Corso di Laurea inFISICA. Fisica dell'informazione. Porte reversibili. Prof. Luca
Gammaitoni. Informazioni sul corso: www.fisica.unipg.it/gammaitoni/fisinfo ...
Corso di Laurea in FISICA
Fisica dell’informazione Porte reversibili Prof. Luca Gammaitoni
Informazioni sul corso: www.fisica.unipg.it/gammaitoni/fisinfo
Computer reversibili
Ciò non è realizzabile con le porte logiche tradizionali
Computer reversibili
Ciò non è realizzabile con le porte logiche tradizionali
NOT
OR
AND
E’ necessario che il numero delle uscite sia non minore del numero degli ingressi
Porte logiche di Fredkin e Toffoli
Edward Fredkin Edward Fredkin was an early pioneer of digital physics. ! Edward Fredkin dropped out of Caltech after one year and, at age 19, joined the USAF and became a jet fighter pilot. Fredkinʼs computer career started in 1956 when the Air Force assigned him to work at MIT Lincoln Laboratory. He worked at BBN in the early 1960s where he wrote the PDP-1 assembler. ! In 1968 Fredkin returned to academia, starting at MIT as a full professor. From 1971 to 1974 he was Director of Project MAC. He spent a year at Caltech as a Fairchild Distinguished Scholar, working with Richard Feynman, and was a Professor of Physics at Boston University for 6 years. ! More recently he has been a Distinguished Career Professor at Carnegie Mellon University and also a Visiting Professor at MIT.! Fredkin founded Information International Inc. and has served as the CEO of a diverse set of companies, including Information International, Three Rivers Computer Corporation, New England Television Corporation (owner of Boston's then CBS affiliate, WNEV, channel 7) and others.Fredkin has been broadly interested in computation: hardware and software. He has also been involved in computer vision, chess and other areas of Artificial Intelligence research. Fredkin also works at the intersection of theoretical issues in the physics of computation and computational models of physics. He recently developed Salt, a model of computation based on fundamental conservation laws from physics.
!
Da Wikipedia
Tommaso Toffoli
Tommaso Toffoli is a professor of electrical and computer engineering at Boston University. ! He joined the faculty in 1995. He received his doctorate in physics from the University of Rome in 1967. ! In 1976 he received a Ph.D. in computer and communication science from the University of Michigan.! In 1977, he joined the faculty of Massachusetts Institute of Technology.He worked on the theory of artificial life and Automata theory in such publications as his PhD thesis, and many other published articles.!
Porte di Friedkin
v = u
y1 = u x1 + u’x2
y2 = u’x1 + ux2
Porte di Friedkin
v = u
y1 = u x1 + u’x2
y2 = u’x1 + ux2
AND
?
OR
?
NOT
?
v = u
y1 = u x1 + u’x2
y2 = u’x1 + ux2
AND
y1 = u x1 + u’0
OR
y1 = u 1 + u’x2
NOT
y2 = u’1 + u0
Notazione e nuove porte logiche
Nel Controlled-NOT se b=0 allora b’=a FAN-OUT (duplicatore)
Control line
Controlled-NOT
a’ = a
b’ = a XOR b
La presenza di a’ rende la porta reversibile
Control line
Controlled-Controlled NOT ----------- Toffoli gate
