Reversible versus irreversible computation

Whenever an irreversible process happens, entropy increases. This can be seen from a simple example taken from standard thermodynamics consider two isolated objects, A and B, at different temperatures, Ta and Tb. Let us assume that Ta 7r. Suppose the two objects are brought together, and an amount of heat AQ flows from A to B. This is clearly an example of irreversible process. Thermodynamics tells us that the entropy of A will decrease by an amount ASa = AQ/Ta and the entropy of B will increase by ASb = AQ/Tb. But since Ta Tb, the increase of the entropy in B will be larger than the decrease of the entropy in A. Consequently, the total entropy increases in the process. 

This discovery of Bennett lead to the idea of quantum computation by Paul Benioff almost a decade after- 

It is obvious to see from Table 1.5 that the input bits can be recovered by applying the gate to the output Therefore, the Toffoli gate is reversible. Now, if a basic set of gates could be built from Toffoli, then it will be demonstrated that computation can be made reversible. In fact, it is a simple matter to implement NAND from Toffoli. All we have to do is to set the target bit as 1 at the input, and Toffoli will work just as NAND. In Table 1.5, these correspond to the 2nd, 5th, 6th and 8th lines. The first two entries of these lines, plus the corresponding bits on the last column, is just NAND logic (see Table 1.6). 

Therefore, computation can be made entirely from reversible logic gates 1  

Reversible computation has a very important consequence until 1961 scientists believed that any computational action would result in an energy cost. But in 1961 Rolth Landauer showed [17] that what do cost energy is erasure. In other words, if no bit is lost during the computation, it can be made at energy-free cost This discovery lead to the solution of a century-old problem in thermodynamics the Maxwell demon problem. 

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