Three-dimensional color code thresholds via statistical-mechanical mapping

Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes. Here we investigate the storage threshold error rates for bit-flip and phase-flip noise in the 3D color code on the body-centererd cubic lattice, assuming perfect syndrome measurements. In particular, by exploiting a connection between error correction and statistical mechanics, we estimate the threshold for 1D string-like and 2D sheet-like logical operators to be $p^{(1)}_\mathrm{3DCC} \simeq 1.9\%$ and $p^{(2)}_\mathrm{3DCC} \simeq 27.6\%$. We obtain these results by using parallel tempering Monte Carlo simulations to study the disorder-temperature phase diagrams of two new 3D statistical-mechanical models: the 4- and 6-body random coupling Ising models.Comment: 4+7 pages, 6 figures, 1 tabl

Cellular automaton decoders for topological quantum codes with noisy measurements and beyond

We propose an error correction procedure based on a cellular automaton, the sweep rule, which is applicable to a broad range of codes beyond topological quantum codes. For simplicity, however, we focus on the three-dimensional toric code on the rhombic dodecahedral lattice with boundaries and prove that the resulting local decoder has a non-zero error threshold. We also numerically benchmark the performance of the decoder in the setting with measurement errors using various noise models. We find that this error correction procedure is remarkably robust against measurement errors and is also essentially insensitive to the details of the lattice and noise model. Our work constitutes a step towards finding simple and high-performance decoding strategies for a wide range of quantum low-density parity-check codes

Concentrations of 137Cs^{137}Cs, 40K^{40}K radionuclides and some heavy metals in soil samples of Chochołowska Valley from Tatra National Park

This paper presents the results of determination of artificial $^{137}Cs$ and natural $^{40}K$ activity concentrations and some heavy metals in soil samples from the region of one of the main valleys of Tatra National Park (Chochołowska). Our investigation concentrated on $^{137}Cs$ and heavy metal levels in mountain soil taken from Chochołowska Valley, which revealed great variability in their concentration. The results show considerably small amounts of radionuclides $^{137}Cs$ and $^{40}K$ in the soils. Larger amounts of those elements can be found in the organic surface horizons of the soils. The evaluation of the content of those elements must be based on the bulk density analysis of the soil

Plasma midregional proadrenomedullin (MR-proADM) concentrations and their biological determinants in a reference population

Background: Midregional proadrenomedullin (MR-proADM) is emerging as a prognostic biomarker for detecting the failure of multiple organs. Establishment of scientifically robust reference intervals facilitates interpretation of laboratory test results. The objectives of this study were (i) to establish reliable reference intervals for plasma MR-proADM using a commercially available automated fluoroimmunoassay in apparently healthy individuals, and (ii) to identify biological determinants of MR-proADM concentrations. Methods: A total of 506 questionnaire-identified apparently healthy adults were enrolled in a single-center, cross-sectional study. A final reference group (n = 172) was selected after exclusion of obese individuals, those with increased values of laboratory biomarkers indicating asymptomatic myocardial injury or dysfunction, ongoing inflammation, diabetes, dyslipidemia and renal dysfunction and outliers. Results: The 2.5th and 97.5th percentile intervals for MR-proADM values in the reference group (90% confidence interval) were 0.21 (0.19-0.23) and 0.57 (0.55-0.59) nmol/L, respectively. Although older age, higher values of HbA(1c), C-reactive protein, B-type natriuretic peptide and body mass index, together with a history of smoking and a decreased estimated glomerular filtration rate were significantly associated with increasing concentrations of MR-proADM in both univariate and multivariate analyses, magnitudes of these relationships were modest and did not substantially influence MR-proADM reference intervals. Sex-dependent difference in MR-proADM reference intervals was not detected [0.19 (0.16-0.22)-0.56 (0.54-0.60) nmol/L in females vs. 0.22 (0.20-0.25)-0.58 (0.57-0.63) nmol/L in males]. Conclusions: Our study successfully established robust reference intervals for MR-proADM concentrations in plasma. Considering the negligible influence of potential biological determinants on plasma MR-proADM, we recommend the adoption of single reference intervals for adult population as a whole

Order preserving pattern matching on trees and DAGs

The order preserving pattern matching (OPPM) problem is, given a pattern string $p$ and a text string $t$, find all substrings of $t$ which have the same relative orders as $p$. In this paper, we consider two variants of the OPPM problem where a set of text strings is given as a tree or a DAG. We show that the OPPM problem for a single pattern $p$ of length $m$ and a text tree $T$ of size $N$ can be solved in $O(m+N)$ time if the characters of $p$ are drawn from an integer alphabet of polynomial size. The time complexity becomes $O(m \log m + N)$ if the pattern $p$ is over a general ordered alphabet. We then show that the OPPM problem for a single pattern and a text DAG is NP-complete

Duel and sweep algorithm for order-preserving pattern matching

Given a text $T$ and a pattern $P$ over alphabet $\Sigma$, the classic exact matching problem searches for all occurrences of pattern $P$ in text $T$. Unlike exact matching problem, order-preserving pattern matching (OPPM) considers the relative order of elements, rather than their real values. In this paper, we propose an efficient algorithm for OPPM problem using the "duel-and-sweep" paradigm. Our algorithm runs in $O(n + m\log m)$ time in general and $O(n + m)$ time under an assumption that the characters in a string can be sorted in linear time with respect to the string size. We also perform experiments and show that our algorithm is faster that KMP-based algorithm. Last, we introduce the two-dimensional order preserved pattern matching and give a duel and sweep algorithm that runs in $O(n^2)$ time for duel stage and $O(n^2 m)$ time for sweeping time with $O(m^3)$ preprocessing time.Comment: 13 pages, 5 figure