Informazione quantistica, computazione quantistica Mario Rasetti Dipartimento di Fisica Politecnico di Torino
Miniaturizzazione: legge di Moore [ la densità di bit (per cm2) nei circuiti integrati al silicio raddoppia ogni 18 mesi ] [ se un cellulare fosse fatto d valvole termoioniche invece che di transistor occuperebbe un edificio grande come il Pantheon ]: oggi stiamo arrivando a quasi 1000000000 (un miliardo) di transistor in un chip; nel mondo vengono prodotti circa 500000000 (cinquecento milioni) di transistor al secondo [ i circuiti incisi su questi chip sono complicati come una mappa stradale dell’intero pianeta ridotta alle dimensioni di un’unghia ]; in un circuito integrato tipico ci sono 5000000 (cinque milioni) di transistor (nel processore Pentium IV sono 42000000 (quarantadue milioni); erano 275000 nel ‘386’): il costo medio di un transistor è 0,000001 (un milionesimo) di centesimo di Euro, negli anni ’50 il costo è sceso da 45$ a 2$. Estrapolando la legge di Moore siamo già oggi prossimi alla densità di un bit per atomo.
Formally, a (one-tape) Turing machine is usually defined as a • 6-tupleM = (Q, Γ, s, b, F, δ), where • Q is a finite set of states • Γ is a finite set of the tape alphabet • is the initial state • is the blank symbol (the only symbol allowed to occur • on the tape infinitely often at any step during the • computation) • is the set of final or accepting states • is a partial function called the transition function, where L is left shift, R is right shift.
gate electrode leads junctions 1 m m • Josephson mesoscopic devices • Al/AlOx/Al junctions, through shadow mask (e-beam lithography) and two-angle evaporation technique • junction size: from 70 nm to 100 nm side • by changing the fabrication parameters, we vary both the Josephson and the charging energy
An interesting application:Quantum Automaton and Gene Antisense Therapy
The Theory The Quantum Automaton • A quantum mechanical system can be conceptually designed, that we call quantum automaton, which has the following properties: • it is endowed with mechanisms input and output of information, • it can measure and record a variety of physical observables (including some of itself); • it has an internal program that it can operate (once more according to the laws of quantum mechanics) which includes a set of rules for predicting the behavior of the measured physical systems (including itself); • its states, which are vectors in a Hilbert space and encode all the features of the automaton (coding what is can measure, know, predict about itself and the external systems) are solutions of quantum mechanical equations of motion; and all its measurable properties correspond to some hermitian operator in that space.
An example:DNAreplication The system wave-function will evolve to incorporate both the correct base C for and the reverse base T for , where refers to the state for which proton has not tunneled, and to that in which the proton did tunnel [ ] . The daughter DNA strand will be described by the wave function ( ) that will evolve as the coding strand is transcribed and translated in a mutated form containing e.g an arginine ( ) histidine ( ) amino acid substitution. The cell will thus move to state that results in a different reading (e.g. due to the formation of lactose, ) of the automaton, while the cell ends up in superposition state
The Application If a particular gene has a role in some disease, and the genetic code of that gene is known, one could use this knowledge to stop that gene specifically. Genes are made of double-helical DNA. When a gene is turned on, the genetic code in that segment of DNA is copied out as a single strand of RNA, called messenger RNA. The messenger RNA is called a "sense" sequence, because it can be translated into a string of amino acids to form a protein. The opposite strand in a DNA double helix (A opposite T, Topposite A, C opposite G, G opposite C) is called the "antisense" strand. The antisense coding sequence of a disease gene can be used to make short antisense DNAs in laboratory acting as drugs which work by binding to messenger RNAs from disease genes, so that the genetic code in the RNA cannot be read, stopping the production of the disease-causing protein.
LDH Interlayer ion Ion exchange Nanohybridization DNA-LDH hybrid Recognition and uptake The Automaton Schematic illustrationof the hybridization and transfer mechanism of the DNA-LDHhybrid into a cell