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