282,234 research outputs found
A Theory of Computation Based on Quantum Logic (I)
The (meta)logic underlying classical theory of computation is Boolean
(two-valued) logic. Quantum logic was proposed by Birkhoff and von Neumann as a
logic of quantum mechanics more than sixty years ago. The major difference
between Boolean logic and quantum logic is that the latter does not enjoy
distributivity in general. The rapid development of quantum computation in
recent years stimulates us to establish a theory of computation based on
quantum logic. The present paper is the first step toward such a new theory and
it focuses on the simplest models of computation, namely finite automata. It is
found that the universal validity of many properties of automata depend heavily
upon the distributivity of the underlying logic. This indicates that these
properties does not universally hold in the realm of quantum logic. On the
other hand, we show that a local validity of them can be recovered by imposing
a certain commutativity to the (atomic) statements about the automata under
consideration. This reveals an essential difference between the classical
theory of computation and the computation theory based on quantum logic
Phase-Tunable Thermal Logic: Computation with Heat
Boolean algebra, the branch of mathematics where variables can assume only
true or false value, is the theoretical basis of classical computation. The
analogy between Boolean operations and electronic switching circuits,
highlighted by Shannon in 1938, paved the way to modern computation based on
electronic devices. The grow of computational power of such devices, after an
exciting exponential -Moore trend, is nowadays blocked by heat dissipation due
to computational tasks, very demanding after the chips miniaturization. Heat is
often a detrimental form of energy which increases the systems entropy
decreasing the efficiency of logic operations. Here, we propose a physical
system able to perform thermal logic operations by reversing the old
heat-disorder epitome into a novel heat-order paradigm. We lay the foundations
of heat computation by encoding logic state variables in temperature and
introducing the thermal counterparts of electronic logic gates. Exploiting
quantum effects in thermally biased Josephson junctions (JJs), we propound a
possible realization of a functionally complete dissipationless logic. Our
architecture ensures high operation stability and robustness with switching
frequencies reaching the GHz
Physics, Topology, Logic and Computation: A Rosetta Stone
In physics, Feynman diagrams are used to reason about quantum processes. In
the 1980s, it became clear that underlying these diagrams is a powerful analogy
between quantum physics and topology: namely, a linear operator behaves very
much like a "cobordism". Similar diagrams can be used to reason about logic,
where they represent proofs, and computation, where they represent programs.
With the rise of interest in quantum cryptography and quantum computation, it
became clear that there is extensive network of analogies between physics,
topology, logic and computation. In this expository paper, we make some of
these analogies precise using the concept of "closed symmetric monoidal
category". We assume no prior knowledge of category theory, proof theory or
computer science.Comment: 73 pages, 8 encapsulated postscript figure
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