18,982 research outputs found
Computation in Physical Systems: A Normative Mapping Account
The relationship between abstract formal procedures and the activities of actual physical systems has proved to be surprisingly subtle and controversial, and there are a number of competing accounts of when a physical system can be properly said to implement a mathematical formalism and hence perform a computation. I defend an account wherein computational descriptions of physical systems are high-level normative interpretations motivated by our pragmatic concerns. Furthermore, the criteria of utility and success vary according to our diverse purposes and pragmatic goals. Hence there is no independent or uniform fact to the matter, and I advance the ‘anti-realist’ conclusion that computational descriptions of physical systems are not founded upon deep ontological distinctions, but rather upon interest-relative human conventions. Hence physical computation is a ‘conventional’ rather than a ‘natural’ kind
The Algebraic View of Computation
We argue that computation is an abstract algebraic concept, and a computer is
a result of a morphism (a structure preserving map) from a finite universal
semigroup.Comment: 13 pages, final version will be published elsewher
The Measurement Calculus
Measurement-based quantum computation has emerged from the physics community
as a new approach to quantum computation where the notion of measurement is the
main driving force of computation. This is in contrast with the more
traditional circuit model which is based on unitary operations. Among
measurement-based quantum computation methods, the recently introduced one-way
quantum computer stands out as fundamental.
We develop a rigorous mathematical model underlying the one-way quantum
computer and present a concrete syntax and operational semantics for programs,
which we call patterns, and an algebra of these patterns derived from a
denotational semantics. More importantly, we present a calculus for reasoning
locally and compositionally about these patterns.
We present a rewrite theory and prove a general standardization theorem which
allows all patterns to be put in a semantically equivalent standard form.
Standardization has far-reaching consequences: a new physical architecture
based on performing all the entanglement in the beginning, parallelization by
exposing the dependency structure of measurements and expressiveness theorems.
Furthermore we formalize several other measurement-based models:
Teleportation, Phase and Pauli models and present compositional embeddings of
them into and from the one-way model. This allows us to transfer all the theory
we develop for the one-way model to these models. This shows that the framework
we have developed has a general impact on measurement-based computation and is
not just particular to the one-way quantum computer.Comment: 46 pages, 2 figures, Replacement of quant-ph/0412135v1, the new
version also include formalization of several other measurement-based models:
Teleportation, Phase and Pauli models and present compositional embeddings of
them into and from the one-way model. To appear in Journal of AC
Discussion: Byrne and Hall on Everett and Chalmers
Byrne and Hall (1999) criticized the argument of Chalmers (1996) in favor of
the Everett-style interpretation. They claimed to show ``the deep and
underappreciated flaw in ANY Everett-style interpretation''. I will argue that
it is possible to interpret Chalmers's writing in such a way that most of the
criticism by Byrne and Hall does not apply. In any case their general criticism
of the many-worlds interpretation is unfounded. The recent recognition that the
Everett-style interpretations are good (if not the best) interpretations of
quantum mechanics has, therefore, not been negated.Comment: 6 page
Universally Composable Quantum Multi-Party Computation
The Universal Composability model (UC) by Canetti (FOCS 2001) allows for
secure composition of arbitrary protocols. We present a quantum version of the
UC model which enjoys the same compositionality guarantees. We prove that in
this model statistically secure oblivious transfer protocols can be constructed
from commitments. Furthermore, we show that every statistically classically UC
secure protocol is also statistically quantum UC secure. Such implications are
not known for other quantum security definitions. As a corollary, we get that
quantum UC secure protocols for general multi-party computation can be
constructed from commitments
The free energy requirements of biological organisms; implications for evolution
Recent advances in nonequilibrium statistical physics have provided
unprecedented insight into the thermodynamics of dynamic processes. The author
recently used these advances to extend Landauer's semi-formal reasoning
concerning the thermodynamics of bit erasure, to derive the minimal free energy
required to implement an arbitrary computation. Here, I extend this analysis,
deriving the minimal free energy required by an organism to run a given
(stochastic) map from its sensor inputs to its actuator outputs. I use
this result to calculate the input-output map of an organism that
optimally trades off the free energy needed to run with the phenotypic
fitness that results from implementing . I end with a general discussion
of the limits imposed on the rate of the terrestrial biosphere's information
processing by the flux of sunlight on the Earth.Comment: 19 pages, 0 figures, presented at 2015 NIMBIoS workshop on
"Information and entropy in biological systems
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