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BackgroundGene covariation networks are commonly used to study biological processes. The inference of gene covariation networks from observational data can be challenging, especially considering the large number of players involved and the small number of biological replicates available for analysis.ResultsWe propose a new statistical method for estimating the number of erroneous edges in reconstructed networks that strongly enhances commonly used inference approaches. This method is based on a special relationship between sign of correlation (positive/negative) and directionality (up/down) of gene regulation, and allows for the identification and removal of approximately half of all erroneous edges. Using the mathematical model of Bayesian networks and positive correlation inequalities we establish a mathematical foundation for our method. Analyzing existing biological datasets, we find a strong correlation between the results of our method and false discovery rate (FDR). Furthermore, simulation analysis demonstrates that our method provides a more accurate estimate of network error than FDR.ConclusionsThus, our study provides a new robust approach for improving reconstruction of covariation networks.ReviewersThis article was reviewed by Eugene Koonin, Sergei Maslov, Daniel Yasumasa Takahashi.Electronic supplementary materialThe online version of this article (doi:10.1186/s13062-016-0155-0) contains supplementary material, which is available to authorized users.

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We introduce maximum-likelihood fragment tomography (MLFT) as an improved circuit cutting technique for running clustered quantum circuits on quantum devices with a limited number of qubits. In addition to minimizing the classical computing overhead of circuit cutting methods, MLFT finds the most likely probability distribution for the output of a quantum circuit, given the measurement data obtained from the circuit’s fragments. We demonstrate the benefits of MLFT for accurately estimating the output of a fragmented quantum circuit with numerical experiments on random unitary circuits. Finally, we show that circuit cutting can estimate the output of a clustered circuit with higher fidelity than full circuit execution, thereby motivating the use of circuit cutting as a standard tool for running clustered circuits on quantum hardware.

We investigate many-body spin squeezing dynamics in an XXZ model with interactions that fall off with distance r as 1/r α in D = 2 and 3 spatial dimensions. In stark contrast to the Ising model, we find a broad parameter regime where spin squeezing comparable to the infinite-range α = 0 limit is achievable even when interactions are short-ranged, α > D. A region of "collective" behavior in which optimal squeezing grows with system size extends all the way to the α → ∞ limit of nearestneighbor interactions, where achievable squeezing is primarily limited by the coherence time of a system. We identify the boundary between collective and Ising-limited squeezing behaviors with a dynamical phase transition between regions of parametrically distinct entanglement growth. Our predictions, made using the discrete truncated Wigner approximation (DTWA), are testable in a variety of experimental cold atomic, molecular, and optical platforms.

A hybrid quantum register consisting of nuclear spins in a solid-state platform coupled to a central electron spin is expected to combine the advantages of its elements. However, the potential to exploit long nuclear spin coherence times is severely limited by magnetic noise from the central electron spin during external interrogation. We overcome this obstacle and present protocols for addressing a decoherence-free nuclear spin subspace, which was not accessible by previously existing methods. We demonstrate the efficacy of our protocols using detailed numerical simulations of a nitrogenvacancy centre with nearby 13 C nuclei, and show that the resulting hybrid quantum register is immune to electron spin noise and external magnetic field drifts. Our work takes an important step toward realizing robust quantum registers that can be easily manipulated, entangled, and, at the same time, well isolated from external noise, with applications from quantum information processing and communication to quantum sensing. arXiv:1708.09414v2 [quant-ph]

Background: Gene covariation networks are commonly used to study biological processes. The inference of gene covariation networks from observational data can be challenging, especially considering the large number of players involved and the small number of biological replicates available for analysis. Results: We propose a new statistical method for estimating the number of erroneous edges in reconstructed networks that strongly enhances commonly used inference approaches. This method is based on a special relationship between sign of correlation (positive/negative) and directionality (up/down) of gene regulation, and allows for the identification and removal of approximately half of all erroneous edges. Using the mathematical model of Bayesian networks and positive correlation inequalities we establish a mathematical foundation for our method. Analyzing existing biological datasets, we find a strong correlation between the results of our method and false discovery rate (FDR). Furthermore, simulation analysis demonstrates that our method provides a more accurate estimate of network error than FDR.

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