that the quasiparticle states have long-range tails in their current and density distributions. These tails are an effect of Landau-level mixing and are absent if the state space is restricted to the lowest Landau level. We also discuss a violation of the spin-statistics relation for the quasiparticles.

Shivaji Lal Sondhi

Papers

On the nature of the Hall insulator

The Nature of the Hall Insulator

A Field theory for the read operator

Magnetothermoelectric response near quantum critical points

Long-range interactions and the quantum Hall effect.