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

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

Thin-film transducers for the detection and imaging of Brillouin oscillations in transmission on cultured cells

Mechanical imaging and characterisation of biological cells has been a subject of interest for the last twenty years. Ultrasonic imaging based on the scanning acoustic microscope (SAM) and mechanical probing have been extensively reported. Large acoustic attenuation at high frequencies and the use of conventional piezo-electric transducers limit the operational frequency of a SAM. This limitation results in lower resolution compared to an optical microscope. Direct mechanical probing in the form of applied stress by contacting probes causes stress to cells and exhibits poor depth resolution. More recently, laser ultrasound has been reported to detect ultrasound in the GHz range via Brillouin oscillations on biological cells. This technique offers a promising new high resolution acoustic cell imaging technique. In this work, we propose, design and apply a thin-film based opto-acoustic transducer for the detection in transmission of Brillouin oscillations on cells. The transducer is used to generate acoustic waves, protect the cells from laser radiation and enhance signal-to-noise ratio (SNR). Experimental traces are presented in water films as well as images of the Brillouin frequency of phantom and fixed 3T3 fibroblast cells

Attempts to locate the expression of chondroitin sulfate during embryonic hindbrain development in mouse

Acoustic emission (AE) is the phenomenon in which elastic or stress waves are emitted from a rapid, localized change of strain energy in a material[1]. AE sensors generate electric signals when they are stimulated by an acoustic wave. They are used for safety control of a structure and evaluation of elastic source event and material. Most of them are piezoelectric sensors employing piezoelectric elements which transform elastic signals into electric signals. AE sensors need to be chracterized before using them and the characteristics of them have been usually examined using the mechanical calibration system composed of a known elastic source and a large transmission medium. Well-defined elastic sources include small steel ball impact[2], electric spark[3], and high power laser[4] that generate delta function forces and glass capillary break[5], pencil lead break[6,7] and capacitive Coulomb force[8] that generate step function forces. Glass capillary break is known to generate step force of relatively high power and short rise time. As theoretical approach, a Green’s function for an ideal elastic medium with simple geometry was studied through the utilization of the generalized ray method[9] and numerically calculated through a Fourier inversion method[10]