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"

Physical Review B

Machine learning (ML) encompasses a broad range of algorithms and modeling tools used for a vast array of data processing tasks, which has entered most scientific disciplines in recent years. This article reviews in a selective way the recent research on the interface between machine learning and the physical sciences. This includes conceptual developments in ML motivated by physical insights, applications of machine learning techniques to several domains in physics, and cross fertilization between the two fields. After giving a basic notion of machine learning methods and principles, examples are described of how statistical physics is used to understand methods in ML. This review then describes applications of ML methods in particle physics and cosmology, quantum many-body physics, quantum computing, and chemical and material physics. Research and development into novel computing architectures aimed at accelerating ML are also highlighted. Each of the sections describe recent successes as well as domain-specific methodology and challenges.

Machine learning and the physical sciences

Quantum spin liquids may be considered "quantum disordered" ground states of spin systems, in which zero point fluctuations are so strong that they prevent conventional magnetic long range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, of a degree sufficient to render these states distinct phases of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons that are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments to study quantum spin liquids, and to the diverse probes used therein.

Quantum Spin Liquids

We suggest concrete models for self-correcting quantum memory by reporting examples of local stabilizer codes in 3D that have no string logical operators. Previously known local stabilizer codes in 3D all have stringlike logical operators, which make the codes non-self-correcting. We introduce a notion of “logical string segments” to avoid difficulties in defining one-dimensional objects in discrete lattices. We prove that every stringlike logical operator of our code can be deformed to a disjoint union of short segments, each of which is in the stabilizer group. The code has surfacelike logical operators whose partial implementation has unsatisfied stabilizers along its boundary.

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Local stabilizer codes in three dimensions without string logical operators

Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the “entanglement tsunami” in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ) equation. The mean entanglement grows linearly in time, while fluctuations grow like ðtimeÞ 1 = 3 and are spatially correlated over a distance ∝ ðtimeÞ 2 = 3 . We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i) a stochastic model of a growing surface, (ii) a “minimal cut” picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii) a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the “velocity” of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the well-studied problem of pinning of a membrane or domain wall by disorder.

Quantum Entanglement Growth under Random Unitary Dynamics

We introduce a generalization of conventional lattice gauge theory to describe fracton topological phases, which are characterized by immobile, pointlike topological excitations, and subextensive topological degeneracy. We demonstrate a duality between fracton topological order and interacting spin systems with symmetries along extensive, lower-dimensional subsystems, which may be used to systematically search for and characterize fracton topological phases. Commutative algebra and elementary algebraic geometry provide an effective mathematical tool set for our results. Our work paves the way for identifying possible material realizations of fracton topological phases.

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Fracton Topological Order, Generalized Lattice Gauge Theory and Duality

Random quantum circuits yield minimally structured models for chaotic quantum dynamics, which are able to capture, for example, universal properties of entanglement growth. We provide exact results and coarse-grained models for the spreading of operators by quantum circuits made of Haar-random unitaries. We study both 1+1D and higher dimensions and argue that the coarse-grained pictures carry over to operator spreading in generic many-body systems. In 1+1D, we demonstrate that the out-of-time-order correlator (OTOC) satisfies a biased diffusion equation, which gives exact results for the spatial profile of the OTOC and determines the butterfly speed vB. We find that in 1+1D, the “front” of the OTOC broadens diffusively, with a width scaling in time as t1/2. We address fluctuations in the OTOC between different realizations of the random circuit, arguing that they are negligible in comparison to the broadening of the front within a realization. Turning to higher dimensions, we show that the averaged OTOC can be understood exactly via a remarkable correspondence with a purely classical droplet growth problem. This implies that the width of the front of the averaged OTOC scales as t1/3 in 2+1D and as t0.240 in 3+1D (exponents of the Kardar-Parisi-Zhang universality class). We support our analytic argument with simulations in 2+1D. We point out that, in two or higher spatial dimensions, the shape of the spreading operator at late times is affected by underlying lattice symmetries and, in general, is not spherical. However, when full spatial rotational symmetry is present in 2+1D, our mapping implies an exact asymptotic form for the OTOC, in terms of the Tracy-Widom distribution. For an alternative perspective on the OTOC in 1+1D, we map it to the partition function of an Ising-like statistical mechanics model. As a result of special structure arising from unitarity, this partition function reduces to a random walk calculation which can be performed exactly. We also use this mapping to give exact results for entanglement growth in 1+1D circuits.

https://link.aps.org/pdf/10.1103/PhysRevX.8.021014

Jeongwan Haah

Papers

Local stabilizer codes in three dimensions without string logical operators

Quantum Entanglement Growth under Random Unitary Dynamics

Fracton Topological Order, Generalized Lattice Gauge Theory and Duality

Operator Spreading in Random Unitary Circuits

Operator Spreading in Random Unitary Circuits