Superstructures and charge-density waves in distorted and intercalated layer materials

Imperial Users onl

Logical gates by code deformation in topological quantum codes

Quantum error correcting codes (QECCs) allow us to protect qubits from noise and are expected to be essential features of any kind of scalable, fault-tolerant quantum computer. By encoding information in a QECC we make unintentional modification of that information less likely, but also make intentional modification more difficult. Operations that perform such modifications are referred to as “logical operations” or “logical gates” and a common, fault-tolerant approach to performing these operations is the use of “transversal” logical gates. However, a fundamental theorem of quantum error correction is that no QECC can possess a universal set of transversal gates. An alternate approach to performing logical gates is the technique of code deformation, which involves a sequence of modifications (deformations) of the code which transform the encoded information. In the class of QECCs called topological codes these deformations have natural mathematical interpretations in terms of transformations of a manifold, and physical interpretations in terms of the motions of quasiparticles in certain condensed matter systems. Here we examine two different code deformation techniques. The first is the braiding of a certain type of defect (a twist defect) in multiple copies of the two- dimensional surface code. We classify the set of logical operations which can be performed in this fashion by drawing a connection to the braiding relations of a hierarchy of anyon models. The second example involves switching between two- and three-dimensional versions of a code and an unorthodox method of decoding called just-in-time (JIT) decoding. We numerically demonstrate the existence of a threshold for this decoding strategy in surface codes and then proceed to examine the errors that occur if partial transversal gates are interleaved with this procedure

Local Probabilistic Decoding of a Quantum Code

flip is an extremely simple and maximally local classical decoder which has been used to great effect in certain classes of classical codes. When applied to quantum codes there exist constant-weight errors (such as half of a stabiliser) which are uncorrectable for this decoder, so previous studies have considered modified versions of flip, sometimes in conjunction with other decoders. We argue that this may not always be necessary, and present numerical evidence for the existence of a threshold for flip when applied to the looplike syndromes of a three-dimensional toric code on a cubic lattice. This result can be attributed to the fact that the lowest-weight uncorrectable errors for this decoder are closer (in terms of Hamming distance) to correctable errors than to other uncorrectable errors, and so they are likely to become correctable in future code cycles after transformation by additional noise. Introducing randomness into the decoder can allow it to correct these "uncorrectable" errors with finite probability, and for a decoding strategy that uses a combination of belief propagation and probabilistic flip we observe a threshold of $\sim5.5\%$ under phenomenological noise. This is comparable to the best known threshold for this code ($\sim7.1\%$) which was achieved using belief propagation and ordered statistics decoding [Higgott and Breuckmann, 2022], a strategy with a runtime of $O(n^3)$ as opposed to the $O(n)$ ($O(1)$ when parallelised) runtime of our local decoder. We expect that this strategy could be generalised to work well in other low-density parity check codes, and hope that these results will prompt investigation of other previously overlooked decoders.Comment: 10 pages + 1 page appendix, 7 figures. Comments welcome.; v3 Published versio

Non-Pauli errors in the three-dimensional surface code

A powerful feature of stabilizer error correcting codes is the fact that stabilizer measurement projects arbitrary errors to Pauli errors, greatly simplifying the physical error correction process as well as classical simulations of code performance. However, logical non-Clifford operations can map Pauli errors to non-Pauli (Clifford) errors, and while subsequent stabilizer measurements will project the Clifford errors back to Pauli errors the resulting distributions will possess additional correlations that depend on both the nature of the logical operation and the structure of the code. Previous work has studied these effects when applying a transversal T gate to the three-dimensional color code and shown the existence of a nonlocal "linking charge"phenomenon between membranes of intersecting errors. In this paper we generalise these results to the case of a CCZ gate in the three-dimensional surface code and find that many aspects of the problem are much more easily understood in this setting. In particular, the emergence of linking charge is a local effect rather than a nonlocal one. We use the relative simplicity of Clifford errors in this setting to simulate their effect on the performance of a single-shot magic state preparation process and find that their effect on the threshold is largely determined by probability of X errors occurring immediately prior to the application of the gate, after the most recent stabilizer measurement

A Fiber-Based Laser Ultrasonic System for Remote Inspection of Limited Access Components

Surface and plate waves are commonly used to nondestructively inspect the near-surface region of a solid component for cracks and other defects due to, for example, structural fatigue. One particularly attractive method of generating and detecting such ultrasonic signals is laser based ultrasonics (LBU) [1]. In particular, because it is non-contact (i.e., does not require couplant), LBU can be implemented for inspection of limited access components using optical fibers, requiring only a small cross-sectional area for access. An example can be found in the inspection of internal surfaces of an aircraft wing as shown in Figure 1 where a contact method would obviously be difficult to apply. Furthermore, in cases where extremely high sensitivity is required, bandwidth reduction can be employed by concentrating the laser generated signal into a narrow frequency band

Longitudinal Wave Precursor Signal from an Optically Penetrating Thermoelastic Laser Source

The thermoelastic laser ultrasonic source depends on the optical absorption of energy at the sample surface to produce a volumetric expansion. This paper presents the results of calculations and measurements on the effects of optical penetration of the laser beam into the sample and the elastic waveforms produced. A central result is prediction of a sharp longitudinal waveform that precedes the main waveform and is very similar to that observed with an ablative source (normal point force). The shape of this precursor signal is strongly dependent on the optical penetration depth of the material. A basic explanation of the origin of the precursor signal is given in terms of a one-dimensional model using point sources imbedded within the material. Experimental measurements on a material with a substantial optical penetration depth directly confirm calculations using 2-D integral transform techniques by taking into account the temperature variation with depth

Interaction of laser generated ultrasonic waves with wedge-shaped samples

Wedge-shaped samples can be used as a model of acoustic interactions with samples ranging from ocean wedges, to angled defects such as rolling contact fatigue, to thickness measurements of samples with non-parallel faces. We present work on laser generated ultrasonic waves on metal samples; one can measure the dominant Rayleigh-wave mode, but longitudinal and shear waves are also generated. We present calculations, models, and measurements giving the dependence of the arrival times and amplitudes of these modes on the wedge apex angle and the separation of generation and detection points, and hence give a measure of the wedge characteristics

Numerical Implementation of Just-In-Time Decoding in Novel Lattice Slices Through the Three-Dimensional Surface Code

We build on recent work by B. Brown (Sci. Adv. 6, eaay4929 (2020)) to develop and simulate an explicit recipe for a just-in-time decoding scheme in three 3D surface codes, which can be used to implement a transversal (non-Clifford) $\overline{CCZ}$ between three 2D surface codes in time linear in the code distance. We present a fully detailed set of bounded-height lattice slices through the 3D codes which retain the code distance and measurement-error detecting properties of the full 3D code and admit a dimension-jumping process which expands from/collapses to 2D surface codes supported on the boundaries of each slice. At each timestep of the procedure the slices agree on a common set of overlapping qubits on which $CCZ$ should be applied. We use these slices to simulate the performance of a simple JIT decoder against stochastic $X$ and measurement errors and find evidence for a threshold $p_c \sim 0.1\%$ in all three codes. We expect that this threshold could be improved by optimisation of the decoder.Comment: 19 pages, 11 figures. Additional supplementary materials at https://github.com/tRowans/JIT-supplementary-materials. v2; removed some claims regarding issues with staircase slices and changed one referenc

A New Concept for a Laser-Based Ultrasonic Phased Array Receiver Using Photo-emf Detection

The virtues of laser-based ultrasound [1], LBU, in general, and phased-array generation and detection in particular, have been appreciated for many years. The ability to improve the spatial resolution of an imaging system, coupled with the potential reduction in local laser intensity at a given location on a component to avoid surface damage while still realizing enhanced performance, represent but two motivating factors that have driven the community to seek methods by which to realize phased-array processing. There has been much activity in demonstrating that phased-array generation of ultrasound can lead to an enhanced directivity of the ultrasound as well as to a decrease (or, increase) in the bandwidth of the generated ultrasound (if desired), be it in the bulk or along the surface of components. Examples of such phased-array generationtechniques (either in the thermoelastic or ablative regimes) include illumination of several discrete spots or locus of points with pulsed lasers [1] on the surface of a workpiece (simultaneously or sequentially), be it a line, an annular ring, or a plurality of spots — or illumination of a scanning pattern of lines along the surface of a sample, the so-called phase-velocity scanning technique [2]. By extension of the phased-array generation concept, one is led to consider the notion of laser-based, phased-array detectionof ultrasound [3]. By reciprocity, this can lead to a receiver of higher resolution relative to a single location for the optical sensing of the ultrasound, as well as to a reduction in the local laser fluence required to achieve a given spatial performance. Moreover, one can, in principle, combine the two modes of phased-array excitation and detection to realize even greater resolution capabilities, which one may refer to as “product processing.” In this case, one has, in essence, a focusing transmitter and an imaging detector, both functioning in concert