-
Book Overview & Buying
-
Table Of Contents
A Practical Guide to Quantum Machine Learning and Quantum Optimization
By :
(1.1) The probability of measuring if the state of a qubit is is exactly

In the same way, the probability of measuring is also . If the state of the qubit is , the probability of measuring is
and the probability of measuring is 
Finally, if the qubit state is , the probability of measuring is
and the probability of measuring is 
(1.2) The inner product of and is 
The inner product of and is 
(1.3) The adjoint of is itself and it holds that . Hence, is unitary and its inverse is itself. The operation takes to .
(1.4) The adjoint of is itself and it holds that . Hence, is unitary and its inverse is itself. The operation takes to and to . Finally, it holds that and that .
(1.5) It holds that
and that
It also holds that
(1.6) Since , it is apparent that . Also, we have by Euler’s identity, so . As a consequence, , so . Also, , and it follows that .
(1.7) By the definition of we have that
Analogously...