148 research outputs found
Survival of the Fittest and Zero Sum Games
Competition for available resources is natural amongst coexisting species,
and the fittest contenders dominate over the rest in evolution. The dynamics of
this selection is studied using a simple linear model. It has similarities to
features of quantum computation, in particular conservation laws leading to
destructive interference. Compared to an altruistic scenario, competition
introduces instability and eliminates the weaker species in a finite time.Comment: 6 pages, formatted according to journal style. Special Issue on Game
Theory and Evolutionary Processes. (v2) Published version. Some
clarifications added. Topological interpretation pointed ou
The Future of Computation
``The purpose of life is to obtain knowledge, use it to live with as much
satisfaction as possible, and pass it on with improvements and modifications to
the next generation.'' This may sound philosophical, and the interpretation of
words may be subjective, yet it is fairly clear that this is what all living
organisms--from bacteria to human beings--do in their life time. Indeed, this
can be adopted as the information theoretic definition of life. Over billions
of years, biological evolution has experimented with a wide range of physical
systems for acquiring, processing and communicating information. We are now in
a position to make the principles behind these systems mathematically precise,
and then extend them as far as laws of physics permit. Therein lies the future
of computation, of ourselves, and of life.Comment: 7 pages, Revtex. Invited lecture at the Workshop on Quantum
Information, Computation and Communication (QICC-2005), IIT Kharagpur, India,
February 200
Testing Quantum Dynamics in Genetic Information Processing
Does quantum dynamics play a role in DNA replication? What type of tests
would reveal that? Some statistical checks that distinguish classical and
quantum dynamics in DNA replication are proposed.Comment: 4 pages, latex. (v2) Several points elaborated. Published version,
formatted according to the journal styl
Optimisation of Quantum Evolution Algorithms
Given a quantum Hamiltonian and its evolution time, the corresponding unitary
evolution operator can be constructed in many different ways, corresponding to
different trajectories between the desired end-points. A choice among these
trajectories can then be made to obtain the best computational complexity and
control over errors. As an explicit example, Grover's quantum search algorithm
is described as a Hamiltonian evolution problem. It is shown that the
computational complexity has a power-law dependence on error when a
straightforward Lie-Trotter discretisation formula is used, and it becomes
logarithmic in error when reflection operators are used. The exponential change
in error control is striking, and can be used to improve many importance
sampling methods. The key concept is to make the evolution steps as large as
possible while obeying the constraints of the problem. In particular, we can
understand why overrelaxation algorithms are superior to small step size
algorithms.Comment: 7 pages. Talk presented at the 32nd International Symposium on
Lattice Field Theory, 23-28 June 2014, Columbia University, New York, US
On how to Produce Entangled States Violating Bell's Inequalities in Quantum Theory
Feynman's path integrals provide a hidden variable description of quantum
mechanics (and quantum field theories). The time evolution kernel is unitary in
Minkowski time, but generically it becomes real and non-negative in Euclidean
time. It follows that the entangled state correlations, that violate Bell's
inequalities in Minkowski time, obey the inequalities in Euclidean time. This
observation emphasises the link between violation of Bell's inequalities in
quantum mechanics and unitarity of the theory. Search for an evolution kernel
that cannot be conveniently made non-negative leads to effective interactions
that violate time reversal invariance. Interactions giving rise to geometric
phases in the effective description of the theory, such as the anomalous
Wess-Zumino interactions, have this feature. I infer that they must be present
in any set-up that produces entangled states violating Bell's inequalities.
Such interactions would be a crucial ingredient in a quantum computer.Comment: 8 pages, two column revtex, arguments elaborated and strengthened,
submitted to Physical Review
Optimal Database Search: Waves and Catalysis
Grover's database search algorithm, although discovered in the context of
quantum computation, can be implemented using any system that allows
superposition of states. A physical realization of this algorithm is described
using coupled simple harmonic oscillators, which can be exactly solved in both
classical and quantum domains. Classical wave algorithms are far more stable
against decoherence compared to their quantum counterparts. In addition to
providing convenient demonstration models, they may have a role in practical
situations, such as catalysis.Comment: 4 pages (v2) 6 pages, RevTeX4. Title changed. Substantially expanded
to include stability considerations, quantum domain analysis, application to
catalysis. (v3) Version accepted for publication. (v4) Error in Eqs.(10,11)
corrected by replacing \omega by \omega^2. No change in implementation and
applicatio
Carbon--The First Frontier of Information Processing
Information is often encoded as an aperiodic chain of building blocks. Modern
digital computers use bits as the building blocks, but in general the choice of
building blocks depends on the nature of the information to be encoded. What
are the optimal building blocks to encode structural information? This can be
analysed by substituting the operations of addition and multiplication of
conventional arithmetic with translation and rotation. It is argued that at the
molecular level, the best component for encoding discretised structural
information is carbon. Living organisms discovered this billions of years ago,
and used carbon as the back-bone for constructing proteins that function
according to their structure. Structural analysis of polypeptide chains shows
that an efficient and versatile structural language of 20 building blocks is
needed to implement all the tasks carried out by proteins. Properties of amino
acids indicate that the present triplet genetic code was preceded by a more
primitive one, coding for 10 amino acids using two nucleotide bases.Comment: (v1) 9 pages, revtex. (v2) 10 pages. Several arguments expanded to
make the article self-contained and to increase clarity. Applications pointed
out. (v3) 11 pages. Published version. Well-known properties of proteins
shifted to an appendix. Reformatted according to journal styl
The Triplet Genetic Code had a Doublet Predecessor
Information theoretic analysis of genetic languages indicates that the
naturally occurring 20 amino acids and the triplet genetic code arose by
duplication of 10 amino acids of class-II and a doublet genetic code having
codons NNY and anticodons . Evidence for this scenario
is presented based on the properties of aminoacyl-tRNA synthetases, amino acids
and nucleotide bases.Comment: 10 pages (v2) Expanded to include additional features, including
likely relation to the operational code of the tRNA-acceptor stem. Version to
be published in Journal of Theoretical Biolog
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