We prove that
Massive gully land consolidation projects, launched in China’s Loess Plateau, aim to restore 2667
 NSFPAR ID:
 10197459
 Publisher / Repository:
 Nature Publishing Group
 Date Published:
 Journal Name:
 Scientific Reports
 Volume:
 10
 Issue:
 1
 ISSN:
 20452322
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Abstract depth local random quantum circuits with two qudit nearestneighbor gates on a$${{\,\textrm{poly}\,}}(t) \cdot n^{1/D}$$ $\phantom{\rule{0ex}{0ex}}\text{poly}\phantom{\rule{0ex}{0ex}}\left(t\right)\xb7{n}^{1/D}$D dimensional lattice withn qudits are approximatet designs in various measures. These include the “monomial” measure, meaning that the monomials of a random circuit from this family have expectation close to the value that would result from the Haar measure. Previously, the best bound was due to Brandão–Harrow–Horodecki (Commun Math Phys 346(2):397–434, 2016) for$${{\,\textrm{poly}\,}}(t)\cdot n$$ $\phantom{\rule{0ex}{0ex}}\text{poly}\phantom{\rule{0ex}{0ex}}\left(t\right)\xb7n$ . We also improve the “scrambling” and “decoupling” bounds for spatially local random circuits due to Brown and Fawzi (Scrambling speed of random quantum circuits, 2012). One consequence of our result is that assuming the polynomial hierarchy ($$D=1$$ $D=1$ ) is infinite and that certain counting problems are$${{\,\mathrm{\textsf{PH}}\,}}$$ $\phantom{\rule{0ex}{0ex}}\mathrm{PH}\phantom{\rule{0ex}{0ex}}$ hard “on average”, sampling within total variation distance from these circuits is hard for classical computers. Previously, exact sampling from the outputs of even constantdepth quantum circuits was known to be hard for classical computers under these assumptions. However the standard strategy for extending this hardness result to approximate sampling requires the quantum circuits to have a property called “anticoncentration”, meaning roughly that the output has nearmaximal entropy. Unitary 2designs have the desired anticoncentration property. Our result improves the required depth for this level of anticoncentration from linear depth to a sublinear value, depending on the geometry of the interactions. This is relevant to a recent experiment by the Google Quantum AI group to perform such a sampling task with 53 qubits on a twodimensional lattice (Arute in Nature 574(7779):505–510, 2019; Boixo et al. in Nate Phys 14(6):595–600, 2018) (and related experiments by USTC), and confirms their conjecture that$$\#{\textsf{P}}$$ $\#P$ depth suffices for anticoncentration. The proof is based on a previous construction of$$O(\sqrt{n})$$ $O\left(\sqrt{n}\right)$t designs by Brandão et al. (2016), an analysis of how approximate designs behave under composition, and an extension of the quasiorthogonality of permutation operators developed by Brandão et al. (2016). Different versions of the approximate design condition correspond to different norms, and part of our contribution is to introduce the norm corresponding to anticoncentration and to establish equivalence between these various norms for lowdepth circuits. For random circuits with longrange gates, we use different methods to show that anticoncentration happens at circuit size corresponding to depth$$O(n\ln ^2 n)$$ $O\left(n{ln}^{2}n\right)$ . We also show a lower bound of$$O(\ln ^3 n)$$ $O\left({ln}^{3}n\right)$ for the size of such circuit in this case. We also prove that anticoncentration is possible in depth$$\Omega (n \ln n)$$ $\Omega (nlnn)$ (size$$O(\ln n \ln \ln n)$$ $O(lnnlnlnn)$ ) using a different model.$$O(n \ln n \ln \ln n)$$ $O(nlnnlnlnn)$ 
Abstract We present a proof of concept for a spectrally selective thermal midIR source based on nanopatterned graphene (NPG) with a typical mobility of CVDgrown graphene (up to 3000
), ensuring scalability to large areas. For that, we solve the electrostatic problem of a conducting hyperboloid with an elliptical wormhole in the presence of an$$\hbox {cm}^2\,\hbox {V}^{1}\,\hbox {s}^{1}$$ ${\text{cm}}^{2}\phantom{\rule{0ex}{0ex}}{\text{V}}^{1}\phantom{\rule{0ex}{0ex}}{\text{s}}^{1}$inplane electric field. The localized surface plasmons (LSPs) on the NPG sheet, partially hybridized with graphene phonons and surface phonons of the neighboring materials, allow for the control and tuning of the thermal emission spectrum in the wavelength regime from to 12$$\lambda =3$$ $\lambda =3$ m by adjusting the size of and distance between the circular holes in a hexagonal or square lattice structure. Most importantly, the LSPs along with an optical cavity increase the emittance of graphene from about 2.3% for pristine graphene to 80% for NPG, thereby outperforming stateoftheart pristine graphene light sources operating in the nearinfrared by at least a factor of 100. According to our COMSOL calculations, a maximum emission power per area of$$\upmu$$ $\mu $ W/$$11\times 10^3$$ $11\times {10}^{3}$ at$$\hbox {m}^2$$ ${\text{m}}^{2}$ K for a bias voltage of$$T=2000$$ $T=2000$ V is achieved by controlling the temperature of the hot electrons through the Joule heating. By generalizing Planck’s theory to any grey body and deriving the completely general nonlocal fluctuationdissipation theorem with nonlocal response of surface plasmons in the random phase approximation, we show that the coherence length of the graphene plasmons and the thermally emitted photons can be as large as 13$$V=23$$ $V=23$ m and 150$$\upmu$$ $\mu $ m, respectively, providing the opportunity to create phased arrays made of nanoantennas represented by the holes in NPG. The spatial phase variation of the coherence allows for beamsteering of the thermal emission in the range between$$\upmu$$ $\mu $ and$$12^\circ$$ ${12}^{\circ}$ by tuning the Fermi energy between$$80^\circ$$ ${80}^{\circ}$ eV and$$E_F=1.0$$ ${E}_{F}=1.0$ eV through the gate voltage. Our analysis of the nonlocal hydrodynamic response leads to the conjecture that the diffusion length and viscosity in graphene are frequencydependent. Using finitedifference time domain calculations, coupled mode theory, and RPA, we develop the model of a midIR light source based on NPG, which will pave the way to graphenebased optical midIR communication, midIR color displays, midIR spectroscopy, and virus detection.$$E_F=0.25$$ ${E}_{F}=0.25$ 
Abstract Let
be a positive map from the$$\phi $$ $\varphi $ matrices$$n\times n$$ $n\times n$ to the$$\mathcal {M}_n$$ ${M}_{n}$ matrices$$m\times m$$ $m\times m$ . It is known that$$\mathcal {M}_m$$ ${M}_{m}$ is 2positive if and only if for all$$\phi $$ $\varphi $ and all strictly positive$$K\in \mathcal {M}_n$$ $K\in {M}_{n}$ ,$$X\in \mathcal {M}_n$$ $X\in {M}_{n}$ . This inequality is not generally true if$$\phi (K^*X^{1}K) \geqslant \phi (K)^*\phi (X)^{1}\phi (K)$$ $\varphi \left({K}^{\ast}{X}^{1}K\right)\u2a7e\varphi {\left(K\right)}^{\ast}\varphi {\left(X\right)}^{1}\varphi \left(K\right)$ is merely a Schwarz map. We show that the corresponding tracial inequality$$\phi $$ $\varphi $ holds for a wider class of positive maps that is specified here. We also comment on the connections of this inequality with various monotonicity statements that have found wide use in mathematical physics, and apply it, and a close relative, to obtain some new, definitive results.$${{\,\textrm{Tr}\,}}[\phi (K^*X^{1}K)] \geqslant {{\,\textrm{Tr}\,}}[\phi (K)^*\phi (X)^{1}\phi (K)]$$ $\phantom{\rule{0ex}{0ex}}\text{Tr}\phantom{\rule{0ex}{0ex}}\left[\varphi \left({K}^{\ast}{X}^{1}K\right)\right]\u2a7e\phantom{\rule{0ex}{0ex}}\text{Tr}\phantom{\rule{0ex}{0ex}}\left[\varphi {\left(K\right)}^{\ast}\varphi {\left(X\right)}^{1}\varphi \left(K\right)\right]$ 
Abstract The double differential cross sections of the Drell–Yan lepton pair (
, dielectron or dimuon) production are measured as functions of the invariant mass$$\ell ^+\ell ^$$ ${\ell}^{+}{\ell}^{}$ , transverse momentum$$m_{\ell \ell }$$ ${m}_{\ell \ell}$ , and$$p_{\textrm{T}} (\ell \ell )$$ ${p}_{\text{T}}\left(\ell \ell \right)$ . The$$\varphi ^{*}_{\eta }$$ ${\phi}_{\eta}^{\ast}$ observable, derived from angular measurements of the leptons and highly correlated with$$\varphi ^{*}_{\eta }$$ ${\phi}_{\eta}^{\ast}$ , is used to probe the low$$p_{\textrm{T}} (\ell \ell )$$ ${p}_{\text{T}}\left(\ell \ell \right)$ region in a complementary way. Dilepton masses up to 1$$p_{\textrm{T}} (\ell \ell )$$ ${p}_{\text{T}}\left(\ell \ell \right)$ are investigated. Additionally, a measurement is performed requiring at least one jet in the final state. To benefit from partial cancellation of the systematic uncertainty, the ratios of the differential cross sections for various$$\,\text {Te\hspace{.08em}V}$$ $\phantom{\rule{0ex}{0ex}}\text{Te}\phantom{\rule{0ex}{0ex}}\text{V}$ ranges to those in the Z mass peak interval are presented. The collected data correspond to an integrated luminosity of 36.3$$m_{\ell \ell }$$ ${m}_{\ell \ell}$ of proton–proton collisions recorded with the CMS detector at the LHC at a centreofmass energy of 13$$\,\text {fb}^{1}$$ $\phantom{\rule{0ex}{0ex}}{\text{fb}}^{1}$ . Measurements are compared with predictions based on perturbative quantum chromodynamics, including softgluon resummation.$$\,\text {Te\hspace{.08em}V}$$ $\phantom{\rule{0ex}{0ex}}\text{Te}\phantom{\rule{0ex}{0ex}}\text{V}$ 
Abstract Measurements of the associated production of a W boson and a charm (
) quark in proton–proton collisions at a centreofmass energy of 8$${\text {c}}$$ $\text{c}$ are reported. The analysis uses a data sample corresponding to a total integrated luminosity of 19.7$$\,\text {TeV}$$ $\phantom{\rule{0ex}{0ex}}\text{TeV}$ collected by the CMS detector at the LHC. The W bosons are identified through their leptonic decays to an electron or a muon, and a neutrino. Charm quark jets are selected using distinctive signatures of charm hadron decays. The product of the cross section and branching fraction$$\,\text {fb}^{1}$$ $\phantom{\rule{0ex}{0ex}}{\text{fb}}^{1}$ , where$$\sigma (\text {p}\text {p}\rightarrow \text {W}+ {\text {c}}+ \text {X}) {\mathcal {B}}(\text {W}\rightarrow \ell \upnu )$$ $\sigma (\text{pp}\to \text{W}+\text{c}+\text{X})B(\text{W}\to \ell \nu )$ or$$\ell = \text {e}$$ $\ell =\text{e}$ , and the cross section ratio$$\upmu $$ $\mu $ are measured in a fiducial volume and differentially as functions of the pseudorapidity and of the transverse momentum of the lepton from the W boson decay. The results are compared with theoretical predictions. The impact of these measurements on the determination of the strange quark distribution is assessed.$$\sigma (\text {p}\text {p}\rightarrow {{\text {W}}^{+} + \bar{{\text {c}}} + \text {X}}) / \sigma (\text {p}\text {p}\rightarrow {{\text {W}}^{} + {\text {c}}+ \text {X}})$$ $\sigma (\text{pp}\to {\text{W}}^{+}+\overline{\text{c}}+\text{X})/\sigma (\text{pp}\to {\text{W}}^{}+\text{c}+\text{X})$