Which of the following gates when applied twice brings the system back to itsoriginal state?

The gate that brings the system back to its original state when applied twice is the NOT gate (also known as a Pauli-X gate in quantum computing).

Here's why:

1. The NOT gate flips the state of a system. If the system is in state 0, the NOT gate changes it to state 1. If the system is in state 1, the NOT gate changes it to state 0.

2. If you apply the NOT gate twice, it will flip the state of the system twice. So, if the system starts in state 0, the first NOT gate changes it to state 1, and the second NOT gate changes it back to state 0. Similarly, if the system starts in state 1, the first NOT gate changes it to state 0, and the second NOT gate changes it back to state 1.

So, no matter what state the system starts in, applying the NOT gate twice will always bring it back to its original state.