5,943 research outputs found
Quantum walk sampling by growing seed sets
This work describes a new algorithm for creating a superposition over the edge set of a graph, encoding a quantum sample of the random walk stationary distribution. The algorithm requires a number of quantum walk steps scaling as Õ(m1/3δ−1/3), with m the number of edges and δ the random walk spectral gap. This improves on existing strategies by initially growing a classical seed set in the graph, from which a quantum walk is then run. The algorithm leads to a number of improvements: (i) it provides a new bound on the setup cost of quantum walk search algorithms, (ii) it yields a new algorithm for st-connectivity, and (iii) it allows to create a superposition over the isomorphisms of an n-node graph in time Õ(2n/3), surpassing the Ω(2n/2) barrier set by index erasure
Quantum Loewner Evolution
What is the scaling limit of diffusion limited aggregation (DLA) in the
plane? This is an old and famously difficult question. One can generalize the
question in two ways: first, one may consider the {\em dielectric breakdown
model} -DBM, a generalization of DLA in which particle locations are
sampled from the -th power of harmonic measure, instead of harmonic
measure itself. Second, instead of restricting attention to deterministic
lattices, one may consider -DBM on random graphs known or believed to
converge in law to a Liouville quantum gravity (LQG) surface with parameter
.
In this generality, we propose a scaling limit candidate called quantum
Loewner evolution, QLE. QLE is defined in terms of the radial
Loewner equation like radial SLE, except that it is driven by a measure valued
diffusion derived from LQG rather than a multiple of a standard
Brownian motion. We formalize the dynamics of using an SPDE. For each
, there are two or three special values of for which
we establish the existence of a solution to these dynamics and explicitly
describe the stationary law of .
We also explain discrete versions of our construction that relate DLA to
loop-erased random walk and the Eden model to percolation. A certain
"reshuffling" trick (in which concentric annular regions are rotated randomly,
like slot machine reels) facilitates explicit calculation.
We propose QLE as a scaling limit for DLA on a random
spanning-tree-decorated planar map, and QLE as a scaling limit for the
Eden model on a random triangulation. We propose using QLE to endow
pure LQG with a distance function, by interpreting the region explored by a
branching variant of QLE, up to a fixed time, as a metric ball in a
random metric space.Comment: 132 pages, approximately 100 figures and computer simulation
Expansion Testing using Quantum Fast-Forwarding and Seed Sets
Expansion testing aims to decide whether an -node graph has expansion at
least , or is far from any such graph. We propose a quantum expansion
tester with complexity . This accelerates the
classical tester by Goldreich and Ron
[Algorithmica '02], and combines the and
quantum speedups by Ambainis, Childs and Liu
[RANDOM '11] and Apers and Sarlette [QIC '19], respectively. The latter
approach builds on a quantum fast-forwarding scheme, which we improve upon by
initially growing a seed set in the graph. To grow this seed set we use a
so-called evolving set process from the graph clustering literature, which
allows to grow an appropriately local seed set.Comment: v3: final version to appear in Quantu
Comparison of drought stress response and gene expression between a GM maize variety and a near-isogenic non-GM variety
Maize MON810, grown and commercialised worldwide, is the only cultivated GM event in the EU. Maize MON810, variety DKC6575, and the corresponding near-isogenic line Tietar were studied in different growth conditions, to compare their behaviour in response to drought. Main photosynthetic parameters were significantly affected by water stress in both GM and non –GM varieties to a similar extents. Though DKC6575 (GM) had a greater sensitivity in the early phase of stress response as compared with Tietar (non GM), after six days of stress they behaved similarly, and both varieties recovered from stress damage.
Profiling gene expression in water deficit regimes and in a generalised water stress condition showed an up-regulation of many stress- responsive genes, but a greater number of differentially expressed genes was observed in Tietar, with genes belonging to transcription factor families and genes encoding HSPs, LEAs and detoxification enzymes. Since induction of these genes have been indicated from the literature as typical of stress responses, their activation in Tietar rather than in DKC6575 may be reminiscent of a more efficient response to drought. DKC6575 was also analysed for the expression of the transgene CryIAb (encoding the delta-endotoxin insecticidal protein) in water deficit conditions. In all the experiments, the CryIAb transcript was not influenced by water stress, but was expressed at a constant level.. This suggests that though possessing a different pattern of sensitivity to stress, the GM variety maintains the same expression level for the transgene
Experimental device-independent certified randomness generation with an instrumental causal structure
The intrinsic random nature of quantum physics offers novel tools for the
generation of random numbers, a central challenge for a plethora of fields.
Bell non-local correlations obtained by measurements on entangled states allow
for the generation of bit strings whose randomness is guaranteed in a
device-independent manner, i.e. without assumptions on the measurement and
state-generation devices. Here, we generate this strong form of certified
randomness on a new platform: the so-called instrumental scenario, which is
central to the field of causal inference. First, we theoretically show that
certified random bits, private against general quantum adversaries, can be
extracted exploiting device-independent quantum instrumental-inequality
violations. To that end, we adapt techniques previously developed for the Bell
scenario. Then, we experimentally implement the corresponding
randomness-generation protocol using entangled photons and active feed-forward
of information. Moreover, we show that, for low levels of noise, our protocol
offers an advantage over the simplest Bell-nonlocality protocol based on the
Clauser-Horn-Shimony-Holt inequality.Comment: Modified Supplementary Information: removed description of extractor
algorithm introduced by arXiv:1212.0520. Implemented security of the protocol
against general adversarial attack
Quantum Loewner evolution
What is the scaling limit of diffusion-limited aggregation (DLA) in the plane? This is an old and famously difficult question. One can generalize the question in two ways: first, one may consider the dielectric breakdown model η-DBM, a generalization of DLA in which particle locations are sampled from the η th power of harmonic measure, instead of harmonic measure itself. Second, instead of restricting attention to deterministic lattices, one may consider η-DBM on random graphs known or believed to conve rge in law to a Liouville quantum gravity (LQG) surface with parameter γ e [0,2]. In this generality, we propose a scaling limit candidate called quantum Loewner evolution, QLE(γ 2 ,η). QLE is defined in terms of the radial Loewner equation like radial stochastic Loewner evolution, except that it is driven by a measure-valued diffusion v t derived from LQG rather than a multiple of a standard Brownian motion. We formalize the dynamics of v t using a stochastic partial differential equation. For each γ e [0, 2], there are two or three special values of η for which we establish the existence of a solution to these dynamics and explicitly describe the stationary law of v t . We also explain discrete versions of our construction that relate DLA to loop-erased random walks and the Eden model to percolation. A certain "reshuffling" trick (in which concentric annular regions are rotated randomly, like slot-machine reels) facilitates explicit calculation. We propose QLE(2, 1) as a scaling limit for DLA on a random spanning-tree-decorated planar map and QLE(8/3, 0) as a scaling limit for the Eden model on a random triangulation. We propose using QLE(8/3, 0) to endow pure LQG with a distance function, by interpreting the region explored by a branching variant of QLE(8/3, 0), up to a fixed time, as a metric ball in a random metric space
Quantum Loewner evolution
What is the scaling limit of diffusion-limited aggregation (DLA) in the plane? This is an old and famously difficult question. One can generalize the question in two ways: first, one may consider the dielectric breakdown model -DBM, a generalization of DLA in which particle locations are sampled from the the power of harmonic measure, instead of harmonic measure itself. Second, instead of restricting attention to deterministic lattices, one may consider -DBM on random graphs known or believed
to converge in law to a Liouville quantum gravity (LQG) surface with parameter 2 Œ0; 2 .
In this generality, we propose a scaling limit candidate called quantum Loewner evolution, QLE.2; /. QLE is defined in terms of the radial Loewner equation like radial stochastic Loewner evolution, except that it is driven by a measure-valued diffusion t derived from LQG rather than a multiple of a standard Brownian motion. We formalize the dynamics of t using a stochastic partial differential equation. For each 2 .0; 2 , there are two or three special values of for which we establish the existence of a solution to these dynamics and explicitly describe the stationary law of t .
We also explain discrete versions of our construction that relate DLA to looperased random walks and the Eden model to percolation. A certain “reshuffling” trick (in which concentric annular regions are rotated randomly, like slot-machine reels) facilitates explicit calculation.
We propose QLE.2; 1/ as a scaling limit for DLA on a random spanning-treedecorated planar map and QLE.8=3; 0/ as a scaling limit for the Eden model on a random triangulation. We propose using QLE.8=3; 0/ to endow pure LQG with a distance function, by interpreting the region explored by a branching variant of QLE.8=3; 0/, up to a fixed time, as a metric ball in a random metric space
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Combinatorial optimization and metaheuristics
Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods
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