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Informazione quantistica, computazione quantistica. Mario Rasetti Dipartimento di Fisica Politecnico di Torino. Miniaturizzazione : legge di Moore [ la densità di bit (per cm 2 ) nei circuiti integrati al silicio raddoppia ogni 18 mesi ]

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informazione quantistica computazione quantistica

Informazione quantistica, computazione quantistica

Mario Rasetti

Dipartimento di Fisica

Politecnico di Torino

slide3

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.

slide9

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.
slide21

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
the theory
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.

slide26

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

slide27

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.

slide29

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