1,004 research outputs found
Quantum Sampling Problems, BosonSampling and Quantum Supremacy
There is a large body of evidence for the potential of greater computational
power using information carriers that are quantum mechanical over those
governed by the laws of classical mechanics. But the question of the exact
nature of the power contributed by quantum mechanics remains only partially
answered. Furthermore, there exists doubt over the practicality of achieving a
large enough quantum computation that definitively demonstrates quantum
supremacy. Recently the study of computational problems that produce samples
from probability distributions has added to both our understanding of the power
of quantum algorithms and lowered the requirements for demonstration of fast
quantum algorithms. The proposed quantum sampling problems do not require a
quantum computer capable of universal operations and also permit physically
realistic errors in their operation. This is an encouraging step towards an
experimental demonstration of quantum algorithmic supremacy. In this paper, we
will review sampling problems and the arguments that have been used to deduce
when sampling problems are hard for classical computers to simulate. Two
classes of quantum sampling problems that demonstrate the supremacy of quantum
algorithms are BosonSampling and IQP Sampling. We will present the details of
these classes and recent experimental progress towards demonstrating quantum
supremacy in BosonSampling.Comment: Survey paper first submitted for publication in October 2016. 10
pages, 4 figures, 1 tabl
Are there new models of computation? Reply to Wegner and Eberbach
Wegner and Eberbach[Weg04b] have argued that there are fundamental limitations
to Turing Machines as a foundation of computability and that these can be overcome
by so-called superTuring models such as interaction machines, the [pi]calculus and the
$-calculus. In this paper we contest Weger and Eberbach claims
Computational complexity of the landscape I
We study the computational complexity of the physical problem of finding
vacua of string theory which agree with data, such as the cosmological
constant, and show that such problems are typically NP hard. In particular, we
prove that in the Bousso-Polchinski model, the problem is NP complete. We
discuss the issues this raises and the possibility that, even if we were to
find compelling evidence that some vacuum of string theory describes our
universe, we might never be able to find that vacuum explicitly.
In a companion paper, we apply this point of view to the question of how
early cosmology might select a vacuum.Comment: JHEP3 Latex, 53 pp, 2 .eps figure
Why Philosophers Should Care About Computational Complexity
One might think that, once we know something is computable, how efficiently
it can be computed is a practical question with little further philosophical
importance. In this essay, I offer a detailed case that one would be wrong. In
particular, I argue that computational complexity theory---the field that
studies the resources (such as time, space, and randomness) needed to solve
computational problems---leads to new perspectives on the nature of
mathematical knowledge, the strong AI debate, computationalism, the problem of
logical omniscience, Hume's problem of induction, Goodman's grue riddle, the
foundations of quantum mechanics, economic rationality, closed timelike curves,
and several other topics of philosophical interest. I end by discussing aspects
of complexity theory itself that could benefit from philosophical analysis.Comment: 58 pages, to appear in "Computability: G\"odel, Turing, Church, and
beyond," MIT Press, 2012. Some minor clarifications and corrections; new
references adde
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