Twist Defects Research Articles

Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement

Calderbank-Shor-Steane (CSS) codes are a class of quantum error correction codes that contains the toric code and fracton models. A procedure called foliation defines a cluster state for a given CSS code. We use the CSS chain complex and its tensor product with other chain complexes to describe the topological structure in the foliated cluster state, and argue that it has a symmetry-protected topological order protected by generalized global symmetries supported on cycles in the foliated CSS chain complex. We demonstrate the so-called anomaly inflow between CSS codes and corresponding foliated cluster states by explicitly showing the equality of the gauge transformations of the bulk and boundary partition functions defined as functionals of defect world-volumes. We show that the bulk and boundary defects are related via measurement of the bulk system. Further, we provide a procedure to obtain statistical models associated with general CSS codes via the foliated cluster state, and derive a generalization of the Kramers-Wannier-Wegner duality for such statistical models with insertion of twist defects. We also study the measurement-assisted gauging method with cluster-state entanglers for CSS/fracton models based on recent proposals in the literature, and demonstrate a non-invertible fusion of duality operators. Using the cluster-state entanglers, we construct the so-called strange correlator for general CSS/fracton models. Finally, we introduce a new family of subsystem-symmetric quantum models each of which is self-dual under the generalized Kramers-Wannier-Wegner duality transformation, which becomes a non-invertible symmetry.

Photonic defect modes in cholesteric liquid crystal resonators with embedded isotropic layers

Photonic defect modes are explored as a viable alternative to standard photonic band edge modes in photonic crystal applications, especially due to their typically high Q-factors and local density of states. For example, they can be used in nonlinearity enhancement, lasing, and cavity quantum electrodynamics. However, they are strongly dependent on any structural change and need to be well-controlled to ensure the desired resonance frequency. Here, we present a study of the photonic defect modes that appear in a structure where a layer of isotropic material is embedded between two layers of cholesteric liquid crystal (CLC), using full electrodynamics numerical simulations. We present typical transmission spectra and electric field profiles of selected defect modes and then analyze the influence of geometrical and material parameters on the eigenfrequencies and Q-factors of the modes within and around the photonic bandgap, including refractive indices and thicknesses of isotropic and liquid crystal layers, and different anchoring orientations at the boundaries of the isotropic defect layer. Additionally, a connection of such defect modes to previously extensively analyzed twist defect modes is given. Eigenmodes in asymmetric resonators are also presented, where CLC layers surrounding the intermediate isotropic layer are not equally thick, enabling biasing of specific directional light emission. More generally, this work aims to contribute to the understanding and design capability in topological soft matter photonics where defect mode lasing could be realized in CLC geometries with different singular and solitonic topological defect structures.

A new twist on the Majorana surface code: Bosonic and fermionic defects for fault-tolerant quantum computation

Majorana zero modes (MZMs) are promising candidates for topologically-protected quantum computing hardware, however their large-scale use will likely require quantum error correction. Majorana surface codes (MSCs) have been proposed to achieve this. However, many MSC properties remain unexplored. We present a unified framework for MSC "twist defects" – anyon-like objects encoding quantum information. We show that twist defects in MSCs can encode twice the amount of topologically protected information as in qubit-based codes or other MSC encoding schemes. This is due to twists encoding both logical qubits and "logical MZMs," with the latter enhancing the protection microscopic MZMs can offer. We explain how to perform universal computation with logical qubits and logical MZMs while potentially using far fewer resources than in other MSC schemes. All Clifford gates can be implemented on logical qubits by braiding twist defects. We introduce lattice-surgery-based techniques for computing with logical MZMs and logical qubits, achieving the effect of Clifford gates with zero time overhead. We also show that logical MZMs may result in improved spatial overheads for sufficiently low rates of quasi-particle poisoning. Finally, we introduce a novel MSC analogue of transversal gates that achieves encoded Clifford gates in small codes by braiding microscopic MZMs. MSC twist defects thus open new paths towards fault-tolerant quantum computation.

Symmetry TFT for subsystem symmetry

We generalize the idea of symmetry topological field theory (SymTFT) for subsystem symmetry. We propose the 2-foliated BF theory with level N in (3 + 1)d as subsystem SymTFT for subsystem ℤN symmetry in (2 + 1)d. Focusing on N = 2, we investigate various topological boundaries. The subsystem Kramers-Wannier and Jordan-Wigner dualities can be viewed as boundary transformations of the subsystem SymTFT and are included in a larger duality web from the subsystem SL(2, ℤ2) symmetry of the bulk foliated BF theory. Finally, we construct the condensation defects and twist defects of S-transformation in the subsystem SL(2, ℤ2), from which the fusion rule of subsystem non-invertible operators can be recovered.

Fault-tolerant quantum computation using low-cost joint measurements

We introduce a new method to implement joint measurements using a 4-qubit twist defect on a rotated surface code. The proposed method enables us to perform logical S (Phase gate), T (π/8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi /8$$\\end{document} gate), and H (Hadamard) with low overhead. Combined with other universal quantum gates, we can implement fault-tolerant quantum computation at the lattice surgery level beyond the gate level while saving considerable resources. We compare our method with previous methods using benchmark circuits by calculating the space and time costs. The proposed method requires additional lines of physical qubits for each encoded patch. Although it slightly increases the space cost for logical H compared to the previous work, it reduces the time cost. In addition, the proposed method decreases the space cost and time cost by introducing a 4-qubit twist defect for logical S and T. Therefore, the overall space-time cost is reduced.

Generalized Kitaev spin liquid model and emergent twist defect

The Kitaev spin liquid model on a honeycomb lattice offers an intriguing feature that encapsulates both Abelian and non-Abelian phases (Alexei Kitaev, 2006). Recent studies suggest that the comprehensive phase diagram of the possible generalized Kitaev model largely depends on the specific details of the discrete lattice, which somewhat deviates from the traditional understanding of “topological” phases. In this paper, we propose an adapted version of the Kitaev spin liquid model on arbitrary planar lattices. Our revised model recovers the surface code model under certain parameter selections within the Hamiltonian terms. Changes in parameters can initiate the emergence of holes, domain walls, or twist defects. Notably, the twist defect, which presents as a lattice dislocation defect, exhibits non-Abelian braiding statistics upon tuning the coefficients of the Hamiltonian. Additionally, we illustrate that the creation, movement, and fusion of these defects can be accomplished through natural time evolution by linearly interpolating the static Hamiltonian. These defects demonstrate the Ising anyon fusion rule as anticipated. Our findings hint at possible implementation in actual physical materials owing to a more realistically achievable two-body interaction.

Inplace Access to the Surface Code Y Basis

In this paper, I cut the cost of Y basis measurement and initialization in the surface code by nearly an order of magnitude. Fusing twist defects diagonally across the surface code patch reaches the Y basis in ⌊d/2⌋+2 rounds, without leaving the bounding box of the patch and without reducing the code distance. I use Monte Carlo sampling to benchmark the performance of the construction under circuit noise, and to analyze the distribution of logical errors. Cheap inplace Y basis measurement reduces the cost of S gates and magic state factories, and unlocks Pauli measurement tomography of surface code qubits on space-limited hardware.

Inderdigitation, double twist, and topological defects in a system of hard lollipops

ABSTRACT Using hard particle Monte Carlo simulations, we studied a three-dimensional system consisting of identical, lollipop-like particles. Each lollipop was built of five identical, tangent balls placed along a line and one larger ball at one side of the particle and modelled the RM734 molecule, for which ferroelectric and splay nematics were recently discovered in the experiment. Although our model did not recreate these phases, we observed inherently polar type A and C interdigitated smectics. Moreover, an intriguing, isotropic phase consisting of double-twisted clusters joined by planar defects was formed for a moderate packing fraction and ball diameter ratio.

Low Energy Twist Defects in Pentatwinned Silver Nanowires

Transmission electron microscopy investigation of networks of pentatwinned silver nanowires has identified the presence of nanoscale defects within individual wires, showing narrow regions of banded contrast normal to the nanowire axis (bamboo faults). Structural analysis using machine learning decomposition of scanning precession electron diffraction data identifies these bamboo faults as a pair of twist boundaries normal to the wire axis creating low energy coincident site lattices between the faulted region and the parent nanowire. This leads to a conservation of the relative misorientation of the twinned structure within the faulted region, leading to an apparent local rotation of the nanowire. Their presence after spraying and nonthermal processing suggests that they may form during nanowire synthesis. However, examination of the networks before and after cyclic straining finds an increase in the density of the defects, indicating that they may also form as a result of mechanical deformation.

The O(N)-flavoured replica twist defect

Replica twist defects are of codimension two and enter in quantum information when finding the Rényi entropy. In particular, they generate n replicas of the bulk conformal field theory. We study the monodromy of such defect and learn how a global O(N)-symmetry is broken. By applying the equation of motion to the bulk-defect operator-product expansion we are able to extract the anomalous dimension of defect-local fields.All of the results in this paper was first presented in my thesis [1], and they generalize previous results on an O(N)-flavoured monodromy twist defect.

Study on twist defect of thin-walled components with asymmetric section during roll forming

With the development of lightweight technology, advanced high strength steel (AHSS) had been widely used in automotive and construction industry. However, twist defect restricts the application of thin-walled components with asymmetric section. In this work, AHSS MS1500 was taken to investigate the complex non-linear elastoplastic behaviors and twist defect in roll forming process. Finite element analysis (FEA) model was established by COPRA software and the material model considered Young’s modulus variation with plastic deformation and material anisotropy was selected. With the developed model, the mechanism of twist defect was discussed and the effect of forming strategy on twist defect was analyzed. For asymmetric hat channel steel, the asymmetric residual longitudinal stress is the principal reason for twist defect. Loading patterns have a significant effect on twist defect and the developed UDT-type (USTB-Durable-type) method can control twist defect effectively. This study has provided theoretical and technical support on large-scale application of AHSS.

Spatial and Temporal Organization of Chromatin at Small and Large Scales

DNA molecules with a total length of two meters contain the genetic information in every cell in our body. To control access to the genes, to organize its spatial structure in the nucleus, and to duplicate and faithfully separate the genetic material, the cell makes use of sophisticated physical mechanisms. Base pair sequences multiplex various layers of information, chromatin remodelers mobilize nucleosomes via twist defects, loop extruders create a system of nonconcatenated rings to spatially organize chromatin, and biomolecular condensates concentrate proteins and nucleic acids in specialized membraneless compartments. In this review, we discuss the current state of understanding of some of these mechanisms that influence the organization of the genetic material in space and time.

Circuit-level protocol and analysis for twist-based lattice surgery

Lattice surgery is a measurement-based technique for performing fault-tolerant quantum computation in two dimensions. When using the surface code, the most general lattice surgery operations require lattice irregularities called twist defects. However, implementing twist-based lattice surgery may require additional resources, such as extra device connectivity, and could lower the threshold and overall performance for the surface code. Here we provide an explicit twist-based lattice surgery protocol and its requisite connectivity layout. We also provide new stabilizer measurement circuits for measuring twist defects which are compatible with our chosen gate scheduling. We undertake the first circuit-level error correction simulations during twist-based lattice surgery using a biased depolarizing noise model. Our results indicate a slight decrease in the threshold for timelike logical failures compared to lattice surgery protocols with no twist defects in the bulk. However, comfortably below threshold (i.e., with CNOT infidelities below $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$), the performance degradation is mild and in fact preferable over proposed alternative twist-free schemes. Lastly, we provide an efficient scheme for measuring $Y$ operators along boundaries of surface codes, which bypasses certain steps that were required in previous schemes.

Activity gradients in two- and three-dimensional active nematics.

We numerically investigate how spatial variations of extensile or contractile active stress affect bulk active nematic systems in two and three dimensions. In the absence of defects, activity gradients drive flows which re-orient the nematic director field and thus act as an effective anchoring force. At high activity, defects are created and the system transitions into active turbulence, a chaotic flow state characterized by strong vorticity. We find that in two-dimensional (2D) systems active torques robustly align +1/2 defects parallel to activity gradients, with defect heads pointing towards contractile regions. In three-dimensional (3D) active nematics disclination lines preferentially lie in the plane perpendicular to activity gradients due to active torques acting on line segments. The average orientation of the defect structures in the plane perpendicular to the line tangent depends on the defect type, where wedge-like +1/2 defects align parallel to activity gradients, while twist defects are aligned anti-parallel. Understanding the response of active nematic fluids to activity gradients is an important step towards applying physical theories to biology, where spatial variations of active stress impact morphogenetic processes in developing embryos and affect flows and deformations in growing cell aggregates, such as tumours.

Charging up the functional bootstrap

We revisit the problem of bootstrapping CFT correlators of charged fields. After discussing in detail how bounds for uncharged fields can be recycled to the charged case, we introduce two sets of analytic functional bases for correlators on the line. The first, which we call “simple”, is essentially a direct sum of analytic functionals for the uncharged case. We use it to establish very general bounds on the OPE density appearing in charged correlators. The second basis is dual to generalized free fields and we explain how it is related to a charged version of the Polyakov bootstrap. We apply these functionals to map out the space of correlators and obtain new improved bounds on the 3d Ising twist defect.

Investigation of Track Geometry Defects on a Heavy-Haul Railway Line

This paper presents an in-depth case study of a heavy-haul railway line in Sweden to analyze the twist and longitudinal level geometry defects. A linear model was applied to model the evolution of the amplitude of the longitudinal level defects and twist over time. Despite the effect of the defect shapes on the dynamic track loads, the amplitude of the defects still is the only criterion used for the assessment of geometry defect severity. The application of first- and second-order derivatives to capture information about the shape of defects was investigated in the case study. In addition, the RUSBoost algorithm was used to classify track sections into healthy and unhealthy sections using the imbalance class data set. In this algorithm, the standard deviation and the kurtosis of the geometry parameters were used as explanatory variables. Finally, the abnormal track geometry degradation patterns identified in the case study were explored in detail. The results of the analysis can be used directly in maintenance modeling and used for the purpose of maintenance scheduling.

Surprising Twists in Nucleosomal DNA with Implication for Higher-order Folding

While nucleosomes are dynamic entities that must undergo structural deformations to perform their functions, the general view from available high-resolution structures is a largely static one. Even though numerous examples of twist defects have been documented, the DNA wrapped around the histone core is generally thought to be overtwisted. Analysis of available high-resolution structures from the Protein Data Bank reveals a heterogeneous distribution of twist along the nucleosomal DNA, with clear patterns that are consistent with the literature, and a significant fraction of structures that are undertwisted. The subtle differences in nucleosomal DNA folding, which extend beyond twist, have implications for nucleosome disassembly and modeled higher-order structures. Simulations of oligonucleosome arrays built with undertwisted models behave very differently from those constructed from overtwisted models, in terms of compaction and inter-nucleosome contacts, introducing configurational changes equivalent to those associated with 2–3 base-pair changes in nucleosome spacing. Differences in the nucleosomal DNA pathway, which underlie the way that DNA enters and exits the nucleosome, give rise to different nucleosome-decorated minicircles and affect the topological mix of configurational states.

Investigation of Twist Defect in Single Point Incremental Forming (SPIF) Process

Single point incremental forming (SPIF) is a choice of interest in many manufacturing industries due to its wide range of applications. Materials such as copper, aluminum, steel, and many others formed various complex shapes through this process. However, the forming process could sometimes result in process defects, which could strongly influence the formed parts' geometric accuracy. The twist defect is one of them, which incrementally twists the forming sheet with a small angle at each forming step. In this paper, twist phenomena in the SPIF process have been investigated both numerically and experimentally. In the experiment, Aluminum Alloy (AA5052) was used to form a truncated pyramid shape, and a room temperature tensile test has been conducted to achieve the material's tensile properties. Then, the material property used in the simulation study of the SPIF using LS-DYNA software, where twist defect, stresses, strain, and thickness distribution are studied. The results from simulation and experiment show significant similarity against the expected results and this conveys that the proposed FE model of the SPIF process can be used to investigate the presence of twist, distributions of stress and strain, and thinning locations in the formed part.

Elastically tuned defect mode within a cholesteric elastomer doped with metallic nano-spheres

A composite material, formed by a cholesteric elastomer slab, doped with randomly but uniformly distributed metallic nano-spheres, is studied. The cholesteric elastomer has a twist jump defect consisting of a finite discontinuity in the helical angle of the structure. The transmittance and reflectance spectra of the elastomer sample are studied when circularly polarized electromagnetic waves are impinging, while it is stretched by the action of an externally imposed agent. It has been observed that the co-polarized and cross-polarized transmittance and reflectance depend on the wavelength of the impinging wave and the amount of metallic spheres parameterized by the filling factor, strain, and magnitude of the twist defect. Additionally, we have found that the position of the line defect within the band reflection is red-shifted either by increasing the filling factor or stretching the sample.

Autoinhibitory elements of the Chd1 remodeler block initiation of twist defects by destabilizing the ATPase motor on the nucleosome

Chromatin remodelers are ATP (adenosine triphosphate)-powered motors that reposition nucleosomes throughout eukaryotic chromosomes. Remodelers possess autoinhibitory elements that control the direction of nucleosome sliding, but underlying mechanisms of inhibition have been unclear. Here, we show that autoinhibitory elements of the yeast Chd1 remodeler block nucleosome sliding by preventing initiation of twist defects. We show that two autoinhibitory elements-the chromodomains and bridge-reinforce each other to block sliding when the DNA-binding domain is not bound to entry-side DNA. Our data support a model where the chromodomains and bridge target nucleotide-free and ADP-bound states of the ATPase motor, favoring a partially disengaged state of the ATPase motor on the nucleosome. By bypassing distortions of nucleosomal DNA prior to ATP binding, we propose that autoinhibitory elements uncouple the ATP binding/hydrolysis cycle from DNA translocation around the histone core.