I'm working my way through the book "Quantum computation and quantum information" by Nielsen and Chuang.

On chapter 3 (talking about reversibility of the computation) exercise 3.32, it is possible to see that the minimum number of Toffoli gates required to simulate Fredkin gate is 4. See Andrew Landahl's notes for more details.

By the end of Chapter 3, it is also stated:

From the point of view of quantum computation and quantum information, reversible computation is enormously important. To harness the full power of quantum computation, any classical subroutines in a quantum computation must be performed reversibly and without the production of garbage bits depending on the classical input.

On chapter 4 exercise 4.25, we construct the Fredkin gate using only 3 Toffoli gates.

The question is: what's the difference between simulation and construction of Fredkin gate using Toffoli gates?

I'm working my way through the book "Quantum computation and quantum information" by Nielsen and Chuang. (EDIT: the 10th anniversary edition).

On chapter 3 (talking about reversibility of the computation) exercise 3.32, it is possible to see that the minimum number of Toffoli gates required to simulate Fredkin gate is 4. See Andrew Landahl's notes for more details.

By the end of Chapter 3, it is also stated:

From the point of view of quantum computation and quantum information, reversible computation is enormously important. To harness the full power of quantum computation, any classical subroutines in a quantum computation must be performed reversibly and without the production of garbage bits depending on the classical input.

On chapter 4 exercise 4.25, we construct the Fredkin gate using only 3 Toffoli gates.

The question is: what's the difference between simulation and construction of Fredkin gate using Toffoli gates?