Pliocene–Pleistocene basin evolution along the Garlock fault zone, Pilot Knob Valley, California

Exposed Pliocene–Pleistocene terrestrial strata provide an archive of the spatial and temporal development of a basin astride the sinistral Garlock fault in California. In the southern Slate Range and Pilot Knob Valley, an ∼2000-m-thick package of Late Cenozoic strata has been uplifted and tilted to the northeast. We name this succession the formation of Pilot Knob Valley and provide new chronologic, stratigraphic, and provenance data for these rocks. The unit is divided into five members that record different source areas and depositional patterns: (1) the lowest exposed strata are conglomeratic rocks derived from Miocene Eagle Crags volcanic field to the south and east across the Garlock fault; (2) the second member consists mostly of fine-grained rocks with coarser material derived from both southern and northern sources; and (3) the upper three members are primarily coarse-grained conglomerates and sandstones derived from the adjacent Slate Range to the north. Tephrochronologic data from four ash samples bracket deposition of the second member to 3.6–3.3 Ma and the fourth member to between 1.1 and 0.6 Ma. A fifth tephrochronologic sample from rocks south of the Garlock fault near Christmas Canyon brackets deposition of a possible equivalent to the second member of the formation of Pilot Knob Valley at ca. 3.1 Ma. Although the age of the base of the lowest member is not directly dated, regional stratigraphic and tectonic associations suggest that the basin started forming ca. 4–5 Ma. By ca. 3.6 Ma, the northward progradation fanglomerate sourced in the Eagle Crags region waned, and subsequent deposition occurred in shallow lacustrine systems. At ca. 3.3 Ma, southward progradation of conglomerates derived from the Slate Range began. Circa 1.1 Ma, continued southward progradation of fanglomerate with Slate Range sources is characterized by a shift to coarser grain sizes, interpreted to reflect uplift of the Slate Range. Overall, basin architecture and the temporal evolution of different source regions were controlled by activity on three regionally important faults—the Garlock, the Marine Gate, and the Searles Valley faults. The timing and style of motions on these faults appear to be directly linked to patterns of basin development

The virtual Haken conjecture: Experiments and examples

A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture says that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. Here, we discuss two interrelated topics concerning this conjecture. First, we describe computer experiments which give strong evidence that the Virtual Haken Conjecture is true for hyperbolic 3-manifolds. We took the complete Hodgson-Weeks census of 10,986 small-volume closed hyperbolic 3-manifolds, and for each of them found finite covers which are Haken. There are interesting and unexplained patterns in the data which may lead to a better understanding of this problem. Second, we discuss a method for transferring the virtual Haken property under Dehn filling. In particular, we show that if a 3-manifold with torus boundary has a Seifert fibered Dehn filling with hyperbolic base orbifold, then most of the Dehn filled manifolds are virtually Haken. We use this to show that every non-trivial Dehn surgery on the figure-8 knot is virtually Haken.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper12.abs.htm

Benchmarking Noisy Intermediate Scale Quantum Error Mitigation Strategies for Ground State Preparation of the HCl Molecule

Due to numerous limitations including restrictive qubit topologies, short coherence times and prohibitively high noise floors, few quantum chemistry experiments performed on existing noisy intermediate-scale quantum hardware have achieved the high bar of chemical precision, namely energy errors to within 1.6 mHa of full configuration interaction. To have any hope of doing so, we must layer contemporary resource reduction techniques with best-in-class error mitigation methods; in particular, we combine the techniques of qubit tapering and the contextual subspace variational quantum eigensolver with several error mitigation strategies comprised of measurement-error mitigation, symmetry verification, zero-noise extrapolation and dual-state purification. We benchmark these strategies across a suite of eight 27-qubit IBM Falcon series quantum processors, taking preparation of the HCl molecule's ground state as our testbed.Comment: 18 pages, 15 figures, 4 tables, supplementary GitHub repository: https://github.com/TimWeaving/quantum-error-mitigatio

A Stabilizer Framework for the Contextual Subspace Variational Quantum Eigensolver and the Noncontextual Projection Ansatz

Quantum chemistry is a promising application for noisy intermediate-scale quantum (NISQ) devices. However, quantum computers have thus far not succeeded in providing solutions to problems of real scientific significance, with algorithmic advances being necessary to fully utilize even the modest NISQ machines available today. We discuss a method of ground state energy estimation predicated on a partitioning of the molecular Hamiltonian into two parts: one that is noncontextual and can be solved classically, supplemented by a contextual component that yields quantum corrections obtained via a Variational Quantum Eigensolver (VQE) routine. This approach has been termed Contextual Subspace VQE (CS-VQE); however, there are obstacles to overcome before it can be deployed on NISQ devices. The problem we address here is that of the ansatz, a parametrized quantum state over which we optimize during VQE; it is not initially clear how a splitting of the Hamiltonian should be reflected in the CS-VQE ansätze. We propose a "noncontextual projection" approach that is illuminated by a reformulation of CS-VQE in the stabilizer formalism. This defines an ansatz restriction from the full electronic structure problem to the contextual subspace and facilitates an implementation of CS-VQE that may be deployed on NISQ devices. We validate the noncontextual projection ansatz using a quantum simulator and demonstrate chemically precise ground state energy calculations for a suite of small molecules at a significant reduction in the required qubit count and circuit depth