2,537 research outputs found
Limits on Fundamental Limits to Computation
An indispensable part of our lives, computing has also become essential to
industries and governments. Steady improvements in computer hardware have been
supported by periodic doubling of transistor densities in integrated circuits
over the last fifty years. Such Moore scaling now requires increasingly heroic
efforts, stimulating research in alternative hardware and stirring controversy.
To help evaluate emerging technologies and enrich our understanding of
integrated-circuit scaling, we review fundamental limits to computation: in
manufacturing, energy, physical space, design and verification effort, and
algorithms. To outline what is achievable in principle and in practice, we
recall how some limits were circumvented, compare loose and tight limits. We
also point out that engineering difficulties encountered by emerging
technologies may indicate yet-unknown limits.Comment: 15 pages, 4 figures, 1 tabl
Quantum Circuits for Incompletely Specified Two-Qubit Operators
While the question ``how many CNOT gates are needed to simulate an arbitrary
two-qubit operator'' has been conclusively answered -- three are necessary and
sufficient -- previous work on this topic assumes that one wants to simulate a
given unitary operator up to global phase. However, in many practical cases
additional degrees of freedom are allowed. For example, if the computation is
to be followed by a given projective measurement, many dissimilar operators
achieve the same output distributions on all input states. Alternatively, if it
is known that the input state is |0>, the action of the given operator on all
orthogonal states is immaterial. In such cases, we say that the unitary
operator is incompletely specified; in this work, we take up the practical
challenge of satisfying a given specification with the smallest possible
circuit. In particular, we identify cases in which such operators can be
implemented using fewer quantum gates than are required for generic completely
specified operators.Comment: 15 page
Study of the spring and autumn daemon-flux maxima at the Baksan Neutrino Observatory
Detection of daemons in low-background conditions in September 2005 and March
2006 has provided evidence for the expected to occur at that times maxima in
the flux of daemons with V ~ 10-15 km s-1, which hit the Earth from near-Earth,
almost circular heliocentric orbits. The ability of some FEU-167-1 PM tubes
with a thicker inner Al coating to detect directly daemon passage through them
has also been demonstrated, an effect increasing ~100-fold the detector
efficiency. As a result, the daemon flux recorded at the maxima was increased
from ~10-9 to ~10-7 cm-2 s-1. The intensity and direction of the flux during
maxima depend on the time of day and latitude of observations (therefore,
synchronous measurements in the Northern and Southern Earth's hemispheres are
desirable). All the experimental results obtained either support the
conclusions following from the daemon paradigm or find a simple interpretation
within it.Comment: 15 pages, including 8 figures and 3 table
Graph Symmetry Detection and Canonical Labeling: Differences and Synergies
Symmetries of combinatorial objects are known to complicate search
algorithms, but such obstacles can often be removed by detecting symmetries
early and discarding symmetric subproblems. Canonical labeling of combinatorial
objects facilitates easy equivalence checking through quick matching. All
existing canonical labeling software also finds symmetries, but the fastest
symmetry-finding software does not perform canonical labeling. In this work, we
contrast the two problems and dissect typical algorithms to identify their
similarities and differences. We then develop a novel approach to canonical
labeling where symmetries are found first and then used to speed up the
canonical labeling algorithms. Empirical results show that this approach
outperforms state-of-the-art canonical labelers.Comment: 15 pages, 10 figures, 1 table, Turing-10
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