We prove that
Massive gully land consolidation projects, launched in China’s Loess Plateau, aim to restore 2667
 Publication Date:
 NSFPAR ID:
 10197459
 Journal Name:
 Scientific Reports
 Volume:
 10
 Issue:
 1
 ISSN:
 20452322
 Publisher:
 Nature Publishing Group
 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 depthmore »$$\#{\textsf{P}}$$ $\#P$ 
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 derivingmore »$$V=23$$ $V=23$ 
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 Consider a quantum cat map
M associated with a matrix , which is a common toy model in quantum chaos. We show that the mass of eigenfunctions of$$A\in {{\,\textrm{Sp}\,}}(2n,{\mathbb {Z}})$$ $A\in \phantom{\rule{0ex}{0ex}}\text{Sp}\phantom{\rule{0ex}{0ex}}(2n,Z)$M on any nonempty open set in the position–frequency space satisfies a lower bound which is uniform in the semiclassical limit, under two assumptions: (1) there is a unique simple eigenvalue ofA of largest absolute value and (2) the characteristic polynomial ofA is irreducible over the rationals. This is similar to previous work (Dyatlov and Jin in Acta Math 220(2):297–339, 2018; Dyatlov et al. in J Am Math Soc 35(2):361–465, 2022) on negatively curved surfaces and (Schwartz in The full delocalization of eigenstates for the quantized cat map, 2021) on quantum cat maps with , but this paper gives the first results of this type which apply in any dimension. When condition (2) fails we provide a weaker version of the result and discuss relations to existing counterexamples. We also obtain corresponding statements regarding semiclassical measures and damped quantum cat maps.$$n=1$$ $n=1$ 
Abstract In a Merlin–Arthur proof system, the proof verifier (Arthur) accepts valid proofs (from Merlin) with probability 1, and rejects invalid proofs with probability arbitrarily close to 1. The running time of such a system is defined to be the length of Merlin’s proof plus the running time of Arthur. We provide new Merlin–Arthur proof systems for some key problems in finegrained complexity. In several cases our proof systems have optimal running time. Our main results include:
Certifying that a list of
n integers has no 3SUM solution can be done in Merlin–Arthur time . Previously, Carmosino et al. [ITCS 2016] showed that the problem has a nondeterministic algorithm running in$$\tilde{O}(n)$$ $\stackrel{~}{O}\left(n\right)$ time (that is, there is a proof system with proofs of length$$\tilde{O}(n^{1.5})$$ $\stackrel{~}{O}\left({n}^{1.5}\right)$ and a deterministic verifier running in$$\tilde{O}(n^{1.5})$$ $\stackrel{~}{O}\left({n}^{1.5}\right)$ time).$$\tilde{O}(n^{1.5})$$ $\stackrel{~}{O}\left({n}^{1.5}\right)$Counting the number of
k cliques with total edge weight equal to zero in ann node graph can be done in Merlin–Arthur time (where$${\tilde{O}}(n^{\lceil k/2\rceil })$$ $\stackrel{~}{O}\left({n}^{\lceil k/2\rceil}\right)$ ). For odd$$k\ge 3$$ $k\ge 3$k , this bound can be further improved for sparse graphs: for example, counting the number of zeroweight triangles in anm edge graph can be done in Merlin–Arthur time . Previous Merlin–Arthur protocols by Williams [CCC’16] and Björklund and Kaski [PODC’16] could only count$${\tilde{O}}(m)$$ $\stackrel{~}{O}\left(m\right)$k cliques in unweighted graphs, and had worse running times for smallk .Computing the AllPairsmore »
Certifying that an
n variablek CNF is unsatisfiable can be done in Merlin–Arthur time . We also observe an algebrization barrier for the previous$$2^{n/2  n/O(k)}$$ ${2}^{n/2n/O\left(k\right)}$ time Merlin–Arthur protocol of R. Williams [CCC’16] for$$2^{n/2}\cdot \textrm{poly}(n)$$ ${2}^{n/2}\xb7\text{poly}\left(n\right)$ SAT: in particular, his protocol algebrizes, and we observe there is no algebrizing protocol for$$\#$$ $\#$k UNSAT running in time. Therefore we have to exploit nonalgebrizing properties to obtain our new protocol.$$2^{n/2}/n^{\omega (1)}$$ ${2}^{n/2}/{n}^{\omega \left(1\right)}$ Due to the centrality of these problems in finegrained complexity, our results have consequences for many other problems of interest. For example, our work implies that certifying there is no Subset Sum solution toCertifying a Quantified Boolean Formula is true can be done in Merlin–Arthur time
. Previously, the only nontrivial result known along these lines was an Arthur–Merlin–Arthur protocol (where Merlin’s proof depends on some of Arthur’s coins) running in$$2^{4n/5}\cdot \textrm{poly}(n)$$ ${2}^{4n/5}\xb7\text{poly}\left(n\right)$ time.$$2^{2n/3}\cdot \textrm{poly}(n)$$ ${2}^{2n/3}\xb7\text{poly}\left(n\right)$n integers can be done in Merlin–Arthur time , improving on the previous best protocol by Nederlof [IPL 2017] which took$$2^{n/3}\cdot \textrm{poly}(n)$$ ${2}^{n/3}\xb7\text{poly}\left(n\right)$ time.$$2^{0.49991n}\cdot \textrm{poly}(n)$$ ${2}^{0.49991n}\xb7\text{poly}\left(n\right)$