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.
David Deutsch
Formally, a (one-tape) Turing machine is usually defined as a
6-tuple M = (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.
Josephson mesoscopic devices
• Al/AlOx/Al junctions, through shadow mask (e-beam lithography)
and two-angle evaporation technique
• junction
from 70 nm to 100 nm side
gate size:
electrode
• by changing the fabrication parameters, we vary both the
Josephson and the charging energy
leads
1mm
junctions
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: DNA replication
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, T opposite 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.
Interlayer
ion
LDH
Ion exchange
Nanohybridization
DNA-LDH
hybrid
Recognition
and uptake
Schematic illustration of
the hybridization and
transfer mechanism of the
DNA-LDH hybrid into a cell
The
Automaton