Introduction to Quantum Logic 2002/10/08 Tuesday Jung-wook Kim

Reversible Logic v Lose information is equal meaning to lose energy in physical view. n The loss of information is associated with laws of physics requiring that one bit of information lost dissipates of Energy. n Whenever we use a logically irreversible gate we dissipate energy into the environment. n Reversible computation can reduce heat dissipation by losing no information through the gate. So, It allows higher densities, higher speed.

Reversible Gate v Irreversible gate v v reversible gate n n Input and Output is one-to-one mapping u u Output reconstruct input. u u No information loss through the gate n n The gate of this type is called Feymann gate (so famous physician). u u This gate is elementary gate of quantum logic

More Reversible Gate v Inverter – Only reversible gate in classic logic v Feymann gate – controlled inverter

More Reversible Gate v Toffoli gate – controlled controlled inverter v Fredkin gate – controlled swap (6 7) Reversible&Universal (1 4 2) (3 6)

Circuit with reversible gate v Swapper with Feymann gate v Full Adder with 5 Fredkin gate

General reversible gate v Four reversible gate n Inverter1-by-1 gate n Feymann2-by-2 gate n Toffoli3-by-3 gate n Fredkin3-by-3 gate n More??4-by-4 gate? … N-by-N gate is possible

General reversible gate v G gate (General gate of inv, Feymann, Toffoli) n n f = arbitrary function of a & b n n G gate is reversible

General reversible gate v H gate (General gate of Fredkin gate) n H gate is reversible gate