Noise-robust quantum sensing via optimal multi-probe spectroscopy

The dynamics of quantum systems are unavoidably influenced by their environment and in turn observing a quantum system (probe) can allow one to measure its environment: Measurements and controlled manipulation of the probe such as dynamical decoupling sequences as an extension of the Ramsey interference measurement allow to spectrally resolve a noise field coupled to the probe. Here, we introduce fast and robust estimation strategies for the characterization of the spectral properties of classical and quantum dephasing environments. These strategies are based on filter function orthogonalization, optimal control filters maximizing the relevant Fisher Information and multi-qubit entanglement. We investigate and quantify the robustness of the schemes under different types of noise such as finite-precision measurements, dephasing of the probe, spectral leakage and slow temporal fluctuations of the spectrum.Comment: 13 pages, 14 figure

Probing Convex Polygons with a Wedge

Minimizing the number of probes is one of the main challenges in reconstructing geometric objects with probing devices. In this paper, we investigate the problem of using an $\omega$-wedge probing tool to determine the exact shape and orientation of a convex polygon. An $\omega$-wedge consists of two rays emanating from a point called the apex of the wedge and the two rays forming an angle $\omega$. To probe with an $\omega$-wedge, we set the direction that the apex of the probe has to follow, the line $\overrightarrow L$, and the initial orientation of the two rays. A valid $\omega$-probe of a convex polygon $O$ contains $O$ within the $\omega$-wedge and its outcome consists of the coordinates of the apex, the orientation of both rays and the coordinates of the closest (to the apex) points of contact between $O$ and each of the rays. We present algorithms minimizing the number of probes and prove their optimality. In particular, we show how to reconstruct a convex $n$-gon (with all internal angles of size larger than $\omega$) using $2n-2$ $\omega$-probes; if $\omega = \pi/2$, the reconstruction uses $2n-3$ $\omega$-probes. We show that both results are optimal. Let $N_B$ be the number of vertices of $O$ whose internal angle is at most $\omega$, (we show that $0 \leq N_B \leq 3$). We determine the shape and orientation of a general convex $n$-gon with $N_B=1$ (respectively $N_B=2$, $N_B=3$) using $2n-1$ (respectively $2n+3$, $2n+5$) $\omega$-probes. We prove optimality for the first case. Assuming the algorithm knows the value of $N_B$ in advance, the reconstruction of $O$ with $N_B=2$ or $N_B=3$ can be achieved with $2n+2$ probes,- which is optimal.Comment: 31 pages, 27 figure

Delineation of individual human chromosomes in metaphase and interphase cells by in situ suppression hybridization using recombinant DNA libraries

A method of in situ hybridization for visualizing individual human chromosomes from pter to qter, both in metaphase spreads and interphase nuclei, is reported. DNA inserts from a single chromosomal library are labeled with biotin and partially preannealed with a titrated amount of total human genomic DNA prior to hybridization with cellular or chromosomal preparations. The cross-hybridization of repetitive sequences to nontargeted chromosomes can be markedly suppressed under appropriate preannealing conditions. The remaining single-stranded DNA is hybridized to specimens of interest and detected with fluorescent or enzymelabeled avidin conjugates following post-hybridization washes. DNA inserts from recombinant libraries for chromosomes 1, 4, 7, 8, 13, 14, 18, 20, 21, 22, and X were assessed for their ability to decorate specifically their cognate chromosome; most libraries proved to be highly specific. Quantitative densitometric analyses indicated that the ratio of specific to nonspecific hybridization signal under optimal preannealing conditions was at least 8:1. Interphase nuclei showed a cohesive territorial organization of chromosomal domains, and laserscanning confocal fluorescence microscopy was used to aid the 3-D visualization of these domains. This method should be useful for both karyotypic studies and for the analysis of chromosome topography in interphase cells

Reconstructing Rational Functions with FireFly\texttt{FireFly}

We present the open-source $\texttt{C++}$ library $\texttt{FireFly}$ for the reconstruction of multivariate rational functions over finite fields. We discuss the involved algorithms and their implementation. As an application, we use $\texttt{FireFly}$ in the context of integration-by-parts reductions and compare runtime and memory consumption to a fully algebraic approach with the program $\texttt{Kira}$.Comment: 46 pages, 3 figures, 6 tables; v2: matches published versio

Time-resolved magnetic sensing with electronic spins in diamond

Quantum probes can measure time-varying fields with high sensitivity and spatial resolution, enabling the study of biological, material, and physical phenomena at the nanometer scale. In particular, nitrogen-vacancy centers in diamond have recently emerged as promising sensors of magnetic and electric fields. Although coherent control techniques have measured the amplitude of constant or oscillating fields, these techniques are not suitable for measuring time-varying fields with unknown dynamics. Here we introduce a coherent acquisition method to accurately reconstruct the temporal profile of time-varying fields using Walsh sequences. These decoupling sequences act as digital filters that efficiently extract spectral coefficients while suppressing decoherence, thus providing improved sensitivity over existing strategies. We experimentally reconstruct the magnetic field radiated by a physical model of a neuron using a single electronic spin in diamond and discuss practical applications. These results will be useful to implement time-resolved magnetic sensing with quantum probes at the nanometer scale.Comment: 8+12 page

Compressive Sensing DNA Microarrays

Compressive sensing microarrays (CSMs) are DNA-based sensors that operate using group testing and compressive sensing (CS) principles. In contrast to conventional DNA microarrays, in which each genetic sensor is designed to respond to a single target, in a CSM, each sensor responds to a set of targets. We study the problem of designing CSMs that simultaneously account for both the constraints from CS theory and the biochemistry of probe-target DNA hybridization. An appropriate cross-hybridization model is proposed for CSMs, and several methods are developed for probe design and CS signal recovery based on the new model. Lab experiments suggest that in order to achieve accurate hybridization profiling, consensus probe sequences are required to have sequence homology of at least 80% with all targets to be detected. Furthermore, out-of-equilibrium datasets are usually as accurate as those obtained from equilibrium conditions. Consequently, one can use CSMs in applications in which only short hybridization times are allowed

Bacterial Community Reconstruction Using A Single Sequencing Reaction

Bacteria are the unseen majority on our planet, with millions of species and comprising most of the living protoplasm. While current methods enable in-depth study of a small number of communities, a simple tool for breadth studies of bacterial population composition in a large number of samples is lacking. We propose a novel approach for reconstruction of the composition of an unknown mixture of bacteria using a single Sanger-sequencing reaction of the mixture. This method is based on compressive sensing theory, which deals with reconstruction of a sparse signal using a small number of measurements. Utilizing the fact that in many cases each bacterial community is comprised of a small subset of the known bacterial species, we show the feasibility of this approach for determining the composition of a bacterial mixture. Using simulations, we show that sequencing a few hundred base-pairs of the 16S rRNA gene sequence may provide enough information for reconstruction of mixtures containing tens of species, out of tens of thousands, even in the presence of realistic measurement noise. Finally, we show initial promising results when applying our method for the reconstruction of a toy experimental mixture with five species. Our approach may have a potential for a practical and efficient way for identifying bacterial species compositions in biological samples.Comment: 28 pages, 12 figure

Noise and nonlinearities in high-throughput data

High-throughput data analyses are becoming common in biology, communications, economics and sociology. The vast amounts of data are usually represented in the form of matrices and can be considered as knowledge networks. Spectra-based approaches have proved useful in extracting hidden information within such networks and for estimating missing data, but these methods are based essentially on linear assumptions. The physical models of matching, when applicable, often suggest non-linear mechanisms, that may sometimes be identified as noise. The use of non-linear models in data analysis, however, may require the introduction of many parameters, which lowers the statistical weight of the model. According to the quality of data, a simpler linear analysis may be more convenient than more complex approaches. In this paper, we show how a simple non-parametric Bayesian model may be used to explore the role of non-linearities and noise in synthetic and experimental data sets.Comment: 12 pages, 3 figure