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

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

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

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

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

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

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 $\overleftarrow{\rm GNN}$. 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