877 research outputs found
The Quantum Frontier
The success of the abstract model of computation, in terms of bits, logical
operations, programming language constructs, and the like, makes it easy to
forget that computation is a physical process. Our cherished notions of
computation and information are grounded in classical mechanics, but the
physics underlying our world is quantum. In the early 80s researchers began to
ask how computation would change if we adopted a quantum mechanical, instead of
a classical mechanical, view of computation. Slowly, a new picture of
computation arose, one that gave rise to a variety of faster algorithms, novel
cryptographic mechanisms, and alternative methods of communication. Small
quantum information processing devices have been built, and efforts are
underway to build larger ones. Even apart from the existence of these devices,
the quantum view on information processing has provided significant insight
into the nature of computation and information, and a deeper understanding of
the physics of our universe and its connections with computation.
We start by describing aspects of quantum mechanics that are at the heart of
a quantum view of information processing. We give our own idiosyncratic view of
a number of these topics in the hopes of correcting common misconceptions and
highlighting aspects that are often overlooked. A number of the phenomena
described were initially viewed as oddities of quantum mechanics. It was
quantum information processing, first quantum cryptography and then, more
dramatically, quantum computing, that turned the tables and showed that these
oddities could be put to practical effect. It is these application we describe
next. We conclude with a section describing some of the many questions left for
future work, especially the mysteries surrounding where the power of quantum
information ultimately comes from.Comment: Invited book chapter for Computation for Humanity - Information
Technology to Advance Society to be published by CRC Press. Concepts
clarified and style made more uniform in version 2. Many thanks to the
referees for their suggestions for improvement
Analysis of pivot sampling in dual-pivot Quicksort: A holistic analysis of Yaroslavskiy's partitioning scheme
The final publication is available at Springer via http://dx.doi.org/10.1007/s00453-015-0041-7The new dual-pivot Quicksort by Vladimir Yaroslavskiy-used in Oracle's Java runtime library since version 7-features intriguing asymmetries. They make a basic variant of this algorithm use less comparisons than classic single-pivot Quicksort. In this paper, we extend the analysis to the case where the two pivots are chosen as fixed order statistics of a random sample. Surprisingly, dual-pivot Quicksort then needs more comparisons than a corresponding version of classic Quicksort, so it is clear that counting comparisons is not sufficient to explain the running time advantages observed for Yaroslavskiy's algorithm in practice. Consequently, we take a more holistic approach and give also the precise leading term of the average number of swaps, the number of executed Java Bytecode instructions and the number of scanned elements, a new simple cost measure that approximates I/O costs in the memory hierarchy. We determine optimal order statistics for each of the cost measures. It turns out that the asymmetries in Yaroslavskiy's algorithm render pivots with a systematic skew more efficient than the symmetric choice. Moreover, we finally have a convincing explanation for the success of Yaroslavskiy's algorithm in practice: compared with corresponding versions of classic single-pivot Quicksort, dual-pivot Quicksort needs significantly less I/Os, both with and without pivot sampling.Peer ReviewedPostprint (author's final draft
Quantum violations in the Instrumental scenario and their relations to the Bell scenario
The causal structure of any experiment implies restrictions on the observable
correlations between measurement outcomes, which are different for experiments
exploiting classical, quantum, or post-quantum resources. In the study of Bell
nonlocality, these differences have been explored in great detail for more and
more involved causal structures. Here, we go in the opposite direction and
identify the simplest causal structure which exhibits a separation between
classical, quantum, and post-quantum correlations. It arises in the so-called
Instrumental scenario, known from classical causal models. We derive
inequalities for this scenario and show that they are closely related to
well-known Bell inequalities, such as the Clauser-Horne-Shimony-Holt
inequality, which enables us to easily identify their classical, quantum, and
post-quantum bounds as well as strategies violating the first two. The
relations that we uncover imply that the quantum or post-quantum advantages
witnessed by the violation of our Instrumental inequalities are not
fundamentally different from those witnessed by the violations of standard
inequalities in the usual Bell scenario. However, non-classical tests in the
Instrumental scenario require fewer input choices than their Bell scenario
counterpart, which may have potential implications for device-independent
protocols.Comment: 12 pages, 3 figures. Comments welcome! v4: published version in
Quantum journa
Modelling and feedback control design for quantum state preparation
The goal of this article is to provide a largely self-contained introduction to the modelling of controlled quantum systems under continuous observation, and to the design of feedback controls that prepare particular quantum states. We describe a bottom-up approach, where a field-theoretic model is subjected to statistical inference and is ultimately controlled. As an example, the formalism is applied to a highly idealized interaction of an atomic ensemble with an optical field. Our aim is to provide a unified outline for the modelling, from first principles, of realistic experiments in quantum control
Are we bootstrapping the right thing? A new approach to quantify uncertainty of Average Treatment Effect Estimate
Existing approaches of using the bootstrap method to derive standard error
and confidence interval of average treatment effect estimate has one potential
issue, which is that they are actually bootstrapping the wrong thing, resulting
in unvalid statistical inference. In this paper, we discuss this important
issue and propose a new non-parametric bootstrap method that can more precisely
quantify the uncertainty associated with average treatment effect estimates. We
demonstrate the validity of this approach through a simulation study and a
real-world example, and highlight the importance of deriving standard error and
confidence interval of average treatment effect estimates that both remove
extra undesired noise and are easy to interpret when applied in real world
scenarios
Is "the theory of everything'' merely the ultimate ensemble theory?
We discuss some physical consequences of what might be called ``the ultimate
ensemble theory'', where not only worlds corresponding to say different sets of
initial data or different physical constants are considered equally real, but
also worlds ruled by altogether different equations. The only postulate in this
theory is that all structures that exist mathematically exist also physically,
by which we mean that in those complex enough to contain self-aware
substructures (SASs), these SASs will subjectively perceive themselves as
existing in a physically ``real'' world. We find that it is far from clear that
this simple theory, which has no free parameters whatsoever, is observationally
ruled out. The predictions of the theory take the form of probability
distributions for the outcome of experiments, which makes it testable. In
addition, it may be possible to rule it out by comparing its a priori
predictions for the observable attributes of nature (the particle masses, the
dimensionality of spacetime, etc) with what is observed.Comment: 29 pages, revised to match version published in Annals of Physics.
The New Scientist article and color figures are available at
http://www.sns.ias.edu/~max/toe_frames.html or from [email protected]
Investigation of light scattering in highly reflecting pigmented coatings. Volume 3 - Monte Carlo and other statistical investigations Final report, 1 May 1963 - 30 Sep. 1966
Monte Carlo methods, Mie theory, and random walk and screen models for predicting reflective properties of paint film
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