3,541 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
Elementary gates for quantum computation
We show that a set of gates that consists of all one-bit quantum gates (U(2))
and the two-bit exclusive-or gate (that maps Boolean values to ) is universal in the sense that all unitary operations on
arbitrarily many bits (U()) can be expressed as compositions of these
gates. We investigate the number of the above gates required to implement other
gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2)
transformation to one input bit if and only if the logical AND of all remaining
input bits is satisfied. These gates play a central role in many proposed
constructions of quantum computational networks. We derive upper and lower
bounds on the exact number of elementary gates required to build up a variety
of two-and three-bit quantum gates, the asymptotic number required for -bit
Deutsch-Toffoli gates, and make some observations about the number required for
arbitrary -bit unitary operations.Comment: 31 pages, plain latex, no separate figures, submitted to Phys. Rev.
A. Related information on http://vesta.physics.ucla.edu:7777
Non-classical computing: feasible versus infeasible
Physics sets certain limits on what is and is not computable. These limits are very far from having been reached by current technologies. Whilst proposals for hypercomputation are almost certainly infeasible, there are a number of non classical approaches that do hold considerable promise. There are a range of possible architectures that could be implemented on silicon that are distinctly different from the von Neumann model. Beyond this, quantum simulators, which are the quantum equivalent of analogue computers, may be constructable in the near future
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