We take some common gates like
Hadamard gate : Hadamard gate is used widely in Qubit literature. Hadamard gate is given by
This we have noticed that is the
. Hence we take the 
as the generalized Qudit gate for the Hadamard gate.NOT Gate : For a Qubit system with canonical states
the not gate acts on a possible state 
as 
We generalize this gate to its Qudit counterpart as
where 
is a canonical qudit state and the operation + is the ring operation over 
."1" is the additive identity of 
Now suppose
then we have 
Like wise we get
Thank you! I'm just trying to understand Quantum computing more. Your post is nice. Couls you recommend me some book which you consider is easy to understand? I'm working with "Quantum computing explained" but when it arrives to some topics such as quantum algorithms I get lost.
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